Advances in integrated quantum photonics for quantum sensing and communication

Abstract

Integrated photonics has significantly transformed the field of quantum technologies throughout the past few years. A timely evaluation of the state-of-the-art and investigation of the different approaches pursued for integrated quantum photonics is highly appropriate in the context of the current second quantum revolution. With this perspective, we discuss the present issues and future developments related to various technological systems, relying on recent developments. Recent advances from a variety of subfields will be discussed, with emphasis on applications in quantum sensing and quantum communication. Significant advances in quantum communication and the quantum internet have been made in recent years in part due to the emergence of quantum photonic chips, whose low-cost, robustness scalability, and stability allow for new device possibilities with smaller footprints. Also discussed here are the achievements in quantum photonic chips with the most widely used photonic integrated fabrication platforms and the essential parts of integrated quantum communication systems. It highlights innovative concepts, advancements in the field, and cutting-edge developments, while addressing possible drawbacks and unresolved challenges.

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Introduction

The Internet of Things (IoT) and communication technologies involve a wide range of sensors and microelectronics, currently being developed and incorporated incessantly into platforms that interact with the real world.^1,2 In particular, optoelectronic devices and photonic systems have been extensively studied in a variety of constantly evolving human–machine interactive applications, including smart image sensors,^3,4 displays,⁵ neuromorphic devices,^6,7 biomedical healthcare systems,^8,9etc. Previously, high-density and scalable optoelectronic integrated circuits and systems could be created with miniaturized, quick, and affordable photonics by using silicon-based complementary metal-oxide–semiconductor (CMOS) technology.^10,11 Unfortunately, due to their restricted sensing and actuator qualities, conventional silicon-based optoelectronics are not able to fully meet the rising demand for more advanced and multifunctional state-of-the-art photonic devices. Furthermore, wearable and flexible applications cannot use silicon devices due to their hard and fragile nature.

To overcome the shortcomings of the technologies in use today, a wide range of extremely sensitive and responsive photonic materials are being extensively investigated. Specifically, a number of nanoscale materials have been determined that satisfy the requirements of next-generation photonic technologies by demonstrating outstanding multifunctional and highly-sensitive characteristics (Fig. 1).^12,13

Fig. 1 Outlook from 2D materials in quantum nano photonics.

Extending nano photonics from nanometer scale to atomic scale is enabled by two-dimensional (2D) materials (Fig. 1). They are attributed with sustaining special optical excitations such as excitons in transition-metal dichalcogenides (TMDs)¹⁴ and plasmons in graphene,^15–17  as well as their atomic thinness which naturally implied. Fundamental advancements in computing, security, sensing, and metrology are made possible by quantum mechanical phenomena, which use the laws of quantum physics to transmit information in a non-classical manner. Recently, from cutting-edge research and experimentation to commercial reality, this field has encompassed a wide range of technologies and applications. Quantum key distribution (QKD) is the most well-known example of this.¹⁸ The fundamental principle of QKD is to transfer secret keys between two distant entities by using the quantum states of photons. With the help of the quantum no-cloning theorem, the two communicating users can identify any attempt by an eavesdropper to obtain the key.¹⁹ Though its practical security has generated discussion in terms of the proof, research in QKD is paving the way towards a quantum internet where information security is ensured by the fundamental laws of physics, instead of complex mathematical problems.²⁰ For instance, QKD studies using fiber-based and satellite-to-ground approaches have been proven at distances of 800 km in ultra-low-loss optical fiber²¹ and 2000 km in free space,²² respectively. More than 110 Mbit per s is now the maximum secure key rate that can be achieved over a single channel.²³ Additionally, a great deal of research has been carried out on the security of everyday life QKD systems in order to overcome the current technological constraints.^20,24 To accomplish both long-term key security and short-term authentication security, post-quantum cryptography has been integrated with QKD.²⁵ Quantum teleportation has attracted a lot of attention despite QKD because it leverages quantum entanglement to transmit sensitive quantum information in a way which nearly impossible to reverse.²⁶ Consequently, different quantum devices can be connected via quantum networks, providing previously unreachable capabilities that are demonstrably impossible with only classical information technology.²⁷ Another significant area of quantum communication, known as quantum secure direct communication (QSDC) techniques,²⁸ also made it possible to communicate data securely via a quantum channel. With the rapid evolution of this approach in recent years, individuals can now immediately send confidential information over secure quantum channels without exchanging encryption keys. Current technology can be used to build a QSDC network with end-to-end (E2E) security while paired with post-quantum cryptography.²⁹ In recent years, nitrogen-vacancy (NV) centers in diamond have gained considerable attention as highly promising candidates for various quantum technologies.³⁰ NV centers exhibit exceptional quantum coherence properties, even at room temperature, making them ideal for a range of applications, including communication, sensing, and information processing.³¹ Discrete optical devices such as single-photon sources and photodetectors, are usually used in the construction of conventional quantum communication systems, which enable fundamental improvement to security, computing, sensing, and metrology. These devices are often built independently using optical crystals (such as calcite – CaCO₃, beta barium borate – BaB₂O₄, and lithium niobate – LiNbO₃) and glasses (such as fused quartz and silica – SiO₂), and coupled by free space or optical fibers. Though it is not very simple to optimize individual components to meet the exacting specifications needed for quantum information applications, such as ultra-low-loss, high efficiency, fast speed, and high fidelity, packaging and interconnects have always presented significant reliability and cost issues for conventional discrete optical designs, especially while interacting with large-scale networks that connect hundreds of thousands of users. For example, in order to reduce space and phase misalignment over time caused by environmental stressors and temperature fluctuations, strong mechanical and thermal stabilities are required. However, achieving these stabilities through global stabilization is challenging in a complex discrete optical system.

Apart from being smaller in size, quantum integrated devices offer two notable benefits over discrete optical systems: stability and scalability.³² By printing the chips as a single unit through lithography used in well-established batch semiconductor fabrication processes instead of building each component separately, scalability and mass production become feasible.^33–35 Due to the circuit capacity to control deviations due to temperature changes or vibrations, stability is accomplished on a strong and lightweight solid-state substrate. For quantum information processing and extremely effective quantum communication, performance and integration levels must be attained, and these two aspects are essential. Integrated photonic chips have the potential to integrate various desirable attributes, including efficiency, affordability, scalability, flexibility, and performance, which are necessary for quantum communication applications. In this review, we discuss recent developments in quantum communication and the implementation of quantum-based sensing devices. We also review the materials used to design photonic devices. Integrated photonic materials, adaptable active and passive components for quantum state manipulation, and integrated single-photon and homodyne sensors are the main components of the chip-based quantum communication systems that we analyze. Then, we explore the development of on-chip devices for useful quantum communication applications like QKD and information-based techniques for example quantum mobility and entanglement distribution throughout. Lastly, we discuss the challenges and future prospects of photonic based quantum sensors.

1. Quantum sensing

Light-based sensors can also be improved through the help of quantum optics.^36,37 The precision of sensors that rely on classical light is restricted by the signal-to-noise ratio (SNR) of the measurements. It is commonly referred to as the shot noise limit of photodetection, where the precision is limited at a fixed intensity of light impinging on the sensor due to the “graininess” of photoelectron counts. A two-path interferometer arm for the measurement of the refractive index changes can be linked to phase shifts measured by the classic optical sensor. Variations in temperature, pressure, presence of contaminating molecules, or other noteworthy characteristics are all related to changes in the refractive index. Under such configuration, the precision Δϕ with which an optical phase shift ϕ might be measured with classical light is set by shot noise. The precision scales as N^−1/2, where N is the average number of utilized photons. Sensors based on quantum effects outperform the classical ones as they offer high precision and ability to operate at the nanoscale level.³⁸ Coherence and entanglement are examples of quantum phenomena that can be used to increase measurement sensitivity, which in turn can increase parameter estimation precision and the spatial and temporal resolution of imaging systems. They can also be used to compensate classical impairments found in the channel such as chromatic dispersion. The most well-known system involves the arrangement of N photons in a superposition in one path. These states, designated as “N00N” states, offer an improvement in precision to the point where Δϕ scales as N⁻¹, also called the Heisenberg limit.^39–42 It has not yet been feasible to demonstrate a true improvement in precision after taking into account all of the photons that are placed into the interferometer but do not pass through or are not detected since such entangled states are extremely sensitive to losses. Thus, recent work has concentrated on how to strengthen the software against noise and flaws that arise in practical scenarios.^43–46 Although it is not always easy to generate the necessary states and uncover which types of quantum states are useful—generally those that have some entanglement, but not the maximum achievable for a specific number of photons.^47,48 Furthermore, in the presence of flaws, it is impossible to reach the Heisenberg limit; yet, for some types of noise, it is conceivable to advance beyond the conventional quantum limits, and in a broader sense, to obtain an important advancement in precision for a given amount of light.^49–51 It has been shown that gravitational wave sensors built on optical interferometers have increased precision. In order to create a “squeezed state” in the optical oscillation, light with extremely low noise in its field amplitude at specific points is injected into the interferometer's “empty” or vacuum input port. One port is used to inject high-power laser light into another. This technique improves the likelihood of detecting gravity waves by replacing the absence of light at the vacuum port with compressed light, which raises the SNR of the measurements by 2.0 dB.⁵²

Nowadays sensors that estimate key parameters beyond the classical strategies are being focused on. These can be used, for instance, in situations where the parameter to be evaluated contains random noise.^38,53 As an example, random phase changes may result from ambient fluctuations or temporal variations in the sample itself in an interferometer when the phase shift due to a material sample is to be determined. Consequently, the phase shift's variance and mean are unknown values. The boundaries of the precision that quantum physics permits in this instance exhibit certain noteworthy characteristics. Specifically, it is more effective to estimate several parameters jointly rather than individually.⁵⁴ Furthermore, imaging can be viewed as an estimation problem with multiple parameters.⁵⁵ The phase shift at each pixel in a picture can be estimated in phase contrast microscopy. The collective estimation of a set of phase shifts is also more efficient than individual estimation of each shift.⁵⁶ However, achieving the necessary quantum states for enhanced accuracy is not easy. In addition, one of the research studies emphasizes evaluating the closest one may proceed to the quantum improved accuracy with quantum light that can be produced in a controlled environment.^57,58 Among the quantum systems under investigation, NV centers in diamond stand out due to their unique sensitivity to strain, magnetic and electric fields.⁵⁹ NV centers can be utilized in quantum magnetometry with high spatial resolution, enabling the measurement of minute variations in magnetic fields.⁶⁰ This capability makes them particularly useful in applications such as nanoscale magnetic resonance imaging and biological sensing.⁶¹ Their spin properties allow for the detection of extremely subtle changes, enabling precise, real-time analysis at the nanoscale.⁶² In addition to their remarkable sensitivity, NV centers can operate effectively at room temperature, without requiring the complex, bulky and expensive cooling systems often necessary for other types of quantum sensors. The latter characteristic broadens their applicability across a variety of fields, allowing them to be easily integrated into systems where maintaining low temperatures is not feasible.³⁸ Moreover, their non-invasive nature permits the measurement of key parameters without disrupting the system under observation, a critical feature for sensitive environments such as biological systems or nanomaterials.⁶³

Using these methods with distributed sensors is a key application; it is possible to combine safe monitoring of remote sensors with improved multi-sensor scanning accuracy. These improvements might prove beneficial for various fields including light-based gravimetry, magnetometry, acceleration measurements, duration and frequency requirements, and imaging technologies like microscopy.⁶⁴

2. Fundamental advances for quantum photonic devices

The road towards more compact quantum communication systems with higher efficiency and complexity has been leveled and smoothed through photonic micro-nano-integration. The three facets of integrated quantum communication are summarized as follows: (i) photonic materials for integration;^65–67 (ii) quantum photonic elements like high rate modulators,^68,69 quantum optical sources,⁷⁰ and extremely effective photodetectors⁷¹ and (iii) their uses in QKD and quantum teleportation (Fig. 2).⁷² Essential photonic components in chip-level configurations must be redesigned and optimized for specific quantum information applications because the materials, preparation techniques, and structural designs used in photonic integration differ significantly from those used in discrete systems. An explanation of the pertinent technical research is provided, including quantum radiation sources, integrated photonic system packaging methods, quantum detectors, encoding and decoding modules. Using periodically poled lithium niobate waveguides and silica-on-silicon planar light-wave circuits (PLCs) for interferometers, the integration of photon sources is considered one of the earliest initiatives in this field.^73,74 These integrated devices had excellent efficiency and temperature-stabilized performance proving their inherent suitability over their separate and bulky discrete components. Later on, a great deal of additional materials was investigated, and significant advancements were made in the creation, modification, and detection of quantum states of light on-chip for applications including quantum communication and other forms of quantum information. The most widely used materials systems for chip-based quantum communication implementations are silicon-on-insulator (SOI), silicon nitride (Si₃N₄), lithium niobate (LiNbO₃), gallium arsenide (GaAs), indium phosphide (InP), and silicon oxynitride (SiO_xN_y).^32,75 Strong optical nonlinearity for nonclassical state generation, a high refractive-index contrast for high-density integration, and excellent compatibility with advanced complementary metal-oxide–semiconductor (CMOS) processes—which have been widely used in the semiconductor industry is provided by SOI. Nevertheless, it is difficult to completely integrate all of the necessary parts of a quantum communication system due to the lack of lasing capabilities.^76,77 Monolithic system integration is possible with III–V semiconductor platforms (GaAs, InP, etc.), but the cost is higher and the integration level is lower. It is evident from the unavoidable flaws in every material and its production method that no other platform can offer every feature needed for quantum communication applications. Hybrid integration, which combines the benefits of several systems, is an achievable solution.⁷⁵ Initiatives such as integrated superconducting nanowire single-photon detectors (SNSPDs) and integrated lasers for weak coherent pulse production have been undertaken in an endeavor to realize heterogeneous quantum photonic systems.^71,78

Fig. 2 An overview of quantum communication based on quantum photonic chips.

These days hybrid integration with 2D materials like graphene, black phosphorous (BP), transition metal dichalcogenides (TMDs) among others, is receiving attention due to their unique properties.^79–81 In them, atomic planes are stacked one layer on top of the other in a predetermined order, commonly known as “van der Waals (VdWs)” heterostructures.⁸² The dangling-bond-free surfaces of atomic sheets offer significant flexibility in enabling the construction of arbitrary VdWs heterostructures, in contrast to conventional heteroepitaxy. Though it can also be used to integrate mixed-dimension materials, such as 2D materials with 0-dimensional quantum dots (QDs), 1-dimensional nanowires, or 3-dimensional bulk materials, this property enables the integration of extremely dissimilar 2D materials.⁸³ In addition to these hybrid systems, nitrogen-vacancy (NV) centers in diamond have emerged as promising platforms for advancing quantum photonic systems. NV centers exhibit good coherence times and stable single-photon emissions, which are critical for quantum communication applications, such as quantum key distribution (QKD), secure quantum networks and quantum sensing.⁸⁴ Their ability to operate in both cryogenic and ambient conditions enhances their reliability in various quantum systems.⁸⁵ NV centers have been successfully embedded in chip-scale photonic platforms, including waveguides and resonators, which allow for precise manipulation and detection of quantum states, making them ideal for scalable, high-performance quantum communication technologies.⁸⁶ Several significant technologies have emerged as alternatives for on-chip quantum communication implementation, such as semiconductor quantum dots (QDs) interfaced with photonic nanostructures, coherent pulse generation, and diamond-on-insulator.^78,87

3. Techniques for integrated photonics

Today, a number of photonic integration materials like LiNbO₃ (often abbreviated “LN”), silica (SiO₂), semiconductor and highly advanced 2D materials are used to assemble the essential building blocks that enable the production and manipulation of quantum states of light on a single chip (Fig. 3).^88,89 We explain them here following significant requirements for ideal quantum integrated photonic systems.

Fig. 3 Advanced photonic materials used in the fabrication of quantum states of light on a single chip.

3.1. Emission of quantum light

This property is directly related to photon entanglement and includes the generation of discrete photon-pairs, vacuum-squeezed states of light, and hybrid states that rely on different distinct and continuous quantum components.^90,91 It can be based on three-wave, four-wave mixing, or biexciton de-excitation.

3.2. Development of a single photon

This feature provides the ability to integrate probabilistic single-photon emitters based on the photon-pair creation, in contrast to consistent genuine single-photon emitters.^92–96

3.3. Nonlinear and linear on-chip components

Filters, beam splitters, and multiplexers are examples of devices which offer the capacity to passively direct and shape light in both the spatial and frequency domains. Electro-optic modulation is another tool which is used for actively modifying the quantum elements of light.^97–100

3.4. Adaptability

It was associated with the potential of a higher integration capability. It comprises the effective sizes of the different components that allow for the estimation of the integration scaling factor, material propagation losses, and refractive index steps in waveguides.^101,102

3.5. Quantum light detectors

Quantum states of light require on-chip detectors with high jitter, low noise, and high efficiency for certain applications. These detectors could be high-performance intensity photodiodes for measuring brilliant nonclassical states of light or single-photon detectors.^103,104 Photodiodes are made from semiconductor materials that are doped with p-type and n-type elements, which determines the observable optical wavelengths based on the appropriate material's bandgap. A charge carrier depletion area with a corresponding internal field forms at the p–n junction. A mobile electron is excited and creates an electron–hole pair when light with enough photon energy strikes the diode. A detectable photocurrent proportional to the quantity of incident photons is produced by an internal field over the depletion area. Photodiode performance is influenced by its noise behavior, which is determined by the dark current, noise-equivalent power, and responsivity. The ratio of incident photons to detected photons, or generated electron–hole pairs, is known as the quantum efficiency (η). The quantum efficiency varies according to the wavelengths and semiconductor materials employed, but it can achieve extremely high values exceeding 95%. Conventional photodiodes lack single-photon sensitivity, which means they cannot detect single photons or light with low photon numbers due to noise contributions from thermal excitations. These noise contributions can be mostly disregarded in bright light, while for an ideal detector with η = 1 the light statistics and photon current are related as

Here, n_e is the number of photoelectrons; e is the elementary charge. An ideal detector preceded by a beam splitter, which represents an effective loss of 1–η, can be used to imitate the real detector. Whereas, single photon detection requires internal amplification of the absorbed photon's signal to generate an electrical output that surpasses the noise level. Avalanche photodiodes (APDs) can achieve this because of their unique architecture, which includes a multiplication zone in addition to an absorption region. In the avalanche process, secondary electrons are produced by high voltage across the multiplication zone if photon absorption produces an electron–hole pair. Therefore, an avalanche process with an exponential development of free carriers that results in macroscopic photocurrents can be initiated by a single electron–hole pair. Lowering the applied voltage is necessary to quench the avalanche, preventing damage and allowing for subsequent detection. The current flow is actively stopped in active quenching circuits to speed up the APD's reset. The quantum efficiency in the context of APDs represents the probability that a single photon will be captured. At wavelengths between 700 and 800 nm, an APD's quantum efficiency typically reaches a maximum value of 60% to 70%; at wavelengths between 1200 and 1700 nm, the most recent generation of APDs achieves efficiencies exceeding 25%. The dark count rate, which indicates the number of detection events that occur in the absence of an optical signal, is a measure of the detector's noise level. For APDs at 800 nm, dark count rates as low as 100 counts per second can be readily attained. The APDs’ dead time indicates the bare minimal amount of time required to record a series of detection events. Active gating requires dead times of more than 1 μs for APDs operating at telecom wavelengths, while dead times as short as 50 ns are typical for 800 nm APDs.¹⁰⁵

3.6. Interaction with CMOS

CMOS exhibits the ability to construct electrically driven devices as well as the possibility of integration with electronic component layers.^106,107 The standard CMOS manufacturing process is suitable for several kinds of microsystem class development, including temperature, optical, and magnetic sensors, which have been commercially available for some time.¹⁰⁸ The combination of CMOS technology with the electrodeposition of metal coils and ferromagnetic cores has resulted in the development of new magnetic sensing devices, including fluxgate sensors and inductive proximity sensors.^109,110 Moreover, CMOS technology in conjunction with appropriate micromachining and thin-film deposition techniques has led to the production of an increasing number of microelectromechanical systems (MEMS). The extra fabrication stages might be carried out in between the standard CMOS processes (intermediate-CMOS), before (pre-CMOS), or after (post-CMOS).^111–114

3.7. Integration with memory

Memories in the context of quantum communication can be built as either emissive systems, which emit a photonic qubit on demand whose state is entangled with an internal degree of freedom of the memory, or as “in–out” systems, which absorb and store an incoming qubit. In the latter case, one “stores” the quantum states by using quantum state teleportation. Every type of memory has its own unique qualities and is used in various protocols.¹¹⁵

4. Integrated photonic materials

Here, we discuss the currently developed integrated photonic materials.

4.1. Lithium niobate (LN)

In the past, one of the key technologies for quantum integrated photonics has been crystalline lithium niobate (LN).^116,117 Large second-order nonlinear coefficients (both opto-optic and electro-optic) and low optical transmission losses are among the well-known optical characteristics of LN waveguides, which make them an ideal choice for the creation of effective integrated photonic devices for both classical and quantum information applications.¹¹⁸ Quantum states can be created in LN with unmatched brightness using spontaneous parametric down-conversion (χ⁽²⁾ based), which is simpler to pump rejection than spontaneous four-wave mixing in Si (χ⁽³⁾ based).¹¹⁹ These states can then be further customized and manipulated through domain engineering. Monolithic LN chip development has been slowed down in favor of LN-on-Insulator (LNOI) as it offers a smaller footprint compared to the cm-scale typical footprint of traditional (i.e., proton-exchanged waveguide) LN circuits. With the potential to achieve Si and SiN chip sizes, this technology is currently opening the door to the realization of novel quantum photonic devices with unprecedented heights of performance and scalability.¹²⁰ For example, the bandwidth of electro-optic modulation has been increased to over 100 GHz, and though the fabrication process is not as advanced, the scaling factor is still equivalent to Si photonics.^97,121 The ability to create electro-optically reconfigurable circuits that can function well at cryogenic temperatures is another crucial aspect of LNOI. Niobium titanium nitride stripes patterned on top of the waveguides have been used to demonstrate their integration with superconducting nanowire single-photon detectors (SNSPDs).^122,123 Due to the usage of rare earth ion-doped crystal, LN waveguides are eventually, even at this early stage of research, compatible with quantum memory.¹²⁴

4.2. Silicon (Si) and silicon carbide (SiC)

Si photonics is a relatively new platform that has made a big splash in the quantum world. It is fully compatible with CMOS technologies and permits the production and manipulation of near-infrared light quantum states on-chip.^125–127 In terms of technical aspects, Si quantum photonics gained attention due to its advanced integration density factor, effective third-order optical nonlinearities, and the precise design and processing workflow. The diameters of the passive and active components are usually about 100 μm in size. Even though it lacks a natural electro-optical coefficient, which causes weak optical modulation through local heating, it can still be used for a number of additional features, including wavelength and photon-routing.¹²⁸ At the moment, the primary impediment to the platform's scalability is the relatively high propagation losses (≤0.1 dB cm⁻¹) and two-photon absorption in Si waveguides (Fig. 4)

Fig. 4 (a) Si ring resonator integration on a 45 nm CMOS SOI chip,¹²⁹ Copyright (2015), Optica publishing group; (b) analysis and development of a two-photon entangled state on-chip. Beyond the SOI chip are detectors and a pump laser,¹³⁰ Copyright (2015) Springer Nature; (c) with silica waveguides, a fully reconfigurable circuit that can execute each linear optical operation feasible for its size could be created,¹³¹ Copyright (2015), Science.

In order to offset a lower third-order nonlinearity, the use of SiN is now addressing this issue by minimizing two photon absorption, extending the transparency range to the visible, and reducing propagation losses down to ≤0.1 dB cm⁻¹. Nitrogen vacancy (N-V) centers in Si and SiC are the most researched solid-state emitters in terms of single-photon emission, mostly due to progressively improved nanofabrication processes.^132–134 Due to wavelength incompatibilities with telecom fibers and recent significant advancements in nuclear magnetic resonance (NMR) spectroscopy,¹³⁵ the platform in the particular case of SiC has been primarily focused on quantum computation, simulation, and quantum rebroadcast techniques.^136,137 Furthermore, SiC has been studied as a platform for integrating nanodiamonds to create scalable hybrid photonic devices. However, one aspect that has prevented the SiC material from being used structurally is its low fracture toughness. In order to overcome this problem, nano powders have been found to improve mechanical and sinterability qualities due to their larger surface areas and specific surface activities compared to micron-sized powders.¹³⁸ Reinforcing phases (such as aluminium, boron, or yttrium-based oxide) are primarily utilized for consolidation in order to achieve fine-grain size and high densification for SiC. The mechanical properties of the composite are frequently improved by the introduction of these reinforcing components.¹³⁹ However, because the oxide phase at the grain boundary can impair the mechanical behaviour at high temperatures, they pose some difficulties when exposed to radiation (neutron swelling or absorption). Because the resulting composites yield a material with improved mechanical properties, the breakthrough in ceramic matrix composites has attracted a lot of interest in overcoming the difficulties of ceramics. As a result, the final products have been highly valued in airframes, aircraft engines, space structures, and other fields where creep and alternating load are common. A useful method for the upcoming development of high-temperature, aerospace, and other lightweight systems is demonstrated by a variety of functional structures that use ceramic matrix composites and coatings. These could be employed in applications that need to operate over a wide range of temperatures and pressures, which could be a problem for future cutting tools and hypersonic materials.

Nanodiamonds containing NV centers are deposited on SiC micro disks, which support high-quality factor whispering gallery modes (WGMs).¹⁴⁰ SiC-based platforms enable light to propagate through both SiC and diamond, increasing light–matter interaction compared to other hybrid platforms.¹⁴¹ Finally, the interaction of light and sound waves at the quantum level, either in opto-mechanics (usually, kHz–MHz range) or through stimulated Brillouin scattering (SBS) (usually, in the 10 GHz range), is a significant area of research for Si-based components.^142,143

4.3. III–V and III–N semiconductors

A direct band gap and well-developed growth and processing methods have historically allowed semiconductor materials to demonstrate quantum dot (QD) structures for the deterministic generation of single photons.^144–146 Later, deterministic entanglement generation was achieved through the use of the biexciton cascade.¹⁴⁷ It is possible to obtain GHz high-purity single photon emission and significantly boost the spontaneous emission rate of QDs by coupling them spectrally and spatially to microcavity modes.¹⁴⁸ Novel experiments tie single-photon sources to photonic circuits to execute optical quantum computing tasks, going beyond the usage of a photonic structure to optimize the extraction of single photons to an optical fiber.¹⁴⁹ GaP, with its high refractive index and strong second-order nonlinearity, is integrated with NV centers in nanodiamonds, allowing efficient coupling of optical fields to these quantum emitters, improving photon emission efficiency.^150,151 Furthermore, GaAs and associated chemicals offer a future pathway. They show enormous integration potential since this platform combines a high second-order optical susceptibility that makes it possible to integrate SNSPDs with entangled photon sources based on nonlinear optical processes (Fig. 5).

Fig. 5 (a) Integrated GaAs wave guides serve for achieving both passive and active photonic elements,¹⁵² Copyright (2014), Elsevier; (b) a ridge waveguide structure with a Nb-NSSPD and a layer of GaAs/InGaAs QDs. The waveguide gathers and detects the fluorescence from a QD on the semiconductor. Insets display the AFM image of a QD, the SEM image of the SNSPD, and the calculated waveguide mode profile,¹⁵³ Copyright (2015), American Chemical Society.

Moreover, they provide a direct on-chip integration of an active laser domain, opening the door for electrically powered devices.^154,155 In a similar vein, GaN is the second most used semiconductor in the world after Si, and it is possible to fully use the knowledge of technology that has been established so far for high-power, high-frequency, and solid-state illumination. There are existing electrical injection and photonic building blocks (air/GaN distributed Bragg reflectors, optical waveguides, in and out couplers, photonic crystals, etc.) for the GaN platform. New material aluminum nitride (AlN) is appropriate for photonic integrated circuits that can be made larger. In addition to showing tremendous promise for the realization of on-chip photon-pair sources based on spontaneous parametric down-conversion (SPDC), its significant intrinsic second-order nonlinearity (χ⁽²⁾) also allows for integrated low-loss and high-speed electrooptic phase modulators.¹⁵⁶ Dense integration and a tiny device footprint are made possible by the strong refractive index contrast between silica-cladding layers and AlN waveguides.

4.4. Silica

Silica provides a very strong and diverse waveguide technology, but it also lacks an electro-optic coefficient and has a weak third-order nonlinear coefficient. Femtosecond laser direct-writing (FLDW) has garnered attention as a method for creating intricate linear waveguide circuits because it has the lowest intrinsic propagation loss of any material in the infrared (IR) regions. It has intrinsic three-dimensional (3D) routing capabilities and enables high-speed device production without the requirement for lithographic masks. Rapid small-scale circuit prototyping has been used in quantum photonics to enable research on single- and entangled-photon production, boson sampling, and hitherto impractical quantum entanglement.^157,158 For instance, silica waveguides and resonators play a crucial role in single-photon generation circuits. When coupled with color centers in nanodiamonds, they enhance light–matter interaction through whispering gallery modes (WGMs), significantly boosting photon emission efficiency.^159,160 Quantum integrated photonics has demonstrated significant promise using a more traditional method, which goes beyond a laser-written waveguide. The first quantum gate was shown in 2008 using a planar waveguide made of silica on a Si wafer.¹⁶¹ Since then, advances in reconfigurable circuits combining up to 15 interferometers have been demonstrated.¹³¹

4.5. 2D materials

Two-dimensional (2D) materials offer a way to push nano photonics into the atomic scale, beyond the nanometer scale. Their atomic thinness is a natural cause of this, but they also support special optical excitations, including graphene plasmons (GP),¹⁵ excitons in transition-metal dichalcogenides (TMDs),¹⁴ nanoparticle-on-metal (NPoM) systems,¹⁶² hexagonal boron nitride (hBN)¹⁶³etc. Due to their distinct optical sensitivity, 2D materials allowed light–matter interaction to be stretched to the atomic limit. For instance, the realization of perfect absorbers and highly reflective mirrors that are only one monolayer thick was made possible by the quantum response of excitons in monolayer semiconductor TMDs.^164,165 Furthermore, these materials’ excitonic properties were relatively easy to control, which made it possible to manipulate their radiative lifetime through optical cavities and achieve quantum nonlinear effects at the single-photon level. These developments could pave the way for the development of new platforms based on strongly correlated photons.^164,166,167 Similar to this, single-plasmon response and quantum effects arise from graphene plasmons (GPs) supported by finitized-sized graphene structures.^168,169 Whereas, a nanoparticle-on-metal (NPoM) system, which is made up of a metal particle with a nanometric size (often a cube or a sphere) separated from a metallic surface by an extremely thin dielectric spacer is one example of a system for light confinement (Fig. 6(a)).¹⁶² The nanoparticle and metal surface can form a gap surface-plasmon mode with a tiny mode volume, large field enhancement (10⁴), and Purcell factor (10⁵–10⁷) due to the presence of NPoM.¹⁷⁰ Thus, it has made possible the response of nano antennas, spontaneous emission sources, and strong coupling at room temperature.^171–173 Quantum nonlocal effects play a significant role in reducing the potential field enhancement, but the NPoM system extinction also causes greater damage because of its plasmonic nature.^174,175 In terms of technology, these enable the construction of NPoM systems with atomic precision layer after layer, reducing the dielectric spacer to a single monolayer (Fig. 6(b)).^176,177

Fig. 6 Techniques for confining optical modes in nanophotonic cavities. (a) The nano cube-on-metal (NCoM) device interacts with an optical emitter while supporting a gap SPP in the VIS/NIR that is confined between a metal nano cube and a metal surface. (b) A vibrational molecular resonance interacts with the graphene-plasmon-magnetic resonator (GPMR) system, which supports a GPs in the MIR/THz confined between a metal nano cube and a graphene sheet. (c) The GPMR system exhibits values four orders of magnitude less than the other, as seen by the normalized mode volume V_mode/V_free-space for both systems. (d) A graphene inserting device in which a few hBN layers split off to become electrically linked graphene layers that have the ability to stimulate GPs by the sinking of electrons. (e) An illustration demonstrating the manner in which excitons in a TMD couple with a metal nanoparticles plasmonic field (top), producing double-peaked spectra (bottom). (f) The anti-crossing observed on monolayer WS₂ was acquired using dark-field microscopy on several Ag nano prisms. Research on strong-coupling nano photonics with materials is very promising, with many exciting prospects such as few-photon nonlinearities or polaritonic lasers with ramifications in chemical reactions monitoring, polaritonic chemistry, condensation and all-optical switching etc.,¹⁷⁸ Copyright (2021), American Chemical Society.

More importantly, by utilizing GPs’ great confinement and minimal loss in the mid-infrared (MIR) region, compared to traditional (metal-based) surface plasmon polaritons (SPPs), electromagnetic fields can be significantly compressed for longer wavelengths.¹⁷⁹ The supported GPs (graphene plasmons) interacting with the metallic nano cube can form localized graphene-plasmon magnetic resonators (GPMRs) and achieve a contraction factor ∼5 × 10¹⁰ times smaller than that of the free-space photon volume by substituting a graphene sheet for the metal surface (Fig. 6(c)).¹⁸⁰ A significant benefit over the SPP-based system is that graphene may be vertically confined to a single atomic layer spacing, even if it is positioned one atomic monolayer away from a metallic grating, without causing prohibitive losses.¹⁷⁷ An additional benefit of graphene photovoltaics (GP) lies in its electrical tunable nature, which may be achieved by varying the density of charge carriers within graphene. This also allows polaritonic phenomena to be electrically controlled, for example GP-based electro-optical detectors and modulators.^181,182 An atomic-scale quantum tunnelling device has also been proposed as the next step into the quantum regime, for electrical excitation of GPs. In this kind of device, the tunnelling takes place between two graphene layers and a barrier of hexagonal boron nitride (hBN) that is only a few angstroms thick. Atomic precision can be used to control this barrier (Fig. 6(d)).^163,183 An all-optical quantum system in the MIR/terahertz (THz) region may be compact and comprehensive. Exciton polaritons can also be used to study strong light–matter interactions in 2D materials.^184,185 These interactions become significant when the coupling rate between the exciton and the optical mode is greater than any system dissipation rate (Fig. 6(e and f)).¹⁸⁶

5. 2D materials combined with single quantum emitters

Single emitters are placed in the near-field of a surface, and their emission is controlled by tuning the emitter-surface separation or the 2D material's optical conductivity (for example, through electrostatic gating). This raises basic physics queries regarding dipolar interactions, such as energy transfer and Casimir forces.^187–189 According to Fig. 7(a), the radiative decay rate can be viewed as an incredibly short-range probe (interactions scaling as d⁻⁴, where d is the separation) to measure quantitatively quantities such as distances, phase transitions of superconductors, formation of excitons and polariton or the basic density of a quantum emitter.^190–192 Future quantum technologies, such as high bandwidth quantum sensors and quantum key distribution, could greatly benefit from the ability to dynamically tune a single-photon source's emission rate (using a radio frequency optomechanical device) or adjust its energy directly through vacuum quantum fluctuations or Stark coupling (Fig. 7(b)).^193,194 By adjusting the local density of states in the 2D membrane in situ, light–matter interactions between single emitters and graphene might be further controlled. This allows single emitters to couple with graphene plasmons, resulting in exceptionally large Purcell enhancement factors.¹⁹⁵ Evidence of modulation occurring more quickly than the emitter decay time is given (Fig. 7(c)), which provides new avenues for investigating interesting phenomena like temporal quantum control of a single emitter, nonlinear light–matter interactions at the quantum level 16, and collective effects.^195,196 In addition, as Fig. 7(d) illustrates, the combination of nitrogen-vacancy (NV) center noise magnetometry techniques with 2D electrical transport devices offers a new tool for investigating fundamental physical phenomena both systematically and continuously (current flow imaging, electron–phonon Cherenkov instability).^197,198 Single-photon sources can also be directly hosted by two-dimensional materials; these sources are already integrated in many devices such as quantum LEDs, quantum Stark-confined modulators, SiN photonic chips, and more. Photonic crystals (PhCs) have been investigated as a means to control and enhance single-photon emission at the nanoscale. PhCs are designed to create highly localized optical modes that significantly improve light–matter interaction when coupled with quantum emitters like NV centers.^199,200 By embedding quantum emitters in photonic crystal cavities, the photon emission rate is enhanced through the Purcell effect, providing greater control and efficiency in quantum photonic applications.²⁰¹ For colour centers in hBN, their emission typically varies from visible to near-IR at low temperatures, and even at room temperature. Since they are situated at the surface, these emitters are extremely sensitive to their immediate surroundings. They typically have well-defined energies (110 GHz line width), and emit across a wide range, from visible (hBN) to near-infrared (TMDs). Currently, the primary method for deterministically generating single-photon sources is strain engineering of the membrane (Fig. 7(e)) using nano pillars and nano constrictions.^202,203 This opens up possibilities for the spatial control of single emitters at subwavelength scales to engineer the collective behavior and strong dipole–dipole interactions; as depicted in Fig. 7(f). The atomic scale mapping of localized excitons revealed by advanced scanning tunnelling microscopy (STM) electroluminescence at low temperatures raised basic concerns related to the type of defect and single-photon source development (Fig. 7(g)).^204,205 Using the Moiré super potential to capture interlayer excitons in MoSe₂/WSe₂ heterostructures is another intriguing approach for producing quantum emitters in 2D materials.^206–208 The preliminary findings demonstrate the presence of single-photon creation by revealing very narrow lines (meV), significant magnetic field dependency, and antibunching photon statistics.^209–211 Achieving a high degree of control over single-photon sources in 2D materials will lead the path for quantum communications (on demand photon sources and quantum key distribution) as well as quantum sensing. Two-dimensional arrays of single quantum emitters are promising tools for building Hubbard systems or exciton trapping.²¹² The current use of graphene plasmons to test nonlocal effects is associated with such sensing abilities.^213,214

Fig. 7 2D materials connected to quantum emitters (a) the rate of decay of a single emitter situated d away from graphene. Non-resonant energy transfer is usually the cause of the decay rate rise at short distances,²¹⁵ Copyright (2013), American Chemical Society; (b) broadband graphene electrode for stark tuning of an ultranarrow (50 MHz) quantum emitter. Due to 2D vertical geometry an exceptionally high electric field, a record-breaking tuning of 4 orders of magnitude greater than the emitter line width was obtained,¹⁹³ Copyright (2019), American Chemical Society; (c) in the vicinity of erbium ions, dynamic manipulation within the plasmon regime utilizing a graphene electrode,¹⁹⁵ Copyright (2020) Springer Nature; (d) NV-center magnetometry measures the current flow close to a graphene defect,¹⁹⁷ Copyright (2017) The American Association for the Advancement of Science; (e) WSe₂ strain fields employing nanopillar arrays to provide the antibunching signature of a single-photon source,¹⁷⁸ Copyright (2021), American Chemical Society; (f) He ion exposure-induced flaws in MoS₂ that emit light in a square pattern,²¹⁶ Copyright (2021), American Chemical Society; (g) single sulfur vacancy in WSe₂ detected by electrically induced photon emission with an STM tip: spatial imaging of photon emission,²⁰⁵ Copyright (2020), The American Association for the Advancement of Science.

6. Nonlocality

The ability to measure both the frequency and momentum-dependence (i.e., nonlocality or spatial dispersion) of graphene's conductivity, σ(q,ω), as well as to probe and tune quantum nonlocal effects, have been made possible by the recent realization of acoustic graphene plasmons (AGPs) in graphene dielectric metal (GDM) heterostructures.^177,180,217 These results demonstrated an unparalleled field canalization and nearly linear dispersion. Nonlocal effects generally affect the electromagnetic response of materials when they are probed at wavevectors, q, that are comparable to the underlying electron system's Fermi wavevector, k_F. Alternatively, when q → ω/n_F (indicating the breakdown of the q ≥ ω/v_F condition) and corresponding to AGP velocities, n_AGP ∼ ω/q, that is, n_AGP → v_F.²¹⁷ Furthermore, because graphene k_F can be electrostatically adjusted by varying its carrier density n through , and because AGPs in GDM structures can achieve large wavevectors (even larger than conventional GPs), these features can be combined to create AGPs with wavevectors that relate to an essential portion of k_F or with plasmon velocities exceeding n_F.

According to Lundeberg, the primary effect of nonlocal response in extended graphene is to cause the plasmon dispersion to move towards smaller q as shown in Fig. 8.²¹⁷ At modest graphene–metal separations, this change can be significant for AGPs in GDM structures.²¹⁸ Additionally, when the graphene–metal separation, d, decreases, the nonlocal description forecasts plasmon velocities that asymptotically approach the electronic velocity v_F without ever exceeding it.^217,219 This is quite different from the local-response prediction, which permits the AGP's dispersion to lie inside the intra-band electron–hole spectrum of restricted graphene. It is surprising that Lundeberg et al. were able to identify interesting many-body effects, such as compressibility correction and Fermi velocity renormalization, in addition to detecting a distinctly nonlocal response.^178,217 This intriguing advancement implies that electron–electron interactions in conventional and twisted graphene can be studied using near-field optical spectroscopy using AGPs.^220,221 Surprisingly, AGPs are significant beyond the context of graphene, since they can be used as incredibly sensitive probes of the nonlocal and quantum response of metals.¹⁸⁶ While the far-infrared classical electromagnetic response of metals mimics that of a perfect conductor, at nanometric graphene–metal separations, t, that approximation becomes less accurate as t approaches intrinsically quantum mechanical length scales related to the gas electron of metals.²²² Gold, a common metal employed in GDM structures, exhibits a nonclassical reaction that causes the AGP's dispersion to move even further, towards smaller q (or bigger ω; blueshift), although simple metals, like Al or Na, should have the opposite shift.²²³ Remarkably, there is no discernible rise in nonlocal dispersion damping from the metal in conjunction with this nonclassical shift. The mesoscopic framework for nanoscale electrodynamics can effectively explain both the nonclassical spectral shifting and the negligible metallic nonlocal broadening. This is because the Feibelman d-parameters, d_⊥(ω) and d_‖(ω), encode the metal quantum surface response.²²⁴ Due to charge neutrality, d_‖ = 0 in a basic jellium treatment.²²⁴ The d_⊥-parameter is particularly significant in this context because it corresponds to the first moment of the induced charge density.²²⁴ As a result, Im (d_⊥) represents surface-enhanced Landau damping, while Re (d_⊥) indicates the metal surface effective position with respect to its jellium edge, which denotes the “classical” surface. The graphene–metal distance thus effectively renormalized by the metallic quantum surface response²²⁵ from t to t̃, where

t̃ = t − Re(d_⊥) (1)

Fig. 8 Nonlocal and quantum plasmonics in graphene–metal hybrids. AGPs are launched and nanoimaging utilizing a standard experimental setup with an s-SNOM; the sample is made of hBN–graphene–hBN–metal,²¹⁷ Copyright (2017), The American Association for the Advancement of Science.

Based on the absolute value and sign of Re (d_⊥), the size of quantum shift, and direction are determined. Specifically, the AGP spectral region of concern lies in the THz and mid-IR frequency range, which is significantly lower than the metal plasma frequency (ω ≪ ω_P).²²⁶ It is demonstrated by

d_⊥ ≈ Re(d_⊥) = ζ (2)

Where,

ζ ≡ Re (d_⊥) (ω → 0) is constant

Im (d_⊥) simultaneously disappears as ω → 0

As a result, the nearly disintegrating Im (d_⊥) and limited capacity of Re (d_⊥) explain recent experimental observations and shed light on the physical mechanisms underlying the metal's quantum surface response, which cause AGP's dispersion shifts to occur without significantly degrading the corresponding quality factor.¹⁷⁷ In coupled systems like the fractional quantum Hall (FQH) system or magic angle graphene, direct compressibility testing using plasmonic excitations is another promising technique.²²⁷ The genesis of incompressibility may be clarified via scattering-type scanning near-field optical microscopy (s-SNOM) to figure out the nonlocal conductivity substantially in the FQH domain. When it comes to the intra Landau level dynamics of the system, the nonlocal conductivity really provides invaluable information on the internal geometrical degree of freedom (internal metric) and the local shape of correlations (pair distribution function). Additionally, collective excitations in the FQH domain can be directly probed by S-SNOM.²²⁸ It would be ideal to construct metallic tips capable of probing these gravitons with s-SNOM, even though they can be excited and explored by surface acoustic waves (SAWs), whose effects in a crystal match those of gravitational waves.²²⁹ From this, it follows that near-field optical spectroscopy (NFS) can be used to investigate nonlocal conductivity, examine electron–electron interactions, and uncover previously undiscovered collective excitations. These investigations can be used to investigate novel electronic phases of matter.

7. Interactive modes within electrodynamic systems

The generally accepted and analytical notion that conduction electrons with excellent conductors can flow like a viscous fluid has recently been confirmed experimentally on graphene, PdCoO₂, WP₂, and WTe₂.^230–233 For instance, electrons in high-quality graphene layers can travel great distances without scattering with elements like phonons or impurities, and at “high” electron temperatures (higher than liquid nitrogen temperature), the electron–electron scattering time is sufficiently short.²³⁴ This means that the predominant momentum-transfer mechanism in this regime is e–e scattering due to phonon-mediated contact and Coulomb interaction.^235,236 Though the effects of this new transport system have been extensively investigated through the use of different scanning techniques and steady-state transport, very little has been learned about the effects of hydrodynamic transport on the optical properties (that is, outside the framework of the hydrodynamic model of the nonlocal optical response of metals).^237,238 Fluid-mechanical and electrical phenomena can be elegantly compared with the help of electron hydrodynamics.²³⁹ It is noteworthy that previous research works demonstrated that plasmon modes with phase velocities less than the Fermi velocity υ_F (more than υ_F/√2) can exist in the hydrodynamic domain of a Fermi liquid.^240,241 Fascinatingly, Fig. 9 shows recent research. This makes it possible to increase the nonlocal effects’ impact to a new level. Analyzing non-Fermi liquid systems should reveal an extremely varied landscape.²⁴²

Fig. 9 A representation of the wavevector-frequency plane exhibiting the acoustic plasmon dispersion (red and orange lines) for two distinct screening levels from an external metallic gate, along with the pertinent frequency and length scales (the orange line indicates moderate screening, the red line indicates very strong screening). The blue dashed line represents the sound dispersion, ω = ν_Fq/π, while the blue solid line represents the electron dispersion. Various linear response regimes are emphasized. The electron liquid can be described by the Navier–Stokes equation in the hydrodynamic domain (blue shaded region). The Navier–Stokes equation still holds true in the overdamped domain (magenta shaded region), but plasmons are significantly damped. The Navier–Stokes equation can still be used in the viscoelastic zone (green shaded region) by taking into account an elastic shear modulus, which is comparable to a frequency-dependent complex viscosity,²⁴⁰ Copyright (2019), American Physical Society.

For instance, quick e–e scattering, very low viscosity, and neutral energy modes have been anticipated for graphene that is close to charge neutrality.^240,243 Due to their high confinement, these modes are difficult to investigate experimentally (resolving momentum on the level of ω/υ_F requires techniques that can accomplish this). It is also important to discuss how the optical properties change with temperature because e–e scattering makes the shift from the collision less to the hydrodynamic regime extremely sensitive to changing electronic temperature. Subsequently, it should be noted that hydrodynamic phenomena are not limit to graphene, and it can be found in a wide range of materials. Additionally, it has been projected that phonons and magnons will fall under this regime.^244,245 Subsequent research endeavors may tackle the optical reaction of increasingly sophisticated quasiparticles as they penetrate the hydrodynamic area. Today, research into electron–electron interactions in graphene and the development of novel approaches for quantum sensing of collective excitations in 2D materials are made possible by the combination of excellent sample quality and cutting-edge experimental techniques.

8. Quantum photonic sensors

While the unstable nature of quantum systems is a major source of constraints for practical quantum technologies, their exquisite sensitivity towards their surroundings can be exploited to measure physical parameters that respond to the environment. High-accuracy measurements of physical quantities such as pressure, temperature, position, time, velocity, acceleration, electrical and magnetic fields, and gravity, are achievable by the intriguing prospect of manipulating the quantum properties of photons to develop unique quantum optical sensors.²⁴⁶ A few year ago, large-scale (bulk) optical systems were the primary method used to evaluate the immense potential. The development of more intricate quantum optical systems faces obstacles by this physical method scale and intrinsic instability, which also precludes the realization of completely scalable quantum optical devices at this time.²⁴⁷ Integrated photonic platforms provide a promising solution, enabling real-time and selective analysis for the development of quantum photonic sensors. The generation and control of quantum photonic states on-chip has advanced scientific research and stimulated early applications. In this context, we discuss here recent research developments in integrated photonics towards optical quantum sensor enhancement and explain how they can be used to evaluate the characteristics of biological species and optical materials.

8.1. Integrated photonic circuits for quantum sensors

To enable quantum optical coherence tomography (QOCT) and enhanced two-photon absorption (TPA), the main prerequisites for optical quantum sensors based on DV are the development of entangled photon pairs via SPDC over a wide spectrum, specifically a quantum white-light source.⁹⁰ The spatiotemporal characteristics of entangled photon pairs and the SPDC spectrum can be altered by effectively modifying the quasi-phase-matching in optical waveguides.^248,249 To boost the efficiency of producing photon pairs, various quasi-phase-matching conditions have been explored.^250,251 It is still difficult to combine both an enhanced photonic flux and a wide emission bandwidth, though. Based on chirped quasi-phase matching type-0 SPDC, recent work has enabled these functionalities utilizing periodically poled stoichiometric lithium tantalate ridge waveguides.²⁵² Scientists demonstrated a MHz photon-pair flow throughout a spectral bandwidth of about 300 nm by installing a chirped structure in a nonlinear waveguide. As required to avoid any stability difficulties, this source of photon pairs could substitute bulk sources favorably in QOCT experiments.²⁵³ Notably, by further utilizing two photon NOON states, Lyons et al. were able to attain route length resolutions on the nm scale, with the goal of achieving pm scales.²⁵³ Configurable quantum circuits are implemented in integrated photonics, which naturally provide techniques to reduce instability along with precise control over the path length.²⁵⁴ Integrated quantum metrology experiments that develop and alter NOON states on a chip are made possible by reconfigurability (Fig. 12(a)).^90,255 Due to the current development of monolithic platforms such as LN, single chips with significant levels of integration have recently become feasible.²⁵⁶ In a heralded single-photon arrangement, proposed methods often depend on the development and deterministic separation of two nondegenerate photon pairs. The use of resistive or electro-optic component reconfiguration demonstrates the transition from a two-photon separable state to a NOON. This achieved two photon interference visibilities, which are usually greater than 90% in the initial data, and exhibit possibilities in the quest to surpass the standard quantum limit with chip devices. Surprisingly, the quantum technique has other benefits besides improved accuracy, including flexibility and a decrease in systematic mistakes. In one instance, Reisner et al. measured the differing core and cladding refractive indices of an optical fiber.²⁵⁷ With low coherence Hong–Ou–Mandel interferometry on the basis of a quantum optical method, they demonstrate an order-of-magnitude improvement in accuracy compared to a classical method. When an interferometer and access to the sample being tested are added, both approaches are very well suited for direct integration on chip. These investigations also demonstrate the effectiveness of quantum photonic metrology as characterization tools for integrated photonic circuits due to its high accuracy and very short length.

8.2. Integrated photonic platforms for quantum sensing with NV centers

Quantum sensing with Nitrogen-Vacancy (NV) centers in diamond offers a powerful platform for precision measurements across various fields.²⁵⁸ To fully harness their potential, NV centers must be integrated into scalable, efficient photonic systems. These integrated systems consist of various components, all working together to develop compact, high-performance quantum sensors capable of operating at room temperature and addressing real-world challenges. Integration offers several advantages, including reduced size, lower cost, improved energy efficiency, and enhanced scalability, making NV-based sensors more practical for real-world applications.⁸⁷ NV centers exist in two charge states, with the negatively charged (NV⁻) being most relevant for quantum sensing due to its unique spin and optical properties.³¹ The ground state of NV⁻ features a zero-field splitting (ZFS) of 2.87 GHz, Fig. 10 shows the basis for optically detected magnetic resonance (ODMR)—one of the most widely used techniques for NV-based sensing.²⁵⁹ In this method, a 532 nm green laser excites the NV center, causing electrons to transition to a higher energy state. Upon relaxation, the system emits red fluorescence, with intensity variations dependent on the NV spin state. By applying a microwave field, a dip appears in the ODMR spectrum at 2.87 GHz, corresponding to the resonance condition of NV centers. This dip shifts in response to external magnetic (B) fields , allowing precise detection of the field variations.^260,261 As a result, ODMR enables highly sensitive quantum sensing at the nanoscale, making NV centers a versatile tool for applications in physics, biology, and material science. Constructing an integrated ODMR-based quantum sensor utilizing NV centers requires multiple key components, each serving a specific role in excitation, control, detection, and signal processing. Optical excitation which initializes the NV centers for quantum sensing can be implemented through optical fibers or on-chip photonic waveguides for guiding light efficiently with low losses for scalable integration.²⁶² Microwave (MW) control is another crucial element, where MW fields manipulate the NV center's spin states, enabling ODMR-based measurements. This can be done with integrated MW circuits and resonators to enhance MW coupling.^263,264 Optimizing the interaction between injected light and NV centers is crucial for enhancing quantum sensing performance. Optical resonators—including microdisks, nanobeam photonic crystal cavities, and ring resonators—can confine light to very small volumes, boosting light-NV center interactions.^265–267 This increases photon emission, improves the signal-to-noise ratio (SNR), and enhances spin state readout efficiency.

Fig. 10 Energy level diagram of the NV centre, illustrating the spin states, optical excitation, and fluorescence emission process.

Integrating these resonators into diamond-on-insulator platforms enables precise control of optical modes and Q-factors, improving the sensitivity (three times) of NV-based quantum sensors.^268,269

Once fluorescence is emitted from the NV centers, it must be collected efficiently for accurate quantum sensing. This is done using integrated photodetectors or superconducting nanowire single-photon detectors (SNSPDs).²⁷⁰ SNSPDs are highly sensitive and ideal for precise photon counting, though they typically require a cryostat to operate.²⁷¹ When integrated with diamond waveguides, SNSPDs enable on-chip detection by placing the detector close to the NV centers, reducing photon loss and improving efficiency.^272,273 An example of the integration of quantum sensors based on NV centers is the work by Stürner et al., who designed an integrated portable magnetometer (Fig. 11(a)) incorporating optical fiber coupling, a gradient index (GRIN) microlens for optical excitation, a microwave (MW) resonator for spin manipulation, and a dedicated photodetection system. By optimizing MW power and modulation depth, the sensor achieved a remarkable sensitivity of 344 pT per √Hz.²⁷⁴ The integration of NV centers with CMOS technology represents a significant step towards scalable and mass-producible quantum sensors. CMOS-compatible NV sensors offer advantages such as reduced footprint, on-chip signal processing, and enhanced scalability.²⁷⁵ Another step towards integration in chip-scale quantum magnetometry comes from Kim et al., who developed an on-chip ODMR system combining NV centers with CMOS technology (Fig. 11(b)). Their CMOS-integrated NV sensor consolidates all essential components—microwave generation, NV spin manipulation, and fluorescence detection—onto a single chip, reducing the footprint to just 200 × 200 μm². They successfully demonstrated ODMR spectra under both zero-field and magnetically biased conditions, achieving a magnetic field sensitivity of 32.1 μT per √Hz.²⁷⁶ However, the key challenge for CMOS-based NV censors is maintaining sufficient MW power output. Traditional ODMR setups utilize MW sources with power levels exceeding +30 dBm, which are difficult to achieve in compact CMOS designs.

Fig. 11 (a) Cross-sectional schematic showing an integrated sensor head,²⁷⁴ Copyright (2021), John Wiley and Sons. (b) Integrated CMOS quantum sensing system.²⁷⁶ Copyright (2019), Springer Nature.

Researchers are also exploring pulsed ODMR techniques, which, unlike continuous-wave (CW) ODMR, require less MW power with improved sensor dynamic range and sensitivity.²⁷⁷

8.3. Uses of nonlinear interferometry

In recent years, the field of quantum sensing with nonlinear interferometry has shown an uptick in research activity.^278,279 Photon detection at visible wavelengths allows for the primary goal of inferring biological features in the mid-IR range. This unique concept called “induced coherence”, was first presented by Mandel et al., and it has recently attracted attention in the context of real-world uses in spectroscopy, imaging, optical coherence tomography, and polarimetry.^280,281 Those recent advances in integrated photonics makes it possible to adapt this particular type of technology to photonic chips. Subsequently taking into consideration the industrial prototype, this miniaturization serves as an important and fundamental phase. Recently, Ono et al. demonstrated high-interference transparency above 96% on Si chips using the first integrated version of a nonlinear interferometer (Fig. 12(b)).²⁸² Interestingly, small-footprint optical quantum sensors for gas traces and biomolecule identification are made possible by the Si platform's 2–4 μm opacity apertures. In addition to demonstrating that nonlinear interferometry can be executed on a chip, this innovative research raises new challenges, such as the necessity of keeping the signal or one of the two entangled photons in the visible range and investigating other spectral ranges for the idler or other of the two entangled photons, at least in the mid-IR, as previously demonstrated in large optics.²⁸³

Fig. 12 Schematic diagram of different photonic circuits for quantum sensors with light. (a) Two-photon Fock states with configurable heralding on a semiconductor,²⁸⁴ Copyright (2021), Optica publishing group; (b) nonlinear interferometer: on a Si photonic device, the first spiral waveguide source (source 1) generates signal and idler photons, while the second source (source 2) either enhances or suppresses these photons,²⁸² Copyright (2019), Optica publishing group; (c) illustration exhibited the three-photon entangled states in a Sagnac loop generated by an integrable high-efficiency generator,²⁸⁵ Copyright (2022), Optica publishing group; (d) schematic of a chip-based multiphase estimation experiment,²⁸⁶ Copyright (2019), Optica publishing group.

8.4. The mitigation of noise

Although entangled states provide precise measurements that are not possible with traditional light resources, noise can affect them significantly. The durability and robustness of the quantum state are balanced by an increase in sensitivity; the more sensitive the materials are, the less resilient they become.²⁸⁷ The unregulated or false coupling with the environment can readily ruin the promised quantum advantage, as demonstrated in the case of interferometry.²⁸⁸ Ensuring the implementation of on-chip quantum sensors requires maintaining this quantum advantage in a practical setting. Regarding quantum communication, multimode entanglement has been studied to enhance the capabilities of quantum metrology. Shettel et al. demonstrated that certain types of graph states retain their quantum advantage even after erasures or dephasing.²⁸⁹ Ye et al. conducted a numerical investigation to demonstrate an improvement in sensitivity in two-photon absorption using entangled triphoton states, also referred to as photon triplets, in comparison to results obtained using bipartite states.²⁹⁰ The fabrication of three-photon entangled states on a photonic chip, as demonstrated in Fig. 12(c), has validated this numerical work recently.²⁸⁵ Viable solutions provided by quantum integrated photonics, which opens the door for the development of intricate but stable interferometers.²⁹¹ For the first time, Polino et al. described an experimental proof of concept for identifying two-optical phases simultaneously based on a reconfigurable integrated multimode interferometer printed on silicon (Fig. 12(d)).²⁸⁶

8.5. Integrated quantum photonics in single photon detectors

Superconducting nanowires were initially developed for single photon detection.²⁹² Since then, the technology of superconducting nanowire single-photon detectors (SNSPDs) has advanced significantly, primarily through the implementation of standard fiber-coupled devices.²⁹³ On-chip integrated SNSPDs operate on the same principle as traditional fiber-coupled detectors.²⁷² Usually, superconducting nanowires are DC-current biassed below their critical current (I_c) and temperature (T_c). When a photon is absorbed, Cooper pairs in the wire are broken, creating quasi-particles. The current is redirected towards the displayed electronics as a result of the wire developing a normal-conducting area. The kinetics of this process rely on the device's kinetic inductance and the readout circuitry. The superconducting nanowires return to their superconducting state after a given recovery time (>1 ns). Large-scale on-chip quantum optics activities with more compact chip-scale design and fabrication would be possible with the integration of numerous SNSPDs on-chip.

The integration of multiple single-photon detectors on a chip has been the subject of intense attention in recent years. In contrast to conventional fiber-coupled SNSPDs, SNSPDs are either positioned in planar photonic crystal cavities or integrated into photonic waveguides with travelling wave geometry to achieve high detection efficiency. Typically, SNSPDs positioned on top of optical waveguides, and long enough superconducting nanowires absorb the travelling light field.^71,294,295 Compared to fiber-coupled devices, these detectors can show a lower dark count rate and more rapid (sub-nanosecond) recovery time because of the on-chip SNSPDs' tiny footprint and reduced kinetic inductance.

Additionally, a higher yield can be anticipated because the probability of introducing defects decreased due to the integrated nanowires’ substantially shorter total length. It is expected that SNSPDs and even SNSPD cameras will be fabricated onto quantum photonic chips in the future to accomplish increasingly complex tasks.

8.5.1. Techniques for single-photon detectors. The quantity of photons accessing the detector within a certain range is closely correlated with the output produced by a photon-number-resolving (PNR) detector.^296,297 This makes it possible to calculate an integer count of photons that have been detected, usually with a high degree of accuracy and little ambiguity. To distinguish them from quasi-PNR detectors, these detectors are also referred to as “intrinsic photon-number resolving detectors”. The main way that non-photon-number resolving (non-PNR) detectors work is by using a predetermined detection threshold to determine whether photons are present or absent. The exact number of photons measured is not disclosed by these instruments. Some common names for these detectors include “click detectors”, “click/no-click detectors”, “on/off detectors”, and “threshold detectors”.^298,299 Temporally and spatially multiplexed detectors, like a detector array or a beam splitter-detector tree, are used in quasi-photon-number-resolving (quasi-PNR) detectors. These detectors do not have the ability to resolve photon numbers on themselves.^300,301 This restriction might have an impact on the efficiency of such systems, especially their n-photon efficiency. When there are substantially fewer incident photons than multiplexed detectors, these systems perform at their best.
8.5.1.1. Single-photon avalanche diodes (SPADs). High-sensitivity semiconductor photodiode detectors known as avalanche photodetectors (APDs) exploit the photoelectric effect to transform light into electrical signals. In terms of functionality, they might be seen as the semiconductor equivalents of photomultiplier tubes, which are well-known for their effectiveness and sensitivity in photon detection. Although, previous investigations focused on avalanche breakdown processes, micro-plasma flaws in silicon and germanium, and optical detection utilising p–n junctions.³⁰² APDs have a wide range of applications in numerous industries. They are widely used in quantum sensing applications, where they are essential to control algorithms, long-range fiber-optic telecommunication systems, and laser rangefinders. APDs’ adaptability and importance in furthering scientific research and technological innovation are further demonstrated by their use in positron emission tomography and particle physics studies, as well as other new applications.

However, avalanche breakdown is typically a positive occurrence in which a single photogenerated electron triggers an avalanche of electrons across the pn-junction's depletion zone, raising the electric field across the region to such a high level that a significant current flow emerges.³⁰³ Based on this phenomena, a single photon detector, commonly known as a single photon avalanche diode (SPAD), can be developed.

Rochas et al. found a method for producing a SPAD detector using the conventional CMOS process.³⁰⁴ The challenge was to avoid early breakdown at the incorrect place by preventing extremely high electric fields at the active region's boundaries, which resulted from a substantial doping profile differential there. Instead of only occurring at the margins, the avalanche breakup should occur evenly throughout the active area. Previously, this issue was typically resolved by encircling the active area with a protective ring using specialised manufacturing techniques. There were no layers available for directly constructing such a protective ring in the traditional CMOS process. Without requiring any extra expensive CMOS manufacturing procedures, an effective n⁺ guard-ring that forms between the n-tubs as a result of lateral diffusion between these n-tubs may be produced to encircle the SPAD. Other, simpler, methods for forming the guard ring have since been discovered.³⁰⁵

The technique used by SPADs is similar to PMT, but it has some differences.³⁰⁶ An electron–hole pair is created inside the semiconductor lattice when a photon is absorbed. SPADs function in a continuous charge multiplication mode, in contrast to PMTs, which use discrete dynos in a vacuum for charge multiplication. A bias voltage higher than the breakdown voltage of the diode is applied in the Geiger mode.^307,308 When a photon produces a charge in this mode, the avalanche continues until it saturates at a current that is frequently constrained by an external circuit. By maintaining this current, the SPAD is able to react to further incoming laser pulses. To detect another photon, the SPAD first needs to reduce the saturated avalanche current by bringing the bias voltage below the breakdown voltage. Because of the saturation issue, it is crucial to remember that the gain idea does not apply in Geiger mode. Geiger-mode SPADs have detection efficiencies up to 85% for silicon SPADs in the visible spectrum, which is higher than photomultipliers (PMTs). When using a 100 kbit per s signal and a bit error ratio of 10⁻⁵, the model described produced a receiver sensitivity of −64 dB m.³⁰⁹ To get close to the quantum limit, SPAD visible light communication receiver architecture still needs to be improved in the future. When compared to the best PMTs, SPADs have the drawback of having a higher timing jitter and dark-count rates. Compared to PMTs, infrared (IR) SPADs have significantly greater dark-count rates and efficiencies that normally fall between 50% and 70%.³¹⁰ In order to reduce dark-count rates, SPADs are frequently cooled with thermoelectric coolers to temperatures between 210 and 250 K. This improves their performance in low light and makes it possible to use them in a variety of sensitive detection systems.

Because of the diverse range of photon counting detector technologies, it is helpful to specify a few performance characteristics that are essential for photon correlation measurements. The probability of detecting a photon incident on the detector is known as the detection efficiency. One of the most crucial parameters when measuring photon correlations is the nth order correlation signal, which increases with the nth power of the detection efficiency. The random variation in the time lag between the incident photon's arrival at the detector and the production of an output electrical pulse is known as timing jitter, and it is the second parameter. Improved temporal resolution results from less timing jitter, making it possible to examine quicker physical processes. Furthermore, most detectors experience dead time, which is the period of time following photon detection, through which they become inactive. In the event that an incoming photon is not present, detectors also show a finite likelihood of registering a signal. The term “dark count rate” (DCR) refers to the quantity of these incorrect detections per moment.³¹¹ Additional settings must be optimised for multipixel detectors.

(i) The ratio of the photosensitive area to the detector's overall area is known as the fill factor.

(ii) The possibility of a false detection in one pixel being detected in another pixel is known as crosstalk. Crosstalk develops spurious zero-delay correlations that can readily overpower photon correlation signals, even though it is normally a very small factor in intensity measurements. Crosstalk must therefore be properly controlled because it significantly impairs correlation function measurements when it occurs.³¹²

(iii) Correlation measurements can be thought of as a sequence of frames, with each pixel representing a binary matrix of detection or no detection. The data acquisition rate in correlation measurements is essentially constrained by the frame rate, or the frequency at which such frames may be obtained.

8.5.1.2. Detectors for single pixels. The most common technology used to quantify temporal photon correlations for a considerable amount of time has been PMTs.³¹³ PMTs, which use vacuum tube technology, have a huge detection area (cm²) with timing fluctuations of about 100 ps. However, due to their superior quantum efficiency for visible light, single photon avalanche diodes (SPADs) have essentially replaced PMTs. The usual operating wavelengths for silicon SPADs are 400–1000 nm. At 600–700 nm, commercial devices based on exclusive SPAD designs frequently attain timing jitters of hundreds of ps and efficiency of >60%. Although efforts are being made to address the latter issue, sub-100 ps jitter has been proven by decreasing the thickness of the photon absorption layer, albeit at the expense of decreased efficiency at longer wavelengths (>600 nm).³¹⁴ A common complementary metal-oxide semiconductor (CMOS) method can also be used to produce Si SPADs. CMOS-SPADs can be designed for greater timing jitter, with recent examples reaching 20 ps, even though their efficiencies are marginally lower than those of their bespoke equivalents. Si SPADs are now the most popular photon detection technique for visible light correlation research because of their effectiveness and timing performance.³¹⁵ While Si-based technologies are fundamentally restricted to the detection of visible light, SPADs based on an InGaAs/InP architecture may detect infrared photons. However, their performance is further hindered by the high dark count rate (10⁻⁴ s⁻¹ at ambient temperature), and their efficiency is now limited to about 30%. A developing class of detectors with a significantly greater infrared detection efficiency are superconducting nanowire SPDs (SNSPDs). Superconductivity of a portion of an SNSPD is broken when a single photon is absorbed by the thin superconductor strip. These detectors' generation is motivated from the requirement for effective SPDs for quantum key distribution and associated technologies as they can function with high efficiency (≈80%) at telecom wavelengths (≈1550 nm). Each of them have not been shown simultaneously, but most recent instances include near-unity efficiency, very low dark counts and <10 ps jitter.^316–319
8.5.1.3. Detectors for multiple pixels. Researchers used single-pixel detectors throughout each of the one-dimensional correlation investigations and a few multidimensional correlation trials. Nevertheless, the scalability of these systems is restricted for measurements that oblige the correlation of numerous SPDs. Multipixel detector technologies would be a huge help for these kinds of tests. From parallel temporal-spectral correlations to photon correlation imaging, the development of high-performance multipixel SPDs has in fact encouraged and supported a large number of research initiatives explored in the second half of this review. Although Si-based CCDs possess integrated physical light amplification, single-photon detection can be achieved through their pixels. Electrons within the Si CCD are multiplied during the readout process in an electron multiplying CCD (EMCCD). A microchannel plate and phosphor screen are used in an intensified CCD (ICCD) camera to enhance light before a Si CCD detects it. Correlations and photon detection resolution are both possible with both.³²⁰ Time-gated photon detection is possible in ICCDs; recent experiments have shown gate intervals of less than 20 ps.^321,322 EMCCDs can achieve detection efficiency of 90%, which is far greater than ICCDs, although lacking the ability of time-gate.³²³ In recent correlation-based imaging experiments, both EMCCDs and ICCDs have been used.^324,325 However, the frame rate (kHz) and readout noise characteristic of CCDs limit both approaches. The latest TimePix cameras boost the frame rate by combining a data-driven readout system, an image intensifier, and a pixelated camera.^326,327 The most recent version, the Tpx3Cam, has been used recently to demonstrate improved background rejection in correlation imaging via spatiotemporal correlation measurements. It can detect photons with an efficiency of about 90% and a timing resolution of about 1.5 ns.³²⁸

A number of photon-counting methods have been scaled up to array detectors with pixel-wise timing circuitry in response to the temporal restrictions of EMCCDs. CMOS SPADs, which are based on industry-standard fabrication techniques, are the most easily scalable to arrays of the technologies discussed in the previous section.¹⁰⁴ Time-digital converters (TDCs) are used in smaller monolithic CMOS SPAD arrays (tens of pixels) to accomplish time stamping, and they already exhibit performance on par with single-pixel SPADs.³¹² Although integrating a TDC with every pixel is feasible, doing so drastically lowers the detector's fill factor; this trade-off must be optimised.³²⁹ Greater flexibility can be rendered feasible by implementing the complete timing circuit on an FPGA, as is the case with the LinoSPAD detector for spectroscopy, where all of the pixels in a linear array share 64 TDCs.³³⁰ Applications like spectroscopy of few-photon emitters, where only a small number of detectors record photons at any given time, are best suited for this kind of architecture.^6,66 More advancements in this field are anticipated with the recent introduction of megapixel-scale CMOS SPAD arrays, which have frame rates two orders of magnitude faster than EMCCDs.³³¹ Nevertheless, the huge arrays have mostly been utilised in fluorescent lifetime imaging (FLIM) demonstrations and are usually only capable of time-gating.³³² The efficiency of CMOS SPADs decreases significantly for wavelengths longer than 600 nm.¹⁰⁴ This has sparked attempts to design specially made Si SPAD arrays.³³³ Although unique Si SPAD arrays are more difficult to scale to large arrays than CMOS SPADs, they are more efficient at longer wavelengths; recent demonstrations showed that it reached 33% at 800 nm.³³⁴ Whereas photon detection in the infrared range has also been investigated using InGaAs/InP SPAD arrays, existing implementations have poor crosstalk of 10%. IR photon counting array detectors are essential for expanding photon-correlation-based and quantum enhanced spectroscopy and imaging into the infrared spectrum; nonetheless, these arrays are still not generally accessible.³³⁵

9. Quantum lab-on-chip systems

Additionally, because of its high reconfigurability, this device serves as a flexible platform to evaluate the multiparameter estimation scenario by utilizing additional phase shifters to expand the amount of control parameters. Integrated, fully functionalized biochemical photonic sensors—also termed as “lab-on-chip” systems. On a single chip, these devices combine all necessary classical components, including transducers, detectors, and lasers.³³⁶ In the context of other quantum technologies, the development of on-chip quantum sensors—specifically for quantum spectroscopy, quantum imaging, and quantum optical communication—represents a typical challenge in quantum integrated photonics. From a material perspective, silicon-based demonstrations continue to dominate on-chip biosensing. These stem from the compatibility of silicon-based microfluidic chips with flow cells, as well as from the sophisticated fabrication technique in semiconductor microelectronics and photonics.³³⁷ Two-photon interferometry provides an example of an average situation. A Mach–Zehnder interferometer built on a silica substrate with a microfluidic channel passing through one arm receives a two-photon NOON state created in a nonlinear bismuth borate BiB₃O₆ (BiBO) crystal using substantial optics.³³⁸ The concentration of the protein in the solution is then ascertained by measuring the refractive index of the solution inside the microfluidic device. It had the most promising proof-of-principle demonstration of an on-chip quantum biosensor due to the strong interference visibility, exceeding the threshold necessary for super sensitivity. Simultaneously, the rate of measured photon pairs is substantially limited by the nondeterministic splitting of photon pairs and the deleterious effect of chip losses, resulting in a measurement precision that is lower than the usual quantum limit. Measurements of this type would not be able to match the absolute precision of standard measurement techniques without significantly higher fluxes, indicating the necessity for fully integrated solutions. Getting over the conventional quantum or interferometric limit in practical, or distorted, sensors is still one of the key obstacles.³³⁹ Naturally, the precise value of the consequences in the interferometer determines the optimal quantum states for distorted phase estimation. Generating frequency nondegenerate entangled photon pairs over a variety of detection ranges is a difficulty in quantum imaging, QOCT, and spectroscopy, particularly in mid-IR and visible spectra. As previously mentioned, using χ⁽²⁾ materials is a reasonable method for achieving this kind of SPDC phase-matching requirement. In addition to the previously stated hybrid solutions, the creation of χ⁽²⁾ artificially on the χ⁽³⁾-based platform seems like a compromise that combines the best aspects of each field. The transition to a quantum regime is still challenging.³⁴⁰ For quantum biosensors, quantum spectroscopy, and quantum imaging, optically adjustable quasi-phase-matching in SiN (transparent from 0.4 to 5 μm) is a promising avenue of research that would open the door for the usage of potential frequency combs over visible and mid-IR spectral areas.³⁴¹ Mitigating the level of integration, the transitional phase between quantum and classical might aid in substituting single-photon detection by conventional photodiodes.³⁴² Vast libraries of silicon-on-insulator waveguide-based design materials will be helpful for realizing integrated elements of the yet-to-be-explored mid-IR region, such as gratings, directional couplers, and wavelength-division multiplexers. Since they are still in their beginnings these quantum grade components need to be tuned to function at various wavelengths. A different class of photonic chips concerns the stage of quantum state manipulation, specifically related to their interaction with biological tissues or chemical species. The ideal requirement for a sensitive biosensor is a modest refraction index value along with a high degree of flexibility. Low expenditures were demonstrated by laser-written waveguides on silica, which also provide 3D routing.^343,344 It should be noted that the SiN platform, which is investigated for the generation of photonic quantum states, is compatible with silica-on-silicon integrated devices, enabling low-loss connections. Furthermore, the silica platform permits surface machining to create microfluidic channels or hollow chambers which are directly attached to the surface. Externally controlled phase elements are usually used in multiport interferometers to enable dynamic operation and reconfiguration.³⁴⁴

The ability of NV centers to measure parameters like temperature, pressure, and magnetic fields makes them a powerful tool for enhancing the precision and non-invasive analysis of LOC devices.³⁴⁵ To integrate NV centers into LOC platforms, several methods have been used so far. One approach is embedding NV centers close to the surface of diamond microstructures, allowing them to interact directly with the sample.^346,347 However, most state-of-the-art experiments have not fully utilized the NV center's capabilities for nano- and microscale sensing, still requiring milliliter-scale sample volumes.³⁴⁸ Additionally, materials like polydimethylsiloxane (PDMS) and tape-based microfluidic channels have been used in early attempts to combine NV centers with LOC platforms, though some of these materials had limitations in biocompatibility and adaptability.^349,350 More advanced methods include using compound parabolic concentrators (CPCs) for enhanced photon collection and integrating microwave antennas for NV spin manipulation, enabling full quantum sensing capabilities within LOC systems.³⁵¹ The integration of electronic and photonic functions onto monolithic integrated devices is still a challenge. This is because it requires the development of overlaid quantum protocols, such as Bayesian and machine learning (ML) algorithms, as well as realization of physical interfaces and adequate control circuits.³⁵²

10. Quantum communication

Transporting quantum states from one location to another provides the premise of quantum communication. The foundational idea is that numerous individuals can share entanglement in quantum states, and these associations might represent shared information between each participant (Fig. 13(a)). These forms of communication include quantum cryptography and the “wiring” of quantum computers, which creates quantum interactions between various components. Quantum key distribution (QKD), which was initially created in the 1980s, is the most sophisticated communication protocol.³⁵³ This protocol, which depends on the capacity for these individuals to interact using quantum entities, allows two distant individuals to establish a shared secret key. Thus, optical fiber, free-space communication lines, and light all play important roles (Fig. 13(b and c)). Because it is impossible to determine the unknown state of a single quantum particle or to create a duplicate of the particle, for example, it is impossible to determine the unknown polarization of a single photon through any kind of measurement technique or to create a second photon with an identical polarization state. This provides a certain level of security because it allows both individuals to have exactly the same set of random numbers and to be almost certain that no one else has them. Then, they can use a one-time pad to securely encrypt messages to one another. When QKD is used at its most sophisticated, it operates at high bit rates and offers real-time key distillation, which offers good security despite authentication issues, finite key effects, and system failures.³⁵⁴ QKD systems can also function in difficult environments. For example, secure satellite-based worldwide communications are soon to be possible thanks to the establishment of secret keys between a moving aircraft and a ground station.³⁵⁵

Fig. 13 Networks of quantum communications. (a) Representation of a long-distance repeater-based star network for long distance communication. In quantum memory, entanglement stored along sub-links coupled by linear optics and measurement-based entanglement-swapping procedures,³⁵⁶ Copyright (2015), The American Association for the Advancement of Science; (b) La Palma and Tenerife, two Canary Islands in Spain, are connected by an entanglement-based QKD setup. The length of the optical link is 144 km. Where, GPS = global positioning system; PBS = polarizing beamsplitter; BS = beamsplitter; HWP = half-wave plate; OGS = optical ground station; (c) schematic diagram of a BB84 QKD decoy-state experiment between a hot-air balloon and the ground. A first step towards achieving QKD between terrestrial and low-Earth orbit satellites may have been taken with this experiment. Where, 532LD, 532 nm laser; 671LD, 671 nm laser; 532D, 532 nm detector; IF = interference filter; MON = monitor window; ATT = attenuator; CMOS = complementary metal–oxide–semiconductor; FSM = fast steering mirror and DM = dichroic mirror,³⁵³ Copyright (2014) Springer Nature.

It is interesting to note that certain variants of QKD techniques do not require cooperation between the photon provider and the sender or recipient via the network. If they employ entangled photons, then a subset of the photons can be used to verify the degree of entanglement, allowing the sender and recipient to determine the reliability of the network. This makes it possible to distribute keys without relying on the internal operations or security of the stations. It allows self-certification of QKD and other protocols that rely on randomness generation, and it is virtually device-independent.³⁵⁷ In the field of telecommunications, which can function with near-terahertz bandwidths using time-frequency encoding, the ability of light to convey information is widely recognized. All these characteristics are inherited by photons, and it is possible to create an ultrahigh bandwidth quantum communications system where a single photon can carry several bits.³⁵⁸ Beyond point-to-point transfers, quantum communication will undoubtedly provide safe connections over multimode networks in the future.³⁵⁹

10.1. Sources of quantum illumination

In a quantum optical system, a photon source that produces certain quantum states of light is an essential component. Quantum communication networks often require single-photon states and entangled photon states, which can be produced probabilistically through parametric nonlinear processes or deterministically by single-photon emitters.^57,360 The recurring nature of QDs’ emission behavior provides one of the most attractive options for the instant production of single photons or entangled photon pairs.³⁶¹

They are particularly desirable for on-chip integration due to their compact footprint and compatibility with semiconductor technology.¹⁵⁴ A single InAs/GaAs self-assembled QD (Fig. 14(a)) and an InGaAs QD (Fig. 14(b)) have achieved single-photon production, purity, extraction efficiency, and photon indistinguishability of 99.1%, 66.0%, 98.5% and 99.7%, 65.0%, 99.6%, respectively.^362,363 The out-of-plane emission property of these micropillar-based QD single-photon sources, however, makes waveguide integration challenging. As an alternative, QDs can be incorporated for very efficient waveguide coupling in heterogeneous waveguide architectures or photonic crystal waveguides (Fig. 12(c)).³⁶⁴ The biexciton-exciton cascaded radiative processes in QDs can also be used to obtain entangled photon pairs.³⁶⁵ An entangled photon pair source was achieved by systematically embedding GaAs QDs in broadband photonic nanostructures, with pair collection probability of 0.650, coupling quality of 0.880, and consistency of 0.901 and 0.903 (Fig. 12(d)).³⁶⁶ Apart from QDs, various other solid-state quantum emitters have also been studied and demonstrated significant potential for producing single or entangled photon pairs on-chip. These include colour centers in diamonds, carbon nanotubes, silicon carbide, and defects in 2D materials.^87,367–369

Fig. 14 QD photon emitters integrated into the chip. (a) Illustration of a single InAs/GaAs self-assembled QD implanted in a micropillar cavity with a diameter of 2.5 μm,³⁶² Copyright (2016), American Physical Society; (b) representation of an InGaAs QD attached to a micropillar; four one-dimensional wires connect the micropillar to the surrounding circular frame,³⁶³ Copyright (2016), Springer Nature; (c) a QD placed within a photonic crystal waveguide. Near-unity probability causes a significant fraction of single photons to be channeled into the waveguide mode,³⁶⁴ Copyright (2014) American Physical Society; (d) an instance of a highly efficient broadband reflector with a single GaAs QD generating entangled photon pairs, use a circular Bragg resonator,³⁶⁶ Copyright (2019), Springer Nature.

When using optical waveguides or other photonic structures, such as micro-disk and ring resonators and photonic crystals, integrated probabilistic quantum light sources typically use the advantage of both spontaneous four-wave mixing (SFWM) or spontaneous parametric down-conversion (SPDC). Due to the stringent confinement of light, these nonlinear parametric processes are significantly improved on a chip, permitting the efficient creation of high-quality photon states in miniature configurations. To produce a pair of signals and idler photons in SFWM, two pump photons are dispersed. For retained energy, the frequencies of the pump (ω_p1, ω_p2), idler (ω_i), and signal (ω_s) must obey

ω_p1 + ω_p2 = ω_s + ω_i

Based on this four-photon process, single-photon or entangled photon sources have been shown in platforms with third order nonlinearity, including Si, SiO₂ (Fig. 15(a)), and Si₃N₄ (Fig. 15(b)).^370,371 SPDC divides a single pump photon into two signal and idler photons, and the frequencies of the pump (ω_p), signal (ω_s), and idler (ω_i) must follow the equation

ω_p = ω_s + ω_i

Fig. 15 Modifications in parametric photon sources-based chips. (a) Heralded single-photon sources (HSPSs) signaled by an array of spontaneous four-wave mixing (SFWM). A germanium-doped silica-on-silicon photonic chip is used to build a number of straight waveguides, each of which is an independent HSPS, using UV laser writing,³⁷¹ Copyright (2017), Optica Publishing group; (b) a nanophotonic visible-telecom SFWM photon-pair source that produces narrow-band photon pairs with previously unheard-of brightness and purity by employing high-quality factor silicon nitride resonators,⁷⁶ Copyright (2023), Springer Nature; (c) an entangled photon source based on spontaneous parametric down-conversion (SPDC) using a periodically poled part of an LN photonic chip; (d) a whole chip structure; (e) an image of the chip with its fiber bunches attached,³⁷² Copyright (2014), American Physical Society.

Third-order nonlinearity platforms, such as periodically poled LN waveguide circuits (Fig. 15(c–e)) and III–V semiconductor chip, have been used to create photon sources based on this three-photon process.^372,373 The main problems with these photon sources are that they do not create photons in a deterministic manner, and the basic trade-off between brightness and multi-photon probability limits the generation rates. A promising approach to solving difficulties through the use of multiplexing techniques.^374,375 The single photon generation probability for two sources pumped independently and two sources pumped through a shared input, respectively, was enhanced by 62.4% and 63.1%, respectively, using an integrated spatially multiplexed heralded single-photon source (HSPS).^375,376 In order to achieve even greater efficiency gains, it is necessary to use ultra-low-loss delay lines that are smaller in size and have faster electronics in order to synchronize activities.³⁷⁴ The decoy-state system 78–80 states that for the majority of prepare-and-measure QKD applications, weak coherent pulses can be used as a reliable substitute for single-photon states.^377,378 As a result, integrated photon sources can be achieved by simply attenuating the coherent pulses generated by on-chip lasers.

10.2. Modified quantum optical components

The processing of quantum information in quantum communication requires the manipulation of quantum states of light, which is easily accomplished with off-the-shelf passive and active integrated photonics components. Photons are frequently processed in the polarization, phase, spatial, spectral, and temporal domains in a typical quantum communication system. As a result, it needs building components such as splitters/switches (Fig. 16(a)), polarization, phase shifters (Fig. 16(b)), intensity modulators (Fig. 16(c)), and directional couplers (Fig. 16(d)) that may affect these photon degrees of freedom; as well as, multi-mode interferometers (MMI) (Fig. 16(e)), ring resonators (Fig. 16(f)), and delay lines (Fig. 16(g)).^379–385 Phase shifters can specifically be achieved for low-speed applications and high-speed applications using the Pockels electro-optic effect and thermo-optic effect, respectively.^68,386 A range of integrated platforms have been used to demonstrate such devices, including an ultraviolet-written silicon photonic chip for quantum teleportation with thermo-optic phase shifters, a GaAs quantum photonic circuit with an adjustable Mach–Zehnder interferometer (MZI) based on the Pockels effect and an adjustable linear optical circuit consisting of an array of 30 silicon wave guided directional couplers with 30 thermo-optic phase shifters (Fig. 16(h)) and an extensive silicon photonics quantum circuit integrating 16 SFWM photon-pair sources, thermo-optical phase shifters, and 122 MMI beam splitters.^152,387,388 On-chip modulators used quantum-confined or free carrier dispersion effects, at frequencies up to GHz. The Stark effect can also be used for qubit encoding and pulse creation.^389–391 For the creation of BB84 polarization states, modulators based on polarization rotators and polarization beam splitters have been built and demonstrated for polarization encoding methods.^391,392 For optical communication between quantum photonic circuits and optical fibers, more integrated components will be required. When there is only one input or output polarization, one can employ off-plane coupling and one-dimensional grating couplers.³⁹³ If there are more polarization channels and a wider spectral range, edge couplers such as inverted tapers for butt coupling can be used instead.³⁹⁴ Furthermore, it has been shown that a two-dimensional grating coupler that supports multi-polarization operation can change path-encoded qubits into polarization-encoded qubits, which are better suited for propagating in optical fibers.³⁹⁵

Fig. 16 Typical quantum photonic chip integrated systems. (a) The evolution of the mode profile and schematic diagram of a polarization splitter/rotator,³⁸¹ Copyright (2015) Optica Publishing group; (b) perspective view and optical micrograph of a silicon thermo-optic phase shifter,³⁷⁹ Copyright (2014) Optica Publishing group; (c) illustration of an electro-optic modulator with high bandwidth, where a Mach–Zehnder interferometer made of silicon is bonded to an unpatroned layer of LN thin film,³⁸⁰ Copyright (2018) Optica Publishing group; (d) illustration exhibiting a directional coupler with a Ge₂Sb₂Te₅ (GST) thin layer,³⁸² Copyright (2019) American Chemical Society; (e) illustration of a 4 × 4 multimode interferometer,³⁸³ Copyright (2011), Springer Nature; (f) illustration showing the integration of an on-chip tunable ring resonator filter into a hybrid quantum photonic circuit,³⁸⁴ Copyright (2017) Springer Nature; (g) illustration of a spiral delay line in a silicon photonic waveguide,³⁸⁵ Copyright (2022) Optica Publishing group; (h) a fully reprogrammable silica chip was utilized to realize a six-mode universal linear-optic device,¹³¹ Copyright (2015), The American Association for the Advancement of Science.

10.3. System integration and chip packing

Prototyping functional devices requires assembling bare quantum photonic chips into robust modules, even though these chips can be characterized with a probe station.³⁹⁶ For practical uses, a variety of methods have been put forth to package quantum photonic chips into compact devices. To create the optical, electrical, mechanical, and thermal connections between a photonic chip and the off-chip components in a photonic module, photonic packaging frequently involves a variety of techniques and technical expertise.³⁹⁷ Due of the significant difference in their mode-field diameters (MFDs), connecting an optical fiber to a standard waveguide on the chip shows its most significant problem.³⁹⁸ For instance, in telecom single-mode fibers (SMFs), the MFD at 1550 nm is approximately 10 μm, although the silicon waveguide's matching strip is typically just 220 × 450 nm in the cross-section. Combinations that effectively extract the mode from the waveguide, such as inverted-taper edge couplers interfaced with lensed SMF fibers (Fig. 17(a)) or ultrahigh numerical aperture fibers and grating couplers interfaced with SMF fibers (Fig. 17(b)), can help to reduce this discrepancy.^393,399,400 Achieving coupling performance up to 81.3% (−0.9 dB) in a 260-nm-thick SOI platform through the use of grating couplers eliminates the requirement for an overlayer or back reflector.⁴⁰¹ Furthermore, edge couplers built on 200-mm SOI wafers have been used in experiments to exhibit efficiencies above 90%.⁴⁰² With a coupling loss of roughly 1 dB at 1550 nm wavelength, the evanescent coupling technique is an alternate method for cheap and panel-level packing.⁴⁰³ Signal routing from electronic drivers, amplifiers, and other control circuitry requires electronic packaging in order to reach the electrical components on quantum photonic chips. Accessing specialized printed circuit boards (PCBs) is a common way to accomplish this (Fig. 17(c)).⁴⁰⁴ Typically, wire-bonds are used to link PCBs to the bond-pads on the chip. Using modified electronic integrated circuits (EICs), 2.5-dimensional or 3-dimensional integration may be used when a very large number of electrical connections or accurate sub-nanosecond control on many channels is required (Fig. 17(d)).⁴⁰⁵ Solder-ball-bump or copper-pillar-bump interconnects can be used for this integration, giving the photonic chips a strong mechanical, electrical, and thermal interface.⁷⁶ For prototypes that need to be highly accurate and repeatable or for field tests where seasonal temperature changes are frequent, global thermal stabilization of quantum photonic devices is crucial. Passive cooling methods or a thermoelectric cooler (TEC) can be used to accomplish this. The local temperature adjustment for various photonic elements (such as micro-ring resonators, thermo-optic phase shifters, etc.) on chip can be made more effective and repeatable by the additional global stability provided by the TEC.⁴⁰⁶ Liquid cooling is an additional option for boosting the cooling system capability.⁴⁰⁷

Fig. 17 Illustrations of integrated circuit packaging. (a) Schematic diagram of a lensed optical fiber connected to a bilayer LN inverse taper; (b) schematic diagram of a dual-level grating coupler interfaced with a SMF on Si₃N₄-on-SOI; (c) image of a thermoelectric cooler, fiber arrays, and PCBs bundled with a quantum photonic processor; (d) an image of a multi-chip module developed using a silicon interposer to connect one photonic integrated circuit (IC) to four electronic ICs,⁷⁶ Copyright (2023), Springer Nature.

11. Systems for secure communication using quantum technology

QKD, the most advanced secure communication technology, is already being tested by governments and banks to ensure high-level data transmission security. It is based on bulk optic or fiber optic components. Expanded applications, however, call for QKD systems that are more flexible, small, and affordable to produce in large quantities. A number of studies aimed at integrated devices for the realization of affordable and compact quantum communication were compiled in the preceding section. Here, we explain recent system-level initiatives towards a fully chip-based QKD platform. Table 1 provides an overview of the common integrated QKD implementations for a degree of integration.

Table 1 Integration factor for standard integrated QKD systems. Where, DPS = differential phase shift; COW = coherent one way; HD-QKD = high-dimensional QKD

Material	Techniques	QRNG	Encoding	Decoding	Detector	Ref.
InP	BB84; DPS	Yes	Yes	No	No	408
Si	BB84	No	Yes	No	No	409
Si	BB84	No	Yes	No	No	410
Si	COW; DPS	No	Yes	Yes	No	411
Si	HD-QKD	No	Yes	Yes	No	412
InP	MDI-QKD	No	Yes	No	No	390
Si	MDI-QKD	No	Yes	Yes	No	392
Si	CV-QKD	No	Yes	Yes	Yes	389
Si, NbN	MDI-QKD	No	No	Yes	Yes	413
InP, SiOxNy	BB84; COW; DPS	No	Yes	Yes	No	414
InP, Si	Modified BB84	Yes	Yes	Yes	No	415

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11.1. Quantum key distribution (QKD)

The core of quantum key distribution (QKD) is the collaboration of randomness between two distant users—typically mentioned and known in cryptography as Alice and Bob. Numerous strategies have been devised to simplify experimental implementation, enhance performance, and improve resilience against device assaults since Bennett and Brassard's original protocol, BB84, which was based on a prepare-and-measure scenario.^416,417 Since QKD addresses the security flaw in traditional asymmetric key protocols like RSA—which bears the names of Ron Rivest, Adi Shamir, and Leonard Adleman—it attracted business attention promptly. The goal was to implement small, reliable, and effective systems quickly with the intention of launching a new market. The advancement of integrated photonics for classical communication has encouraged this trend. An integrated phase modulator, for instance, is used in the plug-and-play system created in 1996 at the University of Geneva to prepare the quantum states.⁴¹⁸ Phase and amplitude modulators are being used by QKD systems, which have set records for distance (421 km) and speed (5 GHz).^419,420 Moreover, these modulators are being used for recently developed techniques like twin-field (TF) QKD and measurement-device-independent (MDI) QKD.^21,421 Furthermore, a multitude of degrees of freedom, such as polarization, time, or frequency, can be addressed using these two strategies.^422–424 The development of specialized integrated devices is an additional strategy. To measure the phase difference between two successive pulses in a differential-phase-shift (DPS) QKD experiment, an innovative study used a planar light-wave circuit in which an unbalanced Mach–Zehnder interferometer is integrated on silica.⁴²⁵ In 2004, a planar light-wave circuit unbalanced Mach–Zehnder interferometer integrated on silica was utilized in the first realization of a QKD system to measure the phase difference between two successive pulses in a differential-phase-shift (DPS) QKD experiment.⁴²⁵ By adjusting the temperature within 0.05 °C, they were able to drastically reduce the size of typical interferometers based on fiber components and enhance phase stability. The subsequent phase is to integrate an entire QKD system, indicating that the electronics and optics are integrated together, in order to minimize the footprint in comparison to traditional “small form-factor pluggable” systems used in classical communication. A common implementation was the “QKarD”, which combines a modulator and an interconnected pulse laser within a packaging box like that of electro-optic modulators.⁴²⁶ In order to build a decoy-state BB84 QKD algorithm, the device is capable of creating polarization states at 1550 nm with three degrees of intensity.^427,428 The electronic device operated on a 10 MHz frequency. By implementing photonic devices on platforms with a high integration density, the transmitters’ size can be decreased. Table 2 provides an overview of all the QKD transmitter chips.

Table 2 Characterization of QKD research with integrated transmitters. Where, MDI = measurement-device-independent; FLWG = femtosecond-laser-written waveguide; CV = continuous variable; DPS = differential phase shift; COW = coherent one way

Materials	Techniques	Measurement	Receiver	Clock rate	Ref.
FLWG	BB84	Polarization	Integrated	100 MHz	429
Si	BB84	Polarization	Fibered	50 MHz	430
Si	BB84 MDI	Polarization	Integrated	0.5 MHz	392
InP	BB84 MDI	Time bin	Fibered	250 MHz	390
InP	BB84; DPS	Time bin	Integrated	1 GHz	408
Si	CV Gaussian-modulated	quadrature	Integrated	10 MHz	389
Si	BB84	Time bin	On chip	100 MHz	431
Si	High-dimension	Path	Integrated	5 kHz	412
InP	BB84; DPS; COW	Time bin/polarization	Integrated	1.76 GHz	414

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A QKD transmitter with two ring modulators, four variable optical attenuators, and a polarization modulator was realized in 2016 by utilizing typical Si photonic foundry methods.⁴⁰⁹ At 10 MHz, a QKD link based on the polarization-encoded BB84 protocol was exhibited. Following this, three transmitters in silicon were created to set up states for the polarization-encoded BB84, time-bin-encoded BB84 QKD, and coherent one-way (COW) protocols (Fig. 18(a)), respectively.⁴³² Similarly, silicon oxynitride (SiO_xN_y) photonic receiver circuits with off-chip single photon detectors were used to guarantee quantum state analysis. For each of these implementations, the photons carrying the quantum states must be produced by an external laser. With the transmitter and receiver built on InP and SiO_xN_y, the first completely integrated QKD link was established.⁷⁶ A variable optical attenuator, an amplitude and phase modulator, and a continuous tunable laser diode are all included in the transmitter chip. The versatility of the technique was confirmed by the realization of all time-coded based QKD protocols, namely COW, BB84, and DPS, at repetition rates of 560 MHz, 860 MHz, and 1.76 GHz, respectively, through the use of this QKD interaction. There have also been improvements in photonic platforms for MDI QKD techniques. The transmitters must be monitored by Hong–Ou–Mandel interference between the states broadcast by two separate transmitters; alternatively, they are identical to those used for BB84 protocols. Achieving two coherent states that are identical across all degrees of freedom—aside from the one used to encode the states—is an essential prerequisite for completing this stage. This strategy has been proven feasible in three experiments: two on Si and one based on InP transmitters (Fig. 18(b)).^391,392 An increasing amount of experiments are concentrating on continuous variable (CV) QKD in addition to QKD systems that take advantage of quantum optical states at the single-photon level. In this case, the electromagnetic field's amplitude and phase quadrature—which are continuous spectrum observables, contain quantum information. Gaussian modulation of a coherent state and homodyne detection of its quadrature at the receiver side are the foundations of most protocols.⁴³³ In 2019, two Si photonic chips were integrated with components for information encoding and detection, such as the homodyne detection and the modulation and multiplexing stages, respectively. Over 100 km in optical fiber, these components enabled a secret key rate of 0.14 kbit per s.³⁸⁹

Fig. 18 Integration of different devices for techniques involving preparation and measurement. (a) QKD integrated silicon photonic devices: COW, BB84 time bin, and BB84 polarization,⁴³⁴ Copyright (2022), MDPI; (b) superconducting nanowire single-photon detectors integrated into a receiver chip, shown in the SEM picture (red) on top of the waveguide (cyan). A time-bin protocol using a single decoy state is made possible by vertical couplers, Mach–Zehnder, and splitters (S1 and S2),⁴³⁵ Copyright (2021), Springer Nature.

Despite the recent advancements in integrated optics for QKD, the difficulty is likely to be integrating such systems into commercial devices. For instance, modern technologies enable the development of quantum states inside a “small form-factor pluggable” module.⁴³⁶ The integration of single-photon detectors on a single photonic device is now the biggest hurdle. A promising recent demonstration of the detection of single photons (using SNSPD) on a photonic circuit point to more advances in the future.²⁹³ In contrast to 2D systems, high-dimensional QKD increases the number of addressable quantum bits by utilizing states in N-dimensional Hilbert spaces. In addition to being a strong contender for information distribution which is completely safe, it also creates new possibilities when taking into account entanglement between various parties. Aside from QKarD, some realizations have begun to take advantage of this strategy.⁹⁰ Among other things, using an integrated transmitter and receiver on Si chips to implement QKD links which require path indicators.^437,438

11.2. Quantum random number generators (QRNGs)

A reliable random number generator is an essential component of several quantum secure communication systems under study, since the security of encryption depends on the quality and unpredictability of exchanged keys.

Because of their deterministic nature, pseudo-random numbers cannot be considered truly unexpected, despite their ease of creation. As a result, QRNGs have been created to generate genuinely random numbers that satisfy the basic principle of quantum physics, which states that it must be unpredictable, irreproducible, and neutral.⁴³⁹ The vacuum state and quantum phase fluctuation technique are the two most widely utilized procedures for QRNGs.⁴⁴⁰ Instead of using single-photon detectors, these systems can readily reach random data rates up to Gbps by using photodetectors. Apart from the output speed in real time, another crucial aspect of QRNG for real-world applications is the module size. Size reduction has shown to be a significant advantage of integrated quantum photonics, a promising technology. Several integrated QRNG implementations with varying degrees of complexity have been demonstrated recently. These implementations make use of a variety of integration technologies. A quantum entropy source has been built in an InP platform, and a QRNG based on a LiNbO₃ platform has achieved a real-time rate of 3.08 Gbps through the use of multiplexed detectors.^441,442 By monitoring phase fluctuations (Fig. 19(a)) and vacuum state, respectively, QRNG implementations have also been described on the SOI platform due to its higher integration density and superior technical maturity as compared to III–V systems.^443,444 On the other hand, it is important to remember that germanium photodiodes on SOI suffer from a significant negative current, which impairs the functionality of on-chip QRNGs and requires careful optimization to mitigate. As a substitute, integrated QRNG based on InGaAs photodiodes was developed with a high bandwidth trans-impedance amplifier (TIA) hybrid packed with an SOI chip, resulting in a real-time output rate of 18.8 Gbps (Fig. 19(b)).¹⁵⁷ Another example of an integrated QRNG is based on a parallel array of individual single-photon avalanche diodes which have co-integrated with logic circuits for postprocessing.²⁴⁶ The array gets homogeneously illuminated by a direct-current-biased light-emitting diode.

Fig. 19 Integrated quantum random number generators (QRNGs). (a) An SOI chip is used to determine phase variations from a laser diode to develop a QRNG,⁴⁴⁵ Copyright (2018), Optica Publishing Group; (b) InGaAs photodiodes packed on an SOI chip in a hybrid integrated QRNG,⁴⁴⁶ Copyright (2021), AIP Publishing.

11.3. Discrete variable-quantum key distribution (DV-QKD) systems

Discrete variables (DVs) like photon phase or polarization are used in most QKD implementations to store secret keys. A very common instance of a DV-QKD protocol is decoy-state BB84, which is extensively used in cutting-edge commercial applications.⁴³² The basic components of a DV-QKD system include light sources, modulators, single-photon detectors, and necessary passive optical components, as per protocols. For differential phase-shift QKD investigations, photonic integration of these elements started with the asymmetric PLC MZIs.⁷⁶ Comparing the on-chip interferometers to their fiber-based cousin, the former demonstrated a far more accurate and reliable phase decoding performance. Subsequently, a plethora of tiny QKD devices were demonstrated. An electro-optic modulator (EOM) including a modulator and a distributed feedback laser, for instance, was used to develop a same size miniature QKD transmitter.⁴⁴⁷ With decoy states, the small-scale transmitter may generate weakly coherent pulses at 1550 nm that encoded in BB84 polarization states. Afterwards, a LiNbO₃ polarization rotator on-chip was developed for user-server frame-independent QKD.⁴⁴⁸ Once a QKD server sent low laser pulses to the user, which eventually evolved into a handheld device, each pulse was attenuated and encoded with a qubit of data for transmission back to the server. A portable QKD transmitter device with an effective size (25 mm × 2 mm × 1 mm) was also designed and evaluated using an integrated optics architecture. Polarization qubits were produced in the device by four vertical cavity surface-emitting lasers connected to four micro polarizers developed via focused ion beam (FIB) milling. To ensure spatial overlap, the qubits were coupled via a borosilicate glass waveguide array. A highly integrated QKD system was demonstrated in Fig. 20(a).¹²⁰ Using materials and manufacturing techniques from the telecommunications sector, the transmitter module within the InP chip and the reception unit with the SiO_xN_y chip were merged. The SiO_xN_y receiver was made up of thermo-optic phase shifters and a reconfigurable delay line that interfaced with off-chip single photon detectors. Whereas, the InP transmitter was composed of a tunable laser, optical interferometers, electro-optic phase modulators (EOPM), and a p–i–n photodiode. Multiple protocols, such as BB84, coherent one-way, and differential phase shift, were implemented with the devices’ reconfigurability, which allowed for clock rates of up to 1.7 GHz, a quantum bit error rate (QBER) as low as 0.88%, and estimated secret key rates up to 568 kbps for an emulated 20 km fiber connection. Recently, wavelength division multiplexing (WDM) was used to improve the data rate of the chip-based system.⁴⁴⁹ Two InP transmitters and one SiO_xN_y receiver with on-chip asymmetric MZI filters for wavelength demultiplexing were used to build this type of WDM-QKD system. Over a 20 km emulated fiber, the secret key rate was boosted to 1.11 Mbit per s by the combined WDM systems. Integrated modulators consisted of a necessity for the previously mentioned chip-based QKD arrangements. It would be feasible to develop a modulator-free QKD transmitter chip with the direct phase modulation method that had been subsequently implemented in bulk optic transmitters. For the distributed phase shift protocol and the decoy state BB84, respectively, secure key rates of 400 kbps and 270 kbps at 20 dB attenuation were obtained using the modulator-free device (Fig. 20(b)).⁴⁵⁰ A QKD system that is completely independent has been created with small modules made of InP photonic integrated circuits.^76,451 The quantum random number generation and key distribution are made possible at gigahertz clock speeds by this system, which integrates the quantum transmitter, receiver, and QRNG chips.

Fig. 20 Hybrid materials for chip-based QKD systems. (a) (i) An integrated, reconfigurable, multi-protocol QKD transmitter for a GHz clock rate measuring 2 mm × 6 mm. A continuous tunable laser diode (LASER), EOPMs, photodiodes, and interferometers made of multi-mode interference (MMI) devices functioning as 50 : 50 beam splitters are all combined in this circuit. Where, P.MOD = pulse modulation; PH.RAND = phase randomization; I.M = intensity modulator and PH.ENC = phase encoding; (ii) a reconfigurable, multi-protocol QKD circuit using a 2 mm x 32 mm silicon oxynitride (SiO_xN_y) photonic receiver circuit that uses off-chip single photon detectors (SPDs) to passively decode the quantum information; (iii) the deep etch waveguide, measuring 1 μm in width and 4 μm in etch depth, appeared in waveguide cross-section 9 of the InP technology platform; (iv) a semiconductor optical amplifier (SOA) measuring 1.1 mm in length and two tunable distributed Bragg reflectors (T-DBR) combine to create a wavelength-tunable continuous wave laser; (v) EOPM microscopic imaging in a multimode interference device (MZI) that functions as a 50 : 50 beamsplitter. Scale bar: 500 μm; (vi) the SiO_xN_y Triplex waveguide cross-section, with metallization for heating elements and a waveguide diameter of approximately 2 μm; (vii) microscopic image of the delay lines in the receiver (1 mm scale bar),⁴¹⁴ Copyright (2017) Springer Nature; (b) a QKD transmitter chip without a modulator that comprises one variable optical attenuator and two cascading high-bandwidth distributed feedback lasers,⁴⁰⁸ Copyright (2019), Springer Nature.

For chip-based QKD systems, silicon photonics is an appealing new platform. For polarization-encoded QKD, a previous investigation demonstrated a Si optical transmitter (Fig. 21(a)).⁴⁰⁹ The chip implemented the BB84 protocol with a QBER of 5.4% and an asymptotic secure key rate of 0.95 kbps over a 5-km fiber link. It had a polarization modulator, variable optical attenuator, intensity modulator, and pulse generator in a 1.3 mm × 3 mm die area. Three parallel implementations of silicon photonic devices for high-speed low-error QKD, as displayed in Fig. 21(a).⁴³² They were able to achieve estimated asymptotic secret key rates of up to 916 kbps and QBERs as low as 1.01% across 20 km of fiber by utilizing a mix of high-bandwidth carrier-depletion modulators and thermo-optic phase modulators. An additional circuit for a silicon photonic transceiver was developed, which produced four BB84 states at gigabit-per-second modulation speed and >30 dB polarization extinction ratios.⁴⁵² With a comparable silicon photonic encoder, polarization encoded QKD field experiments were subsequently observed in Fig. 21(b).⁴¹⁰ The systems were able to obtain composable secret key speeds of 157 kbps in an interstate metropolitan experiment (on a 43 km fiber with 16.4 dB loss) and 1.039 Mbps in a local test (on a 103.6 m fiber with a total simulated loss of 9.2 dB). These days, application of advanced QKD techniques with chip-based devices receives attention because photonic integration significantly improves their performance. Silicon photonic integrated circuits used to demonstrate a noise-tolerant high-dimensional QKD technique based on space division multiplexing in multicore fiber (Fig. 21(c)).⁴¹² These circuits enabled low and steady QBER substantially below the coherence confront and individual attack limits by offering a far more effective technique for generating high-dimensional quantum states. Furthermore, in a chip-based customer-server scenario—in which devices carry inexpensive photonic chips and the server, functioning as an unknown node, includes the costliest components that can be shared by several users—measurement-device-independent (MDI) QKD, which closes all side channel loopholes in detection, remains most appropriate. Two separate investigations using the InP platform and the Si/III–V hybrid platform, respectively, showed that integrated photonics could be used for MDI-QKD.^78,453 The essential element of MDI-QKD, Hong–Ou–Mandel interference, was carried out in these investigations between weak coherent states from the chips. Two III–V on silicon waveguide integrated lasers and two InP transmitters demonstrated high visibilities of 46.5 ± 0.8% and 46.0 ± 2.0%, respectively.^78,453

Fig. 21 (a) (i) Schematic diagram of a Si PIC transmitter for QKD with polarization coding. A micro ring intensity modulator, polarization controller, VOA, and micro ring pulse generator make up the transmitter. (ii) An optical micrograph of the chip,⁴⁰⁹ Copyright (2016), Optica Publishing Grouop. (b) Intercity QKD field test employing a silicon photonic polarization encoder over a 43-km dark fiber link,⁴¹⁰ Copyright (2018), American Physical Society. (c) Integrated silicon photonic circuit for high-dimensional quantum key distribution with noise tolerance,⁴¹² Copyright (2017), Springer Nature.

11.4. Continuous variable-quantum key distribution (CV-QKD) systems

Apart from DV-QKD, multiple QKD techniques have been suggested to incorporate crucial data into continuous variables, including the quantized electromagnetic field's quadrature component values.^454,455 The use of homodyne detectors alone for CV-QKD implementation, as opposed to specialized SPDs for DV-QKD, is a significant technical distinction. This functionality makes a second cryogenic system unnecessary and greatly streamlines the detection setup process. Consequently, chip-based coherence detection methods that have been employed in traditional high-bandwidth communication systems are compatible with CV QKD and naturally suited for photonic integration. In fact, the viability of a homodyne detector integrated onto a photonic chip for detecting quantum states and producing random numbers was demonstrated;⁴⁵⁶ a silicon photonic transceiver design that included all major CV-QKD components as well as entire subsystems was proposed.⁴⁵⁷ A reliable and compact system for CV-QKD was recently developed, combining all optical components aside from the laser source on a silicon photonic chip, which is compatible with the current fiber communication infrastructure (Fig. 22(a)).³⁸⁹ The system's ability to generate a secret key rate of 0.14 kbps over a simulated 100 km in fiber was demonstrated by the proof-of-principle analysis. By further refining the detecting module, chip-based CV-QKD systems can operate more efficiently. As an example, CMOS-compatible silicon and germanium on-silicon nano photonics were interfaced with silicon–germanium integrated amplifier circuits to create a high-speed homodyne detector (Fig. 22(b)).⁴⁵⁸ The detector requires only a 0.84 mm² compact footprint and has a 3.00-dB bandwidth of 1.70 GHz with a shot-noise limitation of 9.00 GHz.

Fig. 22 Integrated circuits with high-speed homodyne detection and continuous variable (CV) QKD. (a) A transmitter for signal modulation and multiplexing and a receiver for signal demultiplexing and homodyne detection comprise an integrated silicon photonic chip platform for CV-QKD,³⁸⁹ Copyright (2019), Springer Nature. (b) An integrated electronics-based silicon photonic homodyne detector interfaced for 9-GHz compressed light measurement,⁴⁵⁸ Copyright (2020), Springer Nature.

11.5. Quantum photonics with multiple modes

In numerous extensive quantum information protocols, multipartite states are applicable in both the DV and CV systems. The base of large alphabet quantum communication,⁴⁵⁹ advanced quantum simulation, multiparter secure quantum networks and quantum metrology is multimode optical coupling.^460,461 Interestingly, cluster states—a unique class of multipartite entangled states are crucial for on-the-spot optical quantum computing that takes advantage of measurement-based techniques. This method was first developed for DV quantum information encoding and has gradually been expanded to include the CV system.^462,463 However, in many cases, the quantum utilization depends on the ability to access a large number of modes whose entanglement properties can be precisely controlled and individually modified and evaluated.⁴⁷ Increasing the number of individuals can soon become a significant difficulty for the traditional bulk optics technique, because of the choice of entangled observations and patterns. The spatial mode, also known as the path observable, was one of the first degrees of freedom to be used and adjusted for the creation of multimode quantum systems. Two single-mode squeezed states on a tunable waveguide coupler with their relative phase electro-optically controlled can be mixed to produce two-mode path entanglement on chip at low dimension in CV regimes.⁴⁶⁴ When networks of optical couplers are used in structures, high-dimension path-entangled states can also be created. Various platforms integrated photonic systems are easily compatible with implementations of this concept. These systems allow for the integration of several optical couplers and phase controllers onto a single optical chip, utilizing a technique that has applications in quantum simulation, boson sampling, and QKD.^{157,446,465,466}

Integrated optics on Si has made it possible to develop a programmable large-scale quantum circuit which incorporates over 550 photonic components—including 16 identical photon pair sources based on spontaneous four-wave mixing (SFWM)—on a single chip (Fig. 23(a)).³⁸⁸ This approach generates a configurable multidimensional bipartite entangled state by superposing a photon pair created by SFWM over 16 optical modes. An array of asymmetric Mach–Zehnder interferometers (MZIs) divides the signal and idler, and a network of crossers routes the signal. This enables linear-optical circuits to manipulate the state locally. It is possible to achieve maximally entangled states by uniformly pumping the sources. Various optical platforms have been utilized to generate multipartite quantum states in both resonant and single-pass modes. With the interaction of cavity effects brought on by Fresnel reflections at the waveguide facets and the relative temporal delay between the two photons of each pair, SPDC in an AlGaAs waveguide has produced broadband biphoton frequency states with controllable symmetry (Fig. 23(b)).⁴⁶⁷ An integrated nonlinear micro ring resonator made of high-refractive-index silica glass (Hydex) and constantly pumped has been found to contain frequency-entangled qubits with the use of SFWM. According to Fig. 23(c), this configuration enables the creation of numerous, highly pure two-photon frequency entangled states, which are then used to experimentally demonstrate qubits of dimensions up to D = 4.⁴⁶⁸ Consequently broadening the Hilbert dimension spaces, an experiment employing entangled frequency audits sourced from silicon nitride (SiN) performed comprehensive tomographic analysis on entangled pairs of qubits with a dimensionality of D = 8.⁴⁶⁹ Recently, the quantum dynamics of soliton microcombs in an integrated SiC micro resonator has been investigated with second-order photon correlations. A persistent temporal lattice of solitons may separate a multimode below the threshold Gaussian state from any mixture of coherent light, according to experiments based on DV measurements.⁴⁷⁰ There has been a steady rise in the quantity of frequency and time modes carrying nonclassical information inside the CV regime. Two-partite intensity correlation in an above threshold SiN micro resonator was demonstrated by a first CV realization.⁹⁰ Further investigation demonstrated that quadrature squeezing occurs among light in two different frequency modes.^471,472

Fig. 23 Multipartite development of states on-chip. (a) High-path entangled state generation architecture: a large-scale integrated quantum photonic circuit based on silicon,³⁸⁸ Copyright (2018), The American Association for the Advancement of Science; (b) schematic diagram of the experimental configuration used to develop and modify biphoton frequency bands,⁴⁶⁷ Copyright (2020), Springer Nature; (c) experimental device for the production and control of high-dimensional quantum states,⁴⁷³ Copyright (2017), Springer Nature.

12. New development in quantum photonics and their future prospects

The demonstration of 20 simultaneous two-mode squeezed pairs at the output of a quantum microcomb produced from a silica micro resonator on a Si chip was made possible by these groundbreaking works. At telecommunication wavelengths, 40 CV quantum modes have been identified, spanning an optical bandwidth of 1 THz.⁴⁷⁴ We discuss here a wide range of well-known and cutting-edge quantum optics applications made possible by on-chip integration of quantum emitters, waveguides, and detectors. Using integrated quantum photonic technology, we also discuss opinions on prospective quantum technologies together with their benchmarks and targets.

12.1. Chip-based quantum communication

Governments and individuals both have high expectations regarding the exchange of safe information in an unconditional manner. From lab demonstrations to the implementation of commercially available systems connecting distant cities, quantum key distribution (QKD) with security essentially guaranteed by the principles of physics has progressed fast over the past few decades. Space-to-ground QKD has connected locations more than 1200 km apart, and intercontinental quantum communication across 7600 km has been achieved and demonstrated by the recently launched quantum satellite.^475,476 A QKD system typically consists of a signal-sending component for creating the necessary photon states and a signal-receiving component for detecting photon states. Lowering the size, cost, and energy consumption of both ends has been the goal of integration initiatives. The ideal “sender chip” would be an integrated light source with integrated polarization, phase, and power attenuators to efficiently generate specific photon states. The “receiver chip” would be an integrated light source with multiple single photon detectors, optical circuits, and control electronics to register the signal photons and decode the information.⁴¹⁵ In an evaluation of intercity metropolitan QKD, a silicon photonics encoder was used to achieve a quantum communication distance of 42 km.⁷⁶ More recently, a chip-based transmitter and receiver for continuous- variable QKD was realized through a demonstration utilizing silicon photonics.³⁸⁹ With wavelength-division de-multiplexing and waveguide-integrated superconducting nanowire single photon detectors, a four-channel silicon nitride-based integrated QKD receiver was demonstrated to reach a total secret-key rate of up to 12.17 Mbit per s at a 3.35 GHz clock rate.⁴⁷⁷ An integrated photonics platform has also been used to demonstrate chip-based quantum teleportation in addition to QKD.⁸⁸ Recently, to gain further insight into QKD protocols, implementation, security analysis, and attack threats, researchers have worked on it.^478,479Fig. 24 shows an overview of integrated QKD chips.

Fig. 24 Integrated QKD systems (a) nanowire single-photon detectors and MZI elements with an on-chip DBR laser used in integrated MDI-QKD,³⁹⁰ Copyright (2020), Optica Publishing Group; (b) SEM image of a QKD receiver chip with four channel time bins,⁴⁸⁰ Copyright (2022), Optica Publishing Group.

12.2. Meta-surface for circuits with integrated quantum optics

In recent years significant advancements and rise of interest have been observed in the field of meta-surfaces, which are characterized by periodic sub-wavelength metallic/dielectric structures that resonantly couple to the electric and magnetic fields of light-waves.⁴⁸¹ Meta-surfaces provide special ways to achieve non-traditional phenomena including electromagnetic cloaking, achromatic focusing, and negative refraction.⁴⁸² Beyond conventional optics, meta-surfaces have also found use in quantum optics, where single-photon sources, entangled photons, and single-photon sensing are essential components. Their application is limited by the drawback of random photon emission, which particularly makes it difficult to manipulate their spin states on demand. Integration of QDs with meta-surface results in on-demand creation and separation of the emitted single photons' spin states along any arbitrary designed direction.⁴⁸³

Additionally, a meta-surface with QDs can be used to provide Purcell enhancement.⁴⁸⁴ In the future, novel approaches for regulating single-photon emission, manipulating single-photon states, and enabling single-photon detection and imaging will become accessible when meta-surface and quantum optics components are combined on-chip.^93,485–487Fig. 25 shows examples of meta-surface integrated emitters and detectors.

Fig. 25 Integrating quantum emitters or quantum detectors with meta-surfaces. (a) Regulating the spin state on demand by manipulating QD emission through the use of meta-surfaces,⁴⁸³ Copyright (2020), The American Association for the Advancement of Science; (b) instance of Purcell improvement using a single quantum emitter interacting with a meta-surface,⁴⁸⁸ Copyright (2019), De Gruyter; (c) meta-surface array single-photon spectrometer with superconducting nanowire inserted between periodic holes,⁴⁸⁹ Copyright (2023), Optica Publishing Group; (d) computational spectrometer with a 4 × 4 superconducting nanowire array and a 3D-printed meta-surface assembly,⁴⁹⁰ Copyright (2022), American Chemical Society.

12.3. Quantum Lidar system integration

The term “Lidar” refers to light detection and ranging, a potent technology used for mapping forests on the surface of the planet, measuring sea fog in the ocean, and monitoring the environment.^491,492 In order to determine the distance or depth of distant targets, it detects reflected or scattered light. Beam splitters, transceivers, time-correlated single-photon counting circuits, pulse laser sources, and photodetectors are the typical components of a Lidar system. Single photon detectors can effectively increase the detection range, depth accuracy, and acquisition time of Lidar systems because, at larger measurement distances, only a small number of photons can return to the detection after tens of kilometers. With its high efficiency, low timing jitters, and dark count rates, superconducting nanowire single-photon detectors have been created in recent decades and increasingly been used in Lidar systems.^293,493,494 Effective mid-infrared detectors and photon number resolving detectors will soon propose Lidar systems with new detection windows and capabilities.^495,496 Furthermore, monolithic Lidar chips would make future Lidar applications more space-compatible and compact due to the advancement of high-power on-chip lasers, photonic integrated circuits, and detector technologies.⁴⁹⁷

12.4. Quantum walks

Quantum walks, in which quantum superposition plays a crucial role, are the quantum analogues of classical random walks, which were first explained in 1993.⁴⁹⁸ The ballistic transport element of the quantum walk occurs due to a quantum particle's unusual behavior, which allows them to simultaneously navigate in several directions in contrast to a classical particle. Discrete quantum walks and continuous quantum walks are the two standard types of quantum walks. There are several ways to conduct quantum walk experiments using the quantum characteristics of photons, such as the superposition, quantum interference, and entanglement. Fiber loops and bulk optics beam splitters perform early-stage quantum walk experiments in the temporal domain.⁹⁰ Integrated circuits, in contrast, provide greater phase stability, which raises the integration level even more.^75,499 A continuously connected waveguide array is shown in Fig. 26(a) to realize correlated photon quantum walks, while Fig. 26(b) demonstrates that femto-second laser-written waveguide arrays are used to build a quantum walk with a glued binary tree structure on photonic chips. According to this, thousands of continuous-time quantum walk evolutions are simulated in Fig. 26(c), an integrated photonic platform made up of controllable on-chip entangled photon pair sources and reconfigurable linear optical networks.⁵⁰⁰

Fig. 26 Schematic diagram of a quantum walk. (a) An experimental and simulation output pattern of 810 nm laser light propagating through the waveguide array; right: a continuously connected waveguide array for achieving correlated photon quantum walks with a 21-waveguide array,⁵⁰¹ Copyright (2010), The American Association for the Advancement of Science; (b) theoretical graphs of two-dimensional hexagonal structures for quantum fast-hitting; bottom: femtosecond laser-written waveguide arrays implemented a quantum walk with a glued binary tree structure on photonic chips,⁵⁰² Copyright (2023) De Gruyter; (c) silicon photonic quantum walk processor to perform graph-theoretic quantum computations, such as creating spatially entangled photons and putting into practice a universal five-dimensional unitary process,⁵⁰⁰ Copyright (2021), The American Association for the Advancement of Science.

13. Challenges and prospects

In this review we discuss quantum sensing and quantum communication which rely on the development of integrated quantum photonics. It not only provides a solid strategy for scaling and miniaturizing of quantum sensing and communication systems but also fosters practical applications of quantum sensing with communication and paves the way for future quantum communication networks and the quantum internet. The field of chip-based quantum technology is still in its early stages and naturally faces various hurdles, despite the significant progress that has been achieved so far. To ensure high accuracy and prevent decoherence of quantum states during preparation, manipulation, transmission, and detection, on-chip elements used in quantum communication require more rigid requirements than those used in classical optical sensing and communication. Therefore, it is essential to search for components which exhibit the right qualities. For instance, modulators that can run at high clock rates and still maintain a respectable extinction ratio for minimal crosstalk between distinct quantum states are needed for high-key-rate QKD. One of the main challenges is ensuring that the QKD devices operate in accordance with the mathematical models that are assumed in the security proofs; this issue is sometimes referred to as “implementation security.” Any variations between the QKD equipment's genuine operation and these models could render the security claims void and possibly create a security gap. The number of quantum hacking attacks that have been discussed over the last few decades shows how serious this issue is.⁵⁰³ Remarkably, the development of twin-field (TF) QKD and its most recent variation, measurement-device-independent (MDI) QKD, represented a breakthrough in this regard.⁵⁰⁴ These approaches eliminate any security gaps from the measuring unit, but they necessitate a flawless characterization of the QKD transmitter's operation. Although fully characterized a QKD transmitter remains an unsolved problem due to the intricacy of its numerous optical and electrical components.⁵⁰⁵ Since it is not required to characterize the internal workings of any device. Device-independent (DI) QKD can be considered the perfect solution to the implementation security challenge in this context.⁵⁰⁶

However, due to the introduction of non-ideal loss characteristics by carrier injection or carrier depletion procedures, this demand is not always satisfied by traditional Si based modulators. It is still not possible to realize fully integrated quantum networks with photonic circuitry, detectors, and photon sources. There are two important challenges in the way of achieving complete integration:

(a) One of the primary obstacles is that there is not a single platform that can offer every functionality needed for quantum communication applications. One practical way to solve this issue might be through hybrid integration. The method is still being refined, though, and more work is needed to reach the end result.⁷⁵

(b) The second obstacle is that various components of an integrated quantum system can function differently under certain circumstances. For instance, cryogenic temperatures are typically required for QD single-photon emitters and single-photon detectors in order to achieve optimal performance. On the other hand, these severe constraints are beyond the capabilities of standard integrated modulators and thermo-optic phase shifters, which are typically designed for room temperature applications. Cryogenic photon manipulation has thus emerged as a critical component of fully integrated systems.

Major obstacles to the realization of cryogenic-compatible systems have recently been removed with the demonstration of an integrated cryogenic Si-barium titanate modulator and micro electromechanical photonic circuits interfaced with SNSPDs on the same chip.⁷⁶ Moreover, integrating optics and electronics will be necessary to target very practical systems that have the potential to be developed industrially. In order to build whole systems on a chip for quantum communication, photonics and silicon nano electronics can be integrated, as exhibited recently.^37,507 Future chip-based QKD systems may find use in entanglement-based QKD in addition to prepare-and-measure QKD. This is now feasible due to the generation of time-bin entangled states in GaAs, Si, and Si₃N₄ chips, as well as the demonstration of quantum teleportation and the chip-to-chip entanglement distribution between two programmable Si chips.^76,508,509 Integrated photonics offer a practical means of realizing tiny entanglement-based systems that facilitate device-independent QKD over kilometer-scale distances, especially when combined with recent experimental advancements.⁵¹⁰

Integrated (quantum) photonics, the science and technology of producing, regulating, and detecting photons on a chip size, has proven beneficial to various businesses and society after decades of development. The rapid development of quantum integrated photonic technology is causing game-changing breakthroughs in other emerging application areas, such as quantum photonic computing, bio-photonics sensing, environmental monitoring, and disease diagnosis. Among these fields are telecommunications, where photonic integrated circuits (PICs) offer a viable solution to the high demands of bandwidth and security. Nowadays, the integration of photonics design and manufacturing has become increasingly prevalent in the electronics industry sector. By combining the advantages of both platforms, these hybrid chips are able to do complex tasks.^511,512Fig. 27 shows the optically pumped (green) and electrically driven (red) nanowire QDs on the hybrid photonic/electronic integrated circuit as single-photon sources.

Fig. 27 An example of a futuristic integrated photonic chip based on nanowire technology. Waveguide-integrated superconducting nanowire single-photon detectors are indicated by cyan wires, integrated control electronic circuits, such as cryo-CMOS or TDCs, are shown in black rectangles with multiple bonding pads, optical connections between various components are highlighted in pink lines, and electrical contacts are represented by orange squares. The sources of optically excited nanowire QDs are shown with green arrows, while the electrically pumped single-photon source is shown with red arrows,⁵⁰² Copyright (2023) De Gruyter.

Further on-chip components like phase shifters, can be used to adjust the photon states after emission.⁵¹³ A certain number of photons with carefully controlled initial states are then released into the linear interferometer to engage in various simulations or photonic quantum computing techniques. Integrated photonic circuits have the capability to produce, transfer, and receive a wide range of optical signals within their chip, as previously mentioned in the sections. Also, one of the most essential requirements for disease diagnosis and medication development is the ability to simultaneously detect and identify several biological objects for example single-virus, proteins, and single-molecules.^514–516 Developing such a multifunctional, highly sensitive platform at the chip level can be facilitated by integrated photonic circuits.

These systems’ sensitivity can also be increased to reach the quantum level by utilizing single-photon sources and detectors. The effective grating couplers enable the transmission of a broadband excitation light signal from free space to the chip. In order to obtain spectrum information using multi-pixel SNSPDs at the detecting ports, the transmitted or scattered photon signal passes through the meta-surface grating. Bio-sample identification or structure can be effectively obtained using accurate spectral information. These chips have enormous potential for use in biochemical and scientific laboratories, and once more, the essential components of the suggested systems are nanowire-based electronics.

Conclusions

Quantum integrated photonics has a lot of fascinating problems that still need to be solved in the future. Progress in the field can be advanced by further progressing the overviewed challenges, which include integrated quality management (QM), scalable quantum applications for creating and modifying high-dimensional photonic states, and self-consistent “prepare and measure QKD” systems with on-chip single-photon detection. Among numerous highly intriguing technologies aimed at enabling the investigation of the essential characteristics of quantum mechanics and the practical application of these phenomena are integrated photonics. While a lot of work has gone into understanding the many components required to conduct integrated experiments, not as much has been done to manage the interconnections between them to accomplish complete integration. Specifically, the implications of loss in quantum devices which are highly different from those in classical devices (bulk and optical fiber systems), up until now, received little attention, despite being the single biggest obstacle facing the field. In this review, we discuss the currently developed integrated photonic materials including 2D materials (e.g. graphene, etc.) and fundamental advancements for quantum photonic devices, in order to explore new avenues in the field of quantum integrated photonics that are needed. A change in perspective will surely be facilitated by connecting these conceptual disturbances with developments in computer science, particularly those related to artificial intelligence (AI) and sophisticated machine learning (ML) techniques. AI helps with the design and optimization of the circuits, while (quantum) integrated photonics offers a platform for creating increasingly potent and effective AI systems. This symbiotic relationship between AI and integrated photonics, with a particular focus on quantum circuits, is promising. By pushing the frontiers of quantum information processing and computation and facilitating the realization of quantum enhanced AI, such an alliance has the potential to spur significant advancements in both fields.^517,518

Author contributions

The manuscript was written through contributions from all authors. All authors have given approval to the final version of the manuscript.

Data availability

No primary research results, software or code have been included and no new data were generated or analysed as part of this review.

Conflicts of interest

The authors declare no conflicts of interest.

Acknowledgements

This work is part of the project SOFIA PID2023-147305OB-C32 funded by MICIU/AEI/10.13039/501100011033 and by FEDER/UE.

References

1. Y. Jung, H. Park, J.-A. Park, J. Noh, Y. Choi, M. Jung, K. Jung, M. Pyo, K. Chen, A. Javey and G. Cho, Sci. Rep., 2015, 5, 8105.
2. C. Wang, D. Hwang, Z. Yu, K. Takei, J. Park, T. Chen, B. Ma and A. Javey, Nat. Mater., 2013, 12, 899–904.
3. C. Choi, M. K. Choi, S. Liu, M. Kim, O. K. Park, C. Im, J. Kim, X. Qin, G. J. Lee and K. W. Cho, Nat. Commun., 2017, 8, 1664.
4. S. Chen, Z. Lou, D. Chen and G. Shen, Adv. Mater., 2018, 30, 1705400.
5. S. Jeon, S.-E. Ahn, I. Song, C. J. Kim, U.-I. Chung, E. Lee, I. Yoo, A. Nathan, S. Lee and K. Ghaffarzadeh, Nat. Mater., 2012, 11, 301–305.
6. S. Seo, S.-H. Jo, S. Kim, J. Shim, S. Oh, J.-H. Kim, K. Heo, J.-W. Choi, C. Choi and S. Oh, Nat. Commun., 2018, 9, 5106.
7. H. Han, H. Yu, H. Wei, J. Gong and W. Xu, Small, 2019, 15, 1900695.
8. S. Park, K. Fukuda, M. Wang, C. Lee, T. Yokota, H. Jin, H. Jinno, H. Kimura, P. Zalar and N. Matsuhisa, Adv. Mater., 2018, 30, 1802359.
9. T. Yokota, P. Zalar, M. Kaltenbrunner, H. Jinno, N. Matsuhisa, H. Kitanosako, Y. Tachibana, W. Yukita, M. Koizumi and T. Someya, Sci. Adv., 2016, 2, e1501856.
10. E. Chanrion, D. J. Niegemann, B. Bertrand, C. Spence, B. Jadot, J. Li, P.-A. Mortemousque, L. Hutin, R. Maurand, X. Jehl, M. Sanquer, S. De Franceschi, C. Bäuerle, F. Balestro, Y.-M. Niquet, M. Vinet, T. Meunier and M. Urdampilleta, Phys. Rev. Appl., 2020, 14, 024066.
11. M. Veldhorst, H. Eenink, C.-H. Yang and A. S. Dzurak, Nat. Commun., 2017, 8, 1766.
12. D. Kufer and G. Konstantatos, ACS Photonics, 2016, 3, 2197–2210.
13. J. S. Ponraj, Z.-Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi and K. Mccoubrey, Nanotechnology, 2016, 27, 462001.
14. G. Wang, A. Chernikov, M. M. Glazov, T. F. Heinz, X. Marie, T. Amand and B. Urbaszek, Rev. Mod. Phys., 2018, 90, 021001.
15. H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris and F. Xia, Nat. Photonics, 2013, 7, 394–399.
16. N. Rivera, T. Christensen and P. Narang, Nano Lett., 2019, 19, 2653–2660.
17. T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno and F. Koppens, Nat. Mater., 2017, 16, 182–194.
18. C. H. Bennett, F. Bessette, G. Brassard, L. Salvail and J. Smolin, J. Cryptol., 1992, 5, 3–28.
19. P. W. Shor and J. Preskill, Phys. Rev. Lett., 2000, 85, 441.
20. F. Xu, X. Ma, Q. Zhang, H.-K. Lo and J.-W. Pan, Rev. Mod. Phys., 2020, 92, 025002.
21. S. Wang, Z.-Q. Yin, D.-Y. He, W. Chen, R.-Q. Wang, P. Ye, Y. Zhou, G.-J. Fan-Yuan, F.-X. Wang and W. Chen, Nat. Photonics, 2022, 16, 154–161.
22. Y.-A. Chen, Q. Zhang, T.-Y. Chen, W.-Q. Cai, S.-K. Liao, J. Zhang, K. Chen, J. Yin, J.-G. Ren and Z. Chen, Nature, 2021, 589, 214–219.
23. W. Li, L. Zhang, H. Tan, Y. Lu, S.-K. Liao, J. Huang, H. Li, Z. Wang, H.-K. Mao and B. Yan, Nat. Photonics, 2023, 17, 416–421.
24. E. Diamanti, H.-K. Lo, B. Qi and Z. Yuan, Npj Quantum Inf., 2016, 2, 1–12.
25. L.-J. Wang, K.-Y. Zhang, J.-Y. Wang, J. Cheng, Y.-H. Yang, S.-B. Tang, D. Yan, Y.-L. Tang, Z. Liu and Y. Yu, Npj Quantum Inf., 2021, 7, 67.
26. A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble and E. S. Polzik, Science, 1998, 282, 706–709.
27. S. Wehner, D. Elkouss and R. Hanson, Science, 2018, 362, eaam9288.
28. G.-L. Long and X.-S. Liu, Phys. Rev. A:At., Mol., Opt. Phys., 2002, 65, 032302.
29. G.-L. Long, D. Pan, Y.-B. Sheng, Q. Xue, J. Lu and L. Hanzo, IEEE Network, 2022, 36, 82–88.
30. J. F. Barry, J. M. Schloss, E. Bauch, M. J. Turner, C. A. Hart, L. M. Pham and R. L. Walsworth, Rev. Mod. Phys., 2020, 92, 015004.
31. M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup and L. C. Hollenberg, Phys. Rep., 2013, 528, 1–45.
32. J. Wang, F. Sciarrino, A. Laing and M. G. Thompson, Nat. Photonics, 2020, 14, 273–284.
33. S. Fruncillo, X. Su, H. Liu and L. S. Wong, ACS Sens., 2021, 6, 2002–2024.
34. S. A. Iyengar, S. Bhattacharyya, S. Roy, N. R. Glavin, A. K. Roy and P. M. Ajayan, ACS Nano, 2023, 17, 12955–12970.
35. D. Khorsandi, J.-W. Yang, S. Jenson, T. Kajino, S. Maity, A. R. C. Salih, V. Jucaud and M. R. Dokmeci, in Lab-on-a-chip Devices for Advanced Biomedicines: Laboratory Scale Engineering to Clinical Ecosystem, ed. A. Parihar and P. Pradeep Mehta, Royal Society of Chemistry, 2024, vol. 25.
36. J. Ye and P. Zoller, Phys. Rev. Lett., 2024, 132, 190001.
37. R. Gupta, R. Singh, A. Gehlot, S. V. Akram, N. Yadav, R. Brajpuriya, A. Yadav, Y. Wu, H. Zheng and A. Biswas, Nanoscale, 2023, 15, 4682–4693.
38. C. L. Degen, F. Reinhard and P. Cappellaro, Rev. Mod. Phys., 2017, 89, 035002.
39. C. C. Gerry and J. Mimih, Contemp. Phys., 2010, 51, 497–511.
40. V. Cimini, E. Polino, F. Belliardo, F. Hoch, B. Piccirillo, N. Spagnolo, V. Giovannetti and F. Sciarrino, Npj Quantum Inf., 2023, 9, 20.
41. A. Z. Goldberg, A. B. Klimov, G. Leuchs and L. L. Sánchez-Soto, J. Phys.: Photonics, 2021, 3, 022008.
42. H. Ferretti, Y. Batuhan Yilmaz, K. Bonsma-Fisher, A. Z. Goldberg, N. Lupu-Gladstein, A. O. T. Pang, L. A. Rozema and A. M. Steinberg, Optica Quantum, 2024, 2, 91–102.
43. H. Ball, M. J. Biercuk, A. R. Carvalho, J. Chen, M. Hush, L. A. De Castro, L. Li, P. J. Liebermann, H. J. Slatyer and C. Edmunds, Quantum Sci. Technol., 2021, 6, 044011.
44. N. P. De Leon, K. M. Itoh, D. Kim, K. K. Mehta, T. E. Northup, H. Paik, B. Palmer, N. Samarth, S. Sangtawesin and D. W. Steuerman, Science, 2021, 372, eabb2823.
45. K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, S. Alperin-Lea, A. Anand, M. Degroote, H. Heimonen, J. S. Kottmann and T. Menke, Rev. Mod. Phys., 2022, 94, 015004.
46. F. Bova, A. Goldfarb and R. G. Melko, EPJ Quantum Technol., 2021, 8, 2.
47. C. Fabre and N. Treps, Rev. Mod. Phys., 2020, 92, 035005.
48. R. Demkowicz-Dobrzański and L. Maccone, Phys. Rev. Lett., 2014, 113, 250801.
49. H.-K. Lau and A. A. Clerk, Nat. Commun., 2018, 9, 4320.
50. Z. H. Saleem, M. Perlin, A. Shaji and S. K. Gray, Phys. Rev. A, 2024, 109, 052615.
51. R. Chaves, J. Brask, M. Markiewicz, J. Kołodyński and A. Acín, Phys. Rev. Lett., 2013, 111, 120401.
52. H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky and H. Vahlbruch, Phys. Rev. Lett., 2013, 110, 181101.
53. H. Y. Teh, A. W. Kempa-Liehr and K. I.-K. Wang, J. Big Data, 2020, 7, 11.
54. M. D. Vidrighin, G. Donati, M. G. Genoni, X.-M. Jin, W. S. Kolthammer, M. Kim, A. Datta, M. Barbieri and I. A. Walmsley, Nat. Commun., 2014, 5, 3532.
55. F. Albarelli, M. Barbieri, M. G. Genoni and I. Gianani, Phys. Lett. A, 2020, 384, 126311.
56. Y.-L. Zhang, H. Wang, L. Jing, L.-Z. Mu and H. Fan, Sci. Rep., 2014, 4, 7390.
57. D. A. Vajner, L. Rickert, T. Gao, K. Kaymazlar and T. Heindel, Adv. Quantum Technol., 2022, 5, 2100116.
58. M. D. Lang and C. M. Caves, Phys. Rev. A:At., Mol., Opt. Phys., 2014, 90, 025802.
59. J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M. Taylor, P. Cappellaro, L. Jiang, M. G. Dutt, E. Togan and A. Zibrov, Nature, 2008, 455, 644–647.
60. L. Rondin, J.-P. Tetienne, T. Hingant, J.-F. Roch, P. Maletinsky and V. Jacques, Rep. Prog. Phys., 2014, 77, 056503.
61. G. Balasubramanian, A. Lazariev, S. R. Arumugam and D.-W. Duan, Curr. Opin. Chem. Biol., 2014, 20, 69–77.
62. G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck and J. Tissler, Nat. Mater., 2009, 8, 383–387.
63. T. Zhang, G. Pramanik, K. Zhang, M. Gulka, L. Wang, J. Jing, F. Xu, Z. Li, Q. Wei and P. Cigler, ACS Sens., 2021, 6, 2077–2107.
64. E. Oh, M. D. Gregoire, A. T. Black, K. Jeramy Hughes, P. D. Kunz, M. Larsen, J. Lautier-Gaud, J. Lee, P. D. D. Schwindt, S. L. Mouradian, F. A. Narducci and C. A. Sackett, AIAA J., 2024, 62, pp. 4029–4053.
65. S. Y. Siew, B. Li, F. Gao, H. Y. Zheng, W. Zhang, P. Guo, S. W. Xie, A. Song, B. Dong and L. W. Luo, J. Light Technol., 2021, 39, 4374–4389.
66. M. Smit, K. Williams and J. Van Der Tol, Appl. Photonics, 2019, 4.
67. J. Wu, H. Ma, P. Yin, Y. Ge, Y. Zhang, L. Li, H. Zhang and H. Lin, Small Sci., 2021, 1, 2000053.
68. M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu and X. Cai, Nat. Photonics, 2019, 13, 359–364.
69. K. Li, D. J. Thomson, S. Liu, W. Zhang, W. Cao, C. G. Littlejohns, X. Yan, M. Ebert, M. Banakar and D. Tran, Nat. Electron., 2023, 6, 910–921.
70. C. Joshi, A. Farsi, S. Clemmen, S. Ramelow and A. L. Gaeta, Nat. Commun., 2018, 9, 847.
71. W. H. Pernice, C. Schuck, O. Minaeva, M. Li, G. Goltsman, A. Sergienko and H. Tang, Nat. Commun., 2012, 3, 1325.
72. D. Llewellyn, Y. Ding, I. I. Faruque, S. Paesani, D. Bacco, R. Santagati, Y.-J. Qian, Y. Li, Y.-F. Xiao and M. Huber, Nat. Phys., 2020, 16, 148–153.
73. S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. DeMicheli, D. B. Ostrowsky and N. Gisin, Eur. Phys. J. D, 2002, 18, 155–160.
74. H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. Fejer, K. Inoue and Y. Yamamoto, New J. Phys., 2005, 7, 232.
75. A. W. Elshaari, W. Pernice, K. Srinivasan, O. Benson and V. Zwiller, Nat. Photonics, 2020, 14, 285–298.
76. W. Luo, L. Cao, Y. Shi, L. Wan, H. Zhang, S. Li, G. Chen, Y. Li, S. Li and Y. Wang, Light:Sci. Appl., 2023, 12, 175.
77. T. K. Paraïso, R. I. Woodward, D. G. Marangon, V. Lovic, Z. Yuan and A. J. Shields, Adv. Quantum Technol., 2021, 4, 2100062.
78. C. Agnesi, B. Da Lio, D. Cozzolino, L. Cardi, B. B. Bakir, K. Hassan, A. Della Frera, A. Ruggeri, A. Giudice and G. Vallone, Opt. Lett., 2019, 44, 271–274.
79. R. Wang, X.-G. Ren, Z. Yan, L.-J. Jiang, W. E. Sha and G.-C. Shan, Front. Phys., 2019, 14, 1–20.
80. A. Autere, H. Jussila, Y. Dai, Y. Wang, H. Lipsanen and Z. Sun, Adv. Mater., 2018, 30, 1705963.
81. T. Dutta, N. Yadav, Y. Wu, G. J. Cheng, X. Liang, S. Ramakrishna, A. Sbai, R. Gupta, A. Mondal, Z. Hongyu and A. Yadav, Nano Mater. Sci., 2024, 6, 1–23.
82. C. Jiao, S. Pei, S. Wu, Z. Wang and J. Xia, Rep. Prog. Phys., 2023, 86, 114503.
83. Q. Ma, G. Ren, A. Mitchell and J. Z. Ou, Nanophotonics, 2020, 9, 2191–2214.
84. N. Lo Piparo, M. Razavi and W. J. Munro, Phys. Rev. A, 2017, 95, 022338.
85. J. Happacher, J. Bocquel, H. T. Dinani, M. A. Tschudin, P. Reiser, D. A. Broadway, J. R. Maze and P. Maletinsky, Phys. Rev. Lett., 2023, 131, 086904.
86. J. Benedikter, H. Kaupp, T. Hümmer, Y. Liang, A. Bommer, C. Becher, A. Krueger, J. M. Smith, T. W. Hänsch and D. Hunger, Phys. Rev. Appl., 2017, 7, 024031.
87. F. Lenzini, N. Gruhler, N. Walter and W. H. Pernice, Adv. Quantum Technol., 2018, 1, 1800061.
88. E. Pelucchi, G. Fagas, I. Aharonovich, D. Englund, E. Figueroa, Q. Gong, H. Hannes, J. Liu, C.-Y. Lu and N. Matsuda, Nat. Rev. Phys., 2022, 4, 194–208.
89. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman and M. S. Strano, Nat. Nanotechnol., 2012, 7, 699–712.
90. L. Labonté, O. Alibart, V. D’Auria, F. Doutre, J. Etesse, G. Sauder, A. Martin, É. Picholle and S. Tanzilli, PRX Quantum, 2024, 5, 010101.
91. R. Degl’Innocenti, S. J. Kindness, H. E. Beere and D. A. Ritchie, Nanophotonics, 2018, 7, 127–144.
92. Y. Wang, K. D. Jöns and Z. Sun, Appl. Phys. Rev., 2021, 8.
93. M. Esmann, S. C. Wein and C. Antón-Solanas, Adv. Funct. Mater., 2024, 2315936.
94. Y. Arakawa and M. J. Holmes, Appl. Phys. Rev., 2020, 7.
95. A. H. Proppe, K. L. K. Lee, A. E. Kaplan, M. Ginterseder, C. J. Krajewska and M. G. Bawendi, Phys. Rev. Lett., 2023, 131, 053603.
96. P. Roy and A. Pandey, J. Chem. Phys., 2024, 160.
97. G. Sinatkas, T. Christopoulos, O. Tsilipakos and E. E. Kriezis, J. Appl. Phys., 2021, 130.
98. T. Xu, Y. Dong, Q. Zhong, S. Zheng, Y. Qiu, X. Zhao, L. Jia, C. Lee and T. Hu, Nanophotonics, 2023, 12, 3683–3706.
99. B. H. Siahkal-Mahalle and K. Abedi, Sci. Rep., 2024, 14, 11900.
100. M. Thomaschewski and S. Bozhevolnyi, Appl. Phys. Rev., 2022, 9.
101. M. W. Puckett, K. Liu, N. Chauhan, Q. Zhao, N. Jin, H. Cheng, J. Wu, R. O. Behunin, P. T. Rakich and K. D. Nelson, Nat. Commun., 2021, 12, 934.
102. A. J. Talib and H. A. Yasser, Optik, 2023, 284, 170940.
103. T. H. Kim, Y. K. Choi, G. M. Lee, M. A. Saeed, B. K. Jung, M. J. Lee, H. J. Choi, S. J. Oh and J. W. Shim, Adv. Mater., 2024, 36, 2309028.
104. M. Benyoucef, Photonic Quantum Technologies: Science and Applications, John Wiley & Sons, 2023.
105. C. Silberhorn, Contemp. Phys., 2007, 48, 143–156.
106. Y. Zhao, M. Gobbi, L. E. Hueso and P. Samorì, Chem. Rev., 2021, 122, 50–131.
107. K. Zhu, C. Wen, A. A. Aljarb, F. Xue, X. Xu, V. Tung, X. Zhang, H. N. Alshareef and M. Lanza, Nat. Electron., 2021, 4, 775–785.
108. S. Middelhoek, Sens. Actuators, A, 1994, 41, 1–8.
109. P. A. Passeraub, P.-A. Besse, A. Bayadroun, S. Hediger, E. Bernasconi and R. Popovic, Sens. Actuators, A, 1999, 76, 273–278.
110. S. Kawahito, C. Maier, M. Schneiher, M. Zimmermann and H. Baltes, IEEE, J. Solid State Circ., 1999, 34, 1843–1851.
111. R. S. Vanha, F. Kroener, T. Olbrich, R. Baresch and H. Baltes, J. Microelectromech. Syst., 2000, 9, 82–87.
112. K.-L. Chau, S. Lewis, Y. Zhao, R. Howe, S. Bart and R. Marcheselli, Sens. Actuators, A, 1996, 54, 472–476.
113. D. Sparks, X. Huang, W. Higdon and J. Johnson, Microsyst. Technol., 1998, 4, 139–142.
114. D. S. Eddy and D. R. Sparks, Proc. IEEE, 1998, 86, 1747–1755.
115. A. Triantafyllou, P. Sarigiannidis and T. D. Lagkas, Wirel. Commun. Mob. Comput., 2018, 5349894.
116. G. Chen, N. Li, J. D. Ng, H.-L. Lin, Y. Zhou, Y. H. Fu, L. Y. T. Lee, Y. Yu, A.-Q. Liu and A. J. J. A. P. Danner, Adv. Photonics, 2022, 4, 034003.
117. Y. Jia, L. Wang and F. Chen, Appl. Phys. Rev., 2021, 8.
118. O. Alibart, V. D’Auria, M. D. Micheli, F. Doutre, F. Kaiser, L. Labonté, T. Lunghi, É. Picholle and S. Tanzilli, J. Opt., 2016, 18, 104001.
119. R. Kruse, L. Sansoni, S. Brauner, R. Ricken, C. S. Hamilton, I. Jex and C. Silberhorn, Phys. Rev. A:At., Mol., Opt. Phys., 2015, 92, 053841.
120. J. Lin, F. Bo, Y. Cheng and J. Xu, Photon. Res., 2020, 8, 1910–1936.
121. C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer and M. Lončar, Nature, 2018, 562, 101–104.
122. E. Lomonte, M. A. Wolff, F. Beutel, S. Ferrari, C. Schuck, W. H. P. Pernice and F. Lenzini, Nat. Commun., 2021, 12, 6847.
123. A. A. Sayem, R. Cheng, S. Wang and H. X. Tang, Appl. Phys. Lett., 2020, 116.
124. Z. Xie, F. Bo, J. Lin, H. Hu, X. Cai, X.-H. Tian, Z. Fang, J. Chen, M. Wang, F. Chen, Y. Cheng, J. Xu and S. Zhu, Adv. Phys.:X, 2024, 9, 2322739.
125. J. K. Poon, A. Govdeli, A. Sharma, X. Mu, F.-D. Chen, T. Xue and T. Liu, Adv. Opt. Photonics, 2024, 16, 1–59.
126. X. Wang and J. Liu, J. Semicond., 2018, 39, 061001.
127. I. A. Fischer, M. Brehm, M. De Seta, G. Isella, D. J. Paul, M. Virgilio and G. Capellini, APL Photonics, 2022, 7.
128. J. C. Adcock, J. Bao, Y. Chi, X. Chen, D. Bacco, Q. Gong, L. K. Oxenløwe, J. Wang and Y. Ding, IEEE J. Sel. Top. Quantum Electron., 2021, 27, 1–24.
129. C. M. Gentry, J. M. Shainline, M. T. Wade, M. J. Stevens, S. D. Dyer, X. Zeng, F. Pavanello, T. Gerrits, S. W. Nam, R. P. Mirin and M. A. Popović, Optica, 2015, 2, 1065–1071.
130. J. W. Silverstone, R. Santagati, D. Bonneau, M. J. Strain, M. Sorel, J. L. O’Brien and M. G. Thompson, Nat. Commun., 2015, 6, 7948.
131. J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien and A. Laing, Sci. Adv., 2015, 349, 711–716.
132. S. Castelletto, A. Peruzzo, C. Bonato, B. C. Johnson, M. Radulaski, H. Ou, F. Kaiser and J. Wrachtrup, ACS Photonics, 2022, 9, 1434–1457.
133. W. Redjem, A. Durand, T. Herzig, A. Benali, S. Pezzagna, J. Meijer, A. Y. Kuznetsov, H. S. Nguyen, S. Cueff, J. M. Gérard, I. Robert-Philip, B. Gil, D. Caliste, P. Pochet, M. Abbarchi, V. Jacques, A. Dréau and G. Cassabois, Nat. Electron., 2020, 3, 738–743.
134. D. M. Lukin, M. A. Guidry and J. Vučković, PRX Quantum, 2020, 1, 020102.
135. C. Babin, R. Stöhr, N. Morioka, T. Linkewitz, T. Steidl, R. Wörnle, D. Liu, E. Hesselmeier, V. Vorobyov, A. Denisenko, M. Hentschel, C. Gobert, P. Berwian, G. V. Astakhov, W. Knolle, S. Majety, P. Saha, M. Radulaski, N. T. Son, J. Ul-Hassan, F. Kaiser and J. Wrachtrup, Nat. Mater., 2022, 21, 67–73.
136. R. Stricker, M. Meth, L. Postler, C. Edmunds, C. Ferrie, R. Blatt, P. Schindler, T. Monz, R. Kueng and M. Ringbauer, PRX Quantum, 2022, 3, 040310.
137. O. L. Hebnes, M. E. Bathen, Ø. S. Schøyen, S. G. Winther-Larsen, L. Vines and M. Hjorth-Jensen, npj Comput. Mater., 2022, 8, 207.
138. Y. Katoh, A. Kohyama, T. Nozawa and M. Sato, J. Nucl. Mater., 2004, 329, 587–591.
139. R. Vaßen, A. Kaiser, J. Förster, H. Buchkremer and D. Stöver, J. Mater. Sci., 1996, 31, 3623–3637.
140. M. Radulaski, T. M. Babinec, K. Müller, K. G. Lagoudakis, J. L. Zhang, S. Buckley, Y. A. Kelaita, K. Alassaad, G. Ferro and J. Vuckovic, ACS Photonics, 2015, 2, 14–19.
141. M. Radulaski, J. L. Zhang, Y. K. Tzeng, K. G. Lagoudakis, H. Ishiwata, C. Dory, K. A. Fischer, Y. A. Kelaita, S. Sun and P. C. Maurer, Laser Photonics Rev., 2019, 13, 1800316.
142. N. Xu, Z.-D. Cheng, J.-D. Tang, X.-M. Lv, T. Li, M.-L. Guo, Y. Wang, H.-Z. Song, Q. Zhou and G.-W. Deng, Nanophotonics, 2021, 10, 2265–2281.
143. B. J. Eggleton, C. G. Poulton, P. T. Rakich, M. J. Steel and G. Bahl, Nat. Photonics, 2019, 13, 664–677.
144. T. Heindel, J.-H. Kim, N. Gregersen, A. Rastelli and S. Reitzenstein, Adv. Opt. Photonics, 2023, 15, 613–738.
145. H. A. Nguyen, G. Dixon, F. Y. Dou, S. Gallagher, S. Gibbs, D. M. Ladd, E. Marino, J. C. Ondry, J. P. Shanahan, E. S. Vasileiadou, S. Barlow, D. R. Gamelin, D. S. Ginger, D. M. Jonas, M. G. Kanatzidis, S. R. Marder, D. Morton, C. B. Murray, J. S. Owen, D. V. Talapin, M. F. Toney and B. M. Cossairt, Chem. Rev., 2023, 123, 7890–7952.
146. C. Becher, W. Gao, S. Kar, C. D. Marciniak, T. Monz, J. G. Bartholomew, P. Goldner, H. Loh, E. Marcellina, K. E. J. Goh, T. S. Koh, B. Weber, Z. Mu, J.-Y. Tsai, Q. Yan, T. Huber-Loyola, S. Höfling, S. Gyger, S. Steinhauer and V. Zwiller, Mater. Quantum Technol., 2023, 3, 012501.
147. Z.-H. Xiang, J. Huwer, J. Skiba-Szymanska, R. M. Stevenson, D. J. P. Ellis, I. Farrer, M. B. Ward, D. A. Ritchie and A. J. Shields, Commun. Phys., 2020, 3, 121.
148. N. Tomm, A. Javadi, N. O. Antoniadis, D. Najer, M. C. Löbl, A. R. Korsch, R. Schott, S. R. Valentin, A. D. Wieck, A. Ludwig and R. J. Warburton, Nat. Nanotechnol., 2021, 16, 399–403.
149. M. Pont, R. Albiero, S. E. Thomas, N. Spagnolo, F. Ceccarelli, G. Corrielli, A. Brieussel, N. Somaschi, H. Huet, A. Harouri, A. Lemaître, I. Sagnes, N. Belabas, F. Sciarrino, R. Osellame, P. Senellart and A. Crespi, Phys. Rev. X, 2022, 12, 031033.
150. M. Gould, S. Chakravarthi, I. R. Christen, N. Thomas, S. Dadgostar, Y. Song, M. L. Lee, F. Hatami and K.-M. C. Fu, J. Opt. Soc. Am. B, 2016, 33, B35–B42.
151. A. Logan, University of Washington, 2023.
152. J. Wang, A. Santamato, P. Jiang, D. Bonneau, E. Engin, J. W. Silverstone, M. Lermer, J. Beetz, M. Kamp and S. Höfling, Opt. Commun., 2014, 327, 49–55.
153. G. Reithmaier, M. Kaniber, F. Flassig, S. Lichtmannecker, K. Müller, A. Andrejew, J. Vuckovic, R. Gross and J. Finley, Nano Lett., 2015, 15, 5208–5213.
154. A. Orieux, M. A. Versteegh, K. D. Jöns and S. Ducci, Rep. Prog. Phys., 2017, 80, 076001.
155. F. Boitier, A. Orieux, C. Autebert, A. Lemaître, E. Galopin, C. Manquest, C. Sirtori, I. Favero, G. Leo and S. Ducci, Phys. Rev. Lett., 2014, 112, 183901.
156. X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng and H. X. Tang, Light:Sci. Appl., 2017, 6, e16249.
157. D. Brod, E. Galvão, A. Crespi, R. Osellame, N. Spagnolo and F. Sciarrino, Adv. Photonics, 2019, 1, 034001.
158. M. Kremer, L. J. Maczewsky, M. Heinrich and A. Szameit, Opt. Mater. Express, 2021, 11, 1014–1036.
159. L. Liebermeister, F. Petersen, A. V. Münchow, D. Burchardt, J. Hermelbracht, T. Tashima, A. W. Schell, O. Benson, T. Meinhardt, A. Krueger, A. Stiebeiner, A. Rauschenbeutel, H. Weinfurter and M. Weber, Appl. Phys. Lett., 2014, 104.
160. T. Schröder, M. Fujiwara, T. Noda, H.-Q. Zhao, O. Benson and S. Takeuchi, Opt. Express, 2012, 20, 10490–10497.
161. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu and J. L. O’brien, Science, 2008, 320, 646–649.
162. J. J. Baumberg, J. Aizpurua, M. H. Mikkelsen and D. R. Smith, Nat. Mater., 2019, 18, 668–678.
163. K. A. Guerrero-Becerra, A. Tomadin and M. Polini, Phys. Rev. B, 2019, 100, 125434.
164. I. Epstein, B. Terrés, A. J. Chaves, V.-V. Pusapati, D. A. Rhodes, B. Frank, V. Zimmermann, Y. Qin, K. Watanabe and T. Taniguchi, Nano Lett., 2020, 20, 3545–3552.
165. G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe and P. Kim, Phys. Rev. Lett., 2018, 120, 037402.
166. A. Ryou, D. Rosser, A. Saxena, T. Fryett and A. Majumdar, Phys. Rev. B, 2018, 97, 235307.
167. P. Gonçalves, T. Christensen, N. Rivera, A.-P. Jauho, N. A. Mortensen and M. Soljačić, Nat. Commun., 2020, 11, 366.
168. J. D. Cox and F. J. Garcia de Abajo, Nano Lett., 2019, 19, 3743–3750.
169. J. D. Cox, I. Silveiro and F. J. García de Abajo, ACS Nano, 2016, 10, 1995–2003.
170. S. Huang, T. Ming, Y. Lin, X. Ling, Q. Ruan, T. Palacios, J. Wang, M. Dresselhaus and J. Kong, Small, 2016, 12, 5190–5199.
171. A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti and D. R. Smith, Nature, 2012, 492, 86–89.
172. R. Chikkaraddy, X. Zheng, F. Benz, L. J. Brooks, B. De Nijs, C. Carnegie, M.-E. Kleemann, J. Mertens, R. W. Bowman and G. A. Vandenbosch, ACS Photonics, 2017, 4, 469–475.
173. T. B. Hoang, G. M. Akselrod, C. Argyropoulos, J. Huang, D. R. Smith and M. H. Mikkelsen, Nat. Commun., 2015, 6, 7788.
174. N.-N. Feng, M. L. Brongersma and L. Dal Negro, IEEE J. Quantum Electron., 2007, 43, 479–485.
175. T. V. Teperik, P. Nordlander, J. Aizpurua and A. G. Borisov, Phys. Rev. Lett., 2013, 110, 263901.
176. M.-E. Kleemann, R. Chikkaraddy, E. M. Alexeev, D. Kos, C. Carnegie, W. Deacon, A. C. de Pury, C. Große, B. de Nijs and J. Mertens, Nat. Commun., 2017, 8, 1296.
177. D. Alcaraz Iranzo, S. Nanot, E. J. Dias, I. Epstein, C. Peng, D. K. Efetov, M. B. Lundeberg, R. Parret, J. Osmond and J.-Y. Hong, Science, 2018, 360, 291–295.
178. A. Reserbat-Plantey, I. Epstein, I. Torre, A. T. Costa, P. Gonçalves, N. A. Mortensen, M. Polini, J. C. Song, N. M. Peres and F. H. Koppens, ACS Photonics, 2021, 8, 85–101.
179. A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale and M. Polini, Nat. Mater., 2015, 14, 421–425.
180. I. Epstein, D. Alcaraz, Z. Huang, V.-V. Pusapati, J.-P. Hugonin, A. Kumar, X. M. Deputy, T. Khodkov, T. G. Rappoport and J.-Y. Hong, Science, 2020, 368, 1219–1223.
181. M. B. Lundeberg, Y. Gao, A. Woessner, C. Tan, P. Alonso-González, K. Watanabe, T. Taniguchi, J. Hone, R. Hillenbrand and F. H. Koppens, Nat. Mater., 2017, 16, 204–207.
182. A. Woessner, Y. Gao, I. Torre, M. B. Lundeberg, C. Tan, K. Watanabe, T. Taniguchi, R. Hillenbrand, J. Hone and M. Polini, Nat. Photonics, 2017, 11, 421–424.
183. S. de Vega and F. J. Garcia de Abajo, ACS Photonics, 2017, 4, 2367–2375.
184. V. Karanikolas, S. Suzuki, S. Li and T. Iwasaki, Appl. Phys. Lett., 2022, 120.
185. L. Huang, A. Krasnok, A. Alú, Y. Yu, D. Neshev and A. E. Miroshnichenko, Rep. Prog. Phys., 2022, 85, 046401.
186. P. Gonçalves, N. Stenger, J. D. Cox, N. A. Mortensen and S. Xiao, Adv. Opt. Mater., 2020, 8, 1901473.
187. G. Gómez-Santos and T. Stauber, Phys. Rev. B:Condens. Matter Mater. Phys., 2011, 84, 165438.
188. C. A. Muschik, S. Moulieras, A. Bachtold, F. H. Koppens, M. Lewenstein and D. E. Chang, Phys. Rev. Lett., 2014, 112, 223601.
189. F. Federspiel, G. Froehlicher, M. Nasilowski, S. Pedetti, A. Mahmood, B. Doudin, S. Park, J.-O. Lee, D. Halley and B. Dubertret, Nano Lett., 2015, 15, 1252–1258.
190. M. Silva Neto, D. Szilard, F. Rosa, C. Farina and F. Pinheiro, Phys. Rev. B, 2017, 96, 235143.
191. V. D. Karanikolas, C. A. Marocico, P. R. Eastham and A. L. Bradley, Phys. Rev. B, 2016, 94, 195418.
192. G. Mazzamuto, A. Tabani, S. Pazzagli, S. Rizvi, A. Reserbat-Plantey, K. Schädler, G. Navickaite, L. Gaudreau, F. S. Cataliotti and F. Koppens, New J. Phys., 2014, 16, 113007.
193. K. G. Schadler, C. Ciancico, S. Pazzagli, P. Lombardi, A. Bachtold, C. Toninelli, A. Reserbat-Plantey and F. H. Koppens, Nano Lett., 2019, 19, 3789–3795.
194. A. Reserbat-Plantey, K. G. Schädler, L. Gaudreau, G. Navickaite, J. Güttinger, D. Chang, C. Toninelli, A. Bachtold and F. H. Koppens, Nat. Commun., 2016, 7, 10218.
195. D. Cano, A. Ferrier, K. Soundarapandian, A. Reserbat-Plantey, M. Scarafagio, A. Tallaire, A. Seyeux, P. Marcus, H. D. Riedmatten, P. Goldner, F. H. L. Koppens and K.-J. Tielrooij, Nat. Commun., 2020, 11, 4094.
196. Y.-X. Zhang, Y. Zhang and K. Mølmer, ACS Photonics, 2019, 6, 871–877.
197. J.-P. Tetienne, N. Dontschuk, D. A. Broadway, A. Stacey, D. A. Simpson and L. C. L. Hollenberg, Sci. Adv., 2017, 3, e1602429.
198. T. I. Andersen, B. L. Dwyer, J. D. Sanchez-Yamagishi, J. F. Rodriguez-Nieva, K. Agarwal, K. Watanabe, T. Taniguchi, E. A. Demler, P. Kim, H. Park and M. D. Lukin, Science, 2019, 364, 154–157.
199. J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff and M. Fischer, Nat. Nanotechnol., 2012, 7, 69.
200. J. Olthaus, P. P. Schrinner, D. E. Reiter and C. Schuck, Adv. Quantum Technol., 2020, 3, 1900084.
201. Y. Chen, A. Ryou, M. R. Friedfeld, T. Fryett, J. Whitehead, B. M. Cossairt and A. Majumdar, Nano Lett., 2018, 18, 6404–6410.
202. T. T. Tran, M. Kianinia, M. Nguyen, S. Kim, Z.-Q. Xu, A. Kubanek, M. Toth and I. Aharonovich, ACS Photonics, 2018, 5, 295–300.
203. J. Kern, I. Niehues, P. Tonndorf, R. Schmidt, D. Wigger, R. Schneider, T. Stiehm, S. Michaelis de Vasconcellos, D. E. Reiter and T. Kuhn, Adv. Mater., 2016, 28, 7101–7105.
204. A. M. Roslawska, Dynamics of nanoscale systems probed by time-resolved STM-induced luminescence, EPFL, 2019.
205. B. Schuler, K. A. Cochrane, C. Kastl, E. S. Barnard, E. Wong, N. J. Borys, A. M. Schwartzberg, D. F. Ogletree, F. J. G. de Abajo and A. Weber-Bargioni, Sci. Adv., 2020, 6, eabb5988.
206. H. Yu, G.-B. Liu, J. Tang, X. Xu and W. Yao, Sci. Adv., 2017, 3, e1701696.
207. P. Rivera, J. R. Schaibley, A. M. Jones, J. S. Ross, S. Wu, G. Aivazian, P. Klement, K. Seyler, G. Clark and N. J. Ghimire, Nat. Commun., 2015, 6, 6242.
208. E. M. Alexeev, D. A. Ruiz-Tijerina, M. Danovich, M. J. Hamer, D. J. Terry, P. K. Nayak, S. Ahn, S. Pak, J. Lee and J. I. Sohn, Nature, 2019, 567, 81–86.
209. K. L. Seyler, P. Rivera, H. Yu, N. P. Wilson, E. L. Ray, D. G. Mandrus, J. Yan, W. Yao and X. Xu, Nature, 2019, 567, 66–70.
210. H. Baek, M. Brotons-Gisbert, Z. X. Koong, A. Campbell, M. Rambach, K. Watanabe, T. Taniguchi and B. D. Gerardot, Sci. Adv., 2020, 6, eaba8526.
211. A. Delhomme, D. Vaclavkova, A. Slobodeniuk, M. Orlita, M. Potemski, D. Basko, K. Watanabe, T. Taniguchi, D. Mauro and C. Barreteau, 2D Mater., 2020, 7, 041002.
212. J. Sung, Y. Zhou, G. Scuri, V. Zólyomi, T. I. Andersen, H. Yoo, D. S. Wild, A. Y. Joe, R. J. Gelly and H. Heo, Nat. Nanotechnol., 2020, 15, 750–754.
213. J. D. Cox and F. J. Garcia de Abajo, Acc. Chem. Res., 2019, 52, 2536–2547.
214. W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua and K. B. Crozier, Nat. Commun., 2016, 7, 1–14.
215. L. Gaudreau, K.-J. Tielrooij, G. Prawiroatmodjo, J. Osmond, F. G. De Abajo and F. H. Koppens, Nano Lett., 2013, 13, 2030–2035.
216. J. Klein, L. Sigl, S. Gyger, K. Barthelmi, M. Florian, S. Rey, T. Taniguchi, K. Watanabe, F. Jahnke, C. Kastl, V. Zwiller, K. D. Jöns, K. Müller, U. Wurstbauer, J. J. Finley and A. W. Holleitner, ACS Photonics, 2021, 8, 669–677.
217. M. B. Lundeberg, Y. Gao, R. Asgari, C. Tan, B. Van Duppen, M. Autore, P. Alonso-González, A. Woessner, K. Watanabe and T. Taniguchi, Science, 2017, 357, 187–191.
218. P. A. Gonçalves, T. Christensen, N. Peres, A.-P. Jauho, I. Epstein, F. Koppens, M. Soljačić and N. Mortensen, Nat. Commun., 2021, 12.
219. A. Principi, E. Van Loon, M. Polini and M. I. Katsnelson, Phys. Rev. B, 2018, 98, 035427.
220. M. Baldovin, A. Browaeys, J. M. De Teresa, C. Draxl, F. Druon, G. Gradenigo, J.-J. Greffet, F. Lépine, J. Lüning and L. Reining, EPS Grand Challenges: Physics for Society in the Horizon 2050, IOP Publishing, 2024.
221. H.-K. Tang, J. Leaw, J. Rodrigues, I. Herbut, P. Sengupta, F. Assaad and S. Adam, Science, 2018, 361, 570–574.
222. A. R. Echarri, J. D. Cox and F. J. G. De Abajo, Optica, 2019, 6, 630–641.
223. E. J. Dias, D. A. Iranzo, P. Gonçalves, Y. Hajati, Y. V. Bludov, A.-P. Jauho, N. A. Mortensen, F. H. Koppens and N. Peres, Phys. Rev. B, 2018, 97, 245405.
224. P. J. Feibelman, Prog. Surf. Sci., 1982, 12, 287–407.
225. P. Gonçalves, T. Christensen, N. M. Peres, A.-P. Jauho, I. Epstein, F. H. Koppens, M. Soljačić and N. A. Mortensen, Nat. Commun., 2021, 12, 3271.
226. B. Persson and P. Apell, Phys. Rev. B:Condens. Matter Mater. Phys., 1983, 27, 6058.
227. H. Polshyn, M. Yankowitz, S. Chen, Y. Zhang, K. Watanabe, T. Taniguchi, C. R. Dean and A. F. Young, Nat. Phys., 2019, 15, 1011–1016.
228. F. Haldane, Phys. Rev. Lett., 2011, 107, 116801.
229. K. Yang, Phys. Rev. B, 2016, 93, 161302.
230. M. Dyakonov and M. Shur, Phys. Rev. B:Condens. Matter Mater. Phys., 1995, 51, 14341.
231. J. Gooth, F. Menges, N. Kumar, V. Süβ, C. Shekhar, Y. Sun, U. Drechsler, R. Zierold, C. Felser and B. Gotsmann, Nat. Commun., 2018, 9, 4093.
232. P. J. Moll, P. Kushwaha, N. Nandi, B. Schmidt and A. P. Mackenzie, Science, 2016, 351, 1061–1064.
233. U. Vool, A. Hamo, G. Varnavides, Y. Wang, T. X. Zhou, N. Kumar, Y. Dovzhenko, Z. Qiu, C. A. Garcia and A. T. Pierce, Nat. Phys., 2021, 17, 1216–1220.
234. D. Bandurin, I. Torre, R. K. Kumar, M. Ben Shalom, A. Tomadin, A. Principi, G. Auton, E. Khestanova, K. Novoselov and I. Grigorieva, Science, 2016, 351, 1055–1058.
235. J. Coulter, R. Sundararaman and P. Narang, Phys. Rev. B, 2018, 98, 115130.
236. A. Principi, G. Vignale, M. Carrega and M. Polini, Phys. Rev. B, 2016, 93, 125410.
237. M. Polini and A. K. Geim, Phys. Today, 2020, 73, 28–34.
238. S. Raza, S. I. Bozhevolnyi, M. Wubs and N. A. Mortensen, J. Phys.: Condens. Matter, 2015, 27, 183204.
239. D. Svintsov, Phys. Rev. B, 2019, 100, 195428.
240. I. Torre, L. Vieira de Castro, B. Van Duppen, D. Barcons Ruiz, F. M. Peeters, F. H. Koppens and M. Polini, Phys. Rev. B, 2019, 99, 144307.
241. A. Lucas and S. Das Sarma, Phys. Rev. B, 2018, 97, 115449.
242. Z. Sun, D. N. Basov and M. M. Fogler, Proc. Natl. Acad. Sci. U. S. A., 2018, 115, 3285–3289.
243. D. Svintsov, Phys. Rev. B, 2018, 97, 121405.
244. Y. Machida, N. Matsumoto, T. Isono and K. Behnia, Science, 2020, 367, 309–312.
245. C. Ulloa, A. Tomadin, J. Shan, M. Polini, B. Van Wees and R. Duine, Phys. Rev. Lett., 2019, 123, 117203.
246. E. Polino, M. Valeri, N. Spagnolo and F. Sciarrino, AVS Quantum Sci., 2020, 2, 024703.
247. A. Laucht, F. Hohls, N. Ubbelohde, M. F. Gonzalez-Zalba, D. J. Reilly, S. Stobbe, T. Schröder, P. Scarlino, J. V. Koski and A. Dzurak, Nanotechnology, 2021, 32, 162003.
248. A. Anwar, C. Perumangatt, F. Steinlechner, T. Jennewein and A. Ling, Rev. Sci. Instrum., 2021, 92, 041101.
249. C. L. Morrison, F. Graffitti, P. Barrow, A. Pickston, J. Ho and A. Fedrizzi, APL Photonics, 2022, 7, 066102.
250. A. Morandi, R. Savo, J. S. Müller, S. Reichen and R. Grange, ACS Photonics, 2022, 9, 1882–1888.
251. T. Liu, M. Qin, S. Feng, X. Tu, T. Guo, F. Wu and S. Xiao, Phys. Rev. B, 2024, 109, 155424.
252. B. Cao, M. Hisamitsu, K. Tokuda, S. Kurimura, R. Okamoto and S. Takeuchi, Opt. Express, 2021, 29, 21615–21628.
253. A. Lyons, G. C. Knee, E. Bolduc, T. Roger, J. Leach, E. M. Gauger and D. Faccio, Sci. Adv., 2018, 4, eaap9416.
254. S. Mukamel, M. Freyberger, W. Schleich, M. Bellini, A. Zavatta, G. Leuchs, C. Silberhorn, R. W. Boyd, L. L. Sánchez-Soto and A. Stefanov, J. Phys. B:At., Mol. Opt. Phys., 2020, 53, 072002.
255. D. W. Berry and H. M. Wiseman, Nat. Photonics, 2009, 3, 317–319.
256. X. Hua, T. Lunghi, F. Doutre, P. Vergyris, G. Sauder, P. Charlier, L. Labonté, V. D’Auria, A. Martin and S. Tascu, Opt. Express, 2021, 29, 415–424.
257. M. Reisner, F. Mazeas, R. Dauliat, B. Leconte, D. Aktas, R. Cannon, P. Roy, R. Jamier, G. Sauder and F. Kaiser, Npj Quantum Inf., 2022, 8, 58.
258. S. Tanzilli, A. Martin, F. Kaiser, M. P. De Micheli, O. Alibart and D. B. Ostrowsky, Laser Photonics Rev., 2012, 6, 115–143.
259. N. Nunn, M. D. Torelli, A. Ajoy, A. I. Smirnov and O. Shenderova, Rev. Adv. Chem., 2022, 12, 1–21.
260. J. S. Toural, V. Marzoa, R. Bernardo-Gavito, J. Pau and D. Granados, IMDEA-Nanociencia, 2022, https://repositorio.imdeananociencia.org/handle/20.500.12614/3165.
261. R. Schirhagl, K. Chang, M. Loretz and C. L. Degen, Annu. Rev. Phys. Chem., 2014, 65, 83–105.
262. J. L. Webb, J. D. Clement, L. Troise, S. Ahmadi, G. J. Johansen, A. Huck and U. L. Andersen, Appl. Phys. Lett., 2019, 114.
263. Z. Zhang, R. Xu, Y. Zhang, B. Du, K. Huang and L. Cheng, IEEE Sens. J., 2023, 23, 6150–6155.
264. Y. Tao, A. Eichler, T. Holzherr and C. L. Degen, Nat. Commun., 2016, 7, 12714.
265. T. Graziosi, S. Mi, M. Kiss and N. Quack, APL Photonics, 2018, 3.
266. T. Schröder, M. Walsh, J. Zheng, S. Mouradian, L. Li, G. Malladi, H. Bakhru, M. Lu, A. Stein and M. Heuck, Opt. Mater. Express, 2017, 7, 1514–1524.
267. A. Faraon, C. Santori, Z. Huang, K.-M. C. Fu, V. M. Acosta, D. Fattal and R. G. Beausoleil, New J. Phys., 2013, 15, 025010.
268. T. Jung, J. Görlitz, B. Kambs, C. Pauly, N. Raatz, R. Nelz, E. Neu, A. M. Edmonds, M. Markham and F. Mücklich, APL Photonics, 2019, 4.
269. S. Sahoo, V. A. Davydov, V. N. Agafonov and S. I. Bogdanov, Opt. Mater. Express, 2022, 13, 191–217.
270. X. Mao, K. Huang, G. Ran, Q. Huang, S. Qu, X. He, Q. Hu and Z. Lin, IEEE Sens. J., 2023, 23, 16161–16167.
271. L. You, Nanophotonics, 2020, 9, 2673–2692.
272. C. M. Natarajan, M. G. Tanner and R. H. Hadfield, Supercond. Sci. Technol., 2012, 25, 063001.
273. O. Kahl, S. Ferrari, P. Rath, A. Vetter, C. Nebel and W. H. Pernice, J. Light Technol., 2016, 34, 249–255.
274. F. M. Stürner, A. Brenneis, T. Buck, J. Kassel, R. Rölver, T. Fuchs, A. Savitsky, D. Suter, J. Grimmel and S. Hengesbach, Adv. Quantum Technol., 2021, 4, 2000111.
275. J. Wang, I. B. Harris, X. Chen, D. R. Englund and R. Han, CMOS-integrated color center pulse-sequence control and detection system, in 2024 IEEE Custom Integrated Circuits Conference (CICC), IEEE, 2024 Apr 21, pp. 1–2 DOI:10.1109/CICC60959.2024.10529078.
276. D. Kim, M. I. Ibrahim, C. Foy, M. E. Trusheim, R. Han and D. R. Englund, Nat. Electron., 2019, 2, 284–289.
277. S. Esmaeili, P. Schmalenberg, S. Wu, Y. Zhou, S. Rodrigues, N. Hussain, T. Kimura, Y. Tadokoro, S. Higashi and D. Banerjee, APL Mater., 2024, 12, 040901.
278. S. Wang, M. Hoffmann, A. K. Yetisen, K. Wang, F. Brändle, W. Kurz, M. Jakobi, Q. Zhou and A. W. Koch, Appl. Spectrosc. Rev., 2024, 59, 382–421.
279. A. S. Clark, M. Chekhova, J. C. Matthews, J. G. Rarity and R. F. Oulton, Appl. Phys. Lett., 2021, 118.
280. M. V. Chekhova and Z. Y. Ou, Adv. Opt. Photon., 2016, 8, 104–155.
281. X. Y. Zou, L. J. Wang and L. Mandel, Phys. Rev. Lett., 1991, 67, 318–321.
282. T. Ono, G. F. Sinclair, D. Bonneau, M. G. Thompson, J. C. Matthews and J. G. Rarity, Opt. Lett., 2019, 44, 1277–1280.
283. D. A. Kalashnikov, A. V. Paterova, S. P. Kulik and L. A. Krivitsky, Nat. Photonics, 2016, 10, 98–101.
284. X. Hua, T. Lunghi, F. Doutre, P. Vergyris, G. Sauder, P. Charlier, L. Labonté, V. D’Auria, A. Martin, S. Tascu, M. P. De Micheli, S. Tanzilli and O. Alibart, Opt. Express, 2021, 29, 415–424.
285. Y. Lu, Z. Liao, F.-L. Li and X.-H. Wang, Photon. Res., 2022, 10, 389–400.
286. E. Polino, M. Riva, M. Valeri, R. Silvestri, G. Corrielli, A. Crespi, N. Spagnolo, R. Osellame and F. Sciarrino, Optica, 2019, 6, 288–295.
287. E. Roccia, V. Cimini, M. Sbroscia, I. Gianani, L. Ruggiero, L. Mancino, M. G. Genoni, M. A. Ricci and M. Barbieri, Optica, 2018, 5, 1171–1176.
288. P. J. Crowley, A. Datta, M. Barbieri and I. A. Walmsley, Phys. Rev. A:At., Mol., Opt. Phys., 2014, 89, 023845.
289. N. Shettell and D. Markham, Phys. Rev. Lett., 2020, 124, 110502.
290. L. Ye and S. Mukamel, Appl. Phys. Lett., 2020, 116, 174003.
291. N. Spagnolo, C. Vitelli, L. Aparo, P. Mataloni, F. Sciarrino, A. Crespi, R. Ramponi and R. Osellame, Nat. Commun., 2013, 4, 1606.
292. G. Gol’Tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams and R. Sobolewski, Appl. Phys. Lett., 2001, 79, 705–707.
293. I. Esmaeil Zadeh, J. Chang, J. W. Los, S. Gyger, A. W. Elshaari, S. Steinhauer, S. N. Dorenbos and V. Zwiller, Appl. Phys. Lett., 2021, 118, 190502.
294. J. Münzberg, A. Vetter, F. Beutel, W. Hartmann, S. Ferrari, W. H. P. Pernice and C. Rockstuhl, Optica, 2018, 5, 658–665.
295. J. Chang, J. Los, J. Tenorio-Pearl, N. Noordzij, R. Gourgues, A. Guardiani, J. Zichi, S. Pereira, H. Urbach and V. Zwiller, APL Photonics, 2021, 6, 036114.
296. R. Cheng, Y. Zhou, S. Wang, M. Shen, T. Taher and H. X. Tang, Nat. Photonics, 2023, 17, 112–119.
297. N. M. Sullivan, B. Braverman, J. Upham and R. W. Boyd, New J. Phys., 2024, 26, 043026.
298. L. Stasi, G. Gras, R. Berrazouane, M. Perrenoud, H. Zbinden and F. Bussières, Phys. Rev. Appl., 2023, 19, 064041.
299. A. E. Lita, D. V. Reddy, V. B. Verma, R. P. Mirin and S. W. Nam, J. Light Technol., 2022, 40, 7578–7597.
300. T. Schapeler, N. Lamberty, T. Hummel, F. Schlue, M. Stefszky, B. Brecht, C. Silberhorn and T. J. Bartley, Phys. Rev. Appl., 2024, 22, 014024.
301. L. Limongi, F. Martini, T. H. Dao, A. Gaggero, H. Hasnaoui, I. Lopez-Gonzalez, F. Chiarello, F. De Matteis, A. Quaranta and A. Salamon, Opt. Commun., 2025, 575, 131244.
302. P. H. Siegel, IEEE Trans. Terahertz Sci. Technol., 2015, 5, 162–169.
303. G. Acconcia, F. Ceccarelli, A. Gulinatti and I. Rech, Opt. Express, 2023, 31, 33963–33999.
304. A. Rochas, M. Gani, B. Furrer, P. Besse, R. Popovic, G. Ribordy and N. Gisin, Rev. Sci. Instrum., 2003, 74, 3263–3270.
305. J. A. Richardson, E. A. G. Webster, L. A. Grant and R. K. Henderson, IEEE Trans. Electron Devices, 2011, 58, 2028–2035.
306. I. Cusini, D. Berretta, E. Conca, A. Incoronato, F. Madonini, A. A. Maurina, C. Nonne, S. Riccardo and F. Villa, Front. Phys., 2022, 10, 906671.
307. T. He, X. Yang, Y. Tang, R. Wang and Y. Liu, Semicond. Sci. Technol., 2022, 37, 055006.
308. M. Vignetti, F. Calmon, R. Cellier, P. Pittet, L. Quiquerez and A. Savoy-Navarro, Microelectron. J., 2015, 46, 900–910.
309. O. Almer, D. Tsonev, N. A. Dutton, T. Al Abbas, S. Videv, S. Gnecchi, H. Haas and R. K. Henderson, A SPAD-based visible light communications receiver employing higher order modulation, in 2015 IEEE Global Communications Conference (GLOBECOM), IEEE, 2015 Dec 6, pp. 1–6 DOI:10.1109/GLOCOM.2015.7417269.
310. C. Yu, Q. Xu and J. Zhang, Meas. Sci. Technol., 2024, 35, 122003.
311. Y. Guan, H. Li, L. Xue, R. Yin, L. Zhang, H. Wang, G. Zhu, L. Kang, J. Chen and P. Wu, Opt. Lasers Eng., 2022, 156, 107102.
312. G. Lubin, R. Tenne, I. Michel Antolovic, E. Charbon, C. Bruschini and D. Oron, Opt. Express, 2019, 27, 32863–32882.
313. A. Aspect, P. Grangier and G. Roger, Phys. Rev. Lett., 1981, 47, 460.
314. B. S. Fong, M. Davies and P. Deschamps, J. Nanophotonics, 2018, 12, 016015.
315. F. Gramuglia, E. Ripiccini, C. A. Fenoglio, M.-L. Wu, L. Paolozzi, C. Bruschini and E. Charbon, Front. Phys., 2022, 10, 849237.
316. D. V. Reddy, R. R. Nerem, S. W. Nam, R. P. Mirin and V. B. Verma, Optica, 2020, 7, 1649–1653.
317. C. Schuck, W. H. Pernice and H. X. Tang, Sci. Rep., 2013, 3, 1893.
318. B. Korzh, Q.-Y. Zhao, J. P. Allmaras, S. Frasca, T. M. Autry, E. A. Bersin, A. D. Beyer, R. M. Briggs, B. Bumble and M. Colangelo, Nat. Photonics, 2020, 14, 250–255.
319. I. Esmaeil Zadeh, J. W. Los, R. Gourgues, V. Steinmetz, G. Bulgarini, S. M. Dobrovolskiy, V. Zwiller and S. N. Dorenbos, APL Photonics, 2017, 2, 111301.
320. O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch and D. Oron, Nano Lett., 2013, 13, 5832–5836.
321. L. Cester, A. Lyons, M. C. Braidotti and D. Faccio, Sensors, 2019, 19, 180.
322. Y. Zhang, A. Sit, F. Bouchard, H. Larocque, F. Grenapin, E. Cohen, A. C. Elitzur, J. L. Harden, R. W. Boyd and E. Karimi, Opt. Express, 2019, 27, 2212–2224.
323. L. Qi, F. Just, G. Leuchs and M. V. Chekhova, Opt. Express, 2016, 24, 26444–26453.
324. E. Toninelli, P.-A. Moreau, T. Gregory, A. Mihalyi, M. Edgar, N. Radwell and M. Padgett, Optica, 2019, 6, 347–353.
325. H. Defienne, J. Zhao, E. Charbon and D. Faccio, Phys. Rev. A, 2021, 103, 042608.
326. A. Nomerotski, Nucl. Instrum. Methods Phys. Res., Sect. A, 2019, 937, 26–30.
327. A. Zhao, M. van Beuzekom, B. Bouwens, D. Byelov, I. Chakaberia, C. Cheng, E. Maddox, A. Nomerotski, P. Svihra and J. Visser, Rev. Sci. Instrum., 2017, 88, 113104.
328. Y. Zhang, D. England, A. Nomerotski, P. Svihra, S. Ferrante, P. Hockett and B. Sussman, Phys. Rev. A, 2020, 101, 053808.
329. R. M. Field, S. Realov and K. L. Shepard, IEEE, J. Solid State Circ., 2014, 49, 867–880.
330. S. Burri, H. Homulle, C. Bruschini and E. Charbon, LinoSPAD: a time-resolved 256x1 CMOS SPAD line sensor system featuring 64 FPGA-based TDC channels running at up to 8.5 giga-events per second, in Optical Sensing and Detection IV, SPIE, 2016 Apr 29, vol. 9899, pp. 57–66 DOI:10.1117/12.2227564.
331. K. Morimoto, A. Ardelean, M.-L. Wu, A. C. Ulku, I. M. Antolovic, C. Bruschini and E. Charbon, Optica, 2020, 7, 346–354.
332. R. Ankri, A. Basu, A. C. Ulku, C. Bruschini, E. Charbon, S. Weiss and X. Michalet, ACS Photonics, 2019, 7, 68–79.
333. B. F. Aull, E. K. Duerr, J. P. Frechette, K. A. McIntosh, D. R. Schuette and R. D. Younger, IEEE J. Sel. Top. Quantum Electron., 2017, 24, 1–10.
334. A. Gulinatti, F. Ceccarelli, M. Ghioni and I. Rech, Opt. Express, 2021, 29, 4559–4581.
335. N. Calandri, M. Sanzaro, L. Motta, C. Savoia and A. Tosi, IEEE Photonics Technol. Lett., 2016, 28, 1767–1770.
336. S. Gyger, J. Zichi, L. Schweickert, A. W. Elshaari, S. Steinhauer, S. F. Covre da Silva, A. Rastelli, V. Zwiller, K. D. Jöns and C. Errando-Herranz, Nat. Commun., 2021, 12, 1408.
337. J. Haas, M. Schwartz, U. Rengstl, M. Jetter, P. Michler and B. Mizaikoff, Analyst, 2018, 143, 593–605.
338. A. Crespi, M. Lobino, J. C. Matthews, A. Politi, C. R. Neal, R. Ramponi, R. Osellame and J. L. O’Brien, Appl. Phys. Lett., 2012, 100, 233704.
339. A. Acín, I. Bloch, H. Buhrman, T. Calarco, C. Eichler, J. Eisert, D. Esteve, N. Gisin, S. J. Glaser and F. Jelezko, New J. Phys., 2018, 20, 080201.
340. R. Dalidet, F. Mazeas, E. Nitiss, O. Yakar, A. Stroganov, S. Tanzilli, L. Labonté and C.-S. Brès, Opt. Express, 2022, 30, 11298–11305.
341. E. Nitiss, J. Hu, A. Stroganov and C.-S. Brès, Nat. Photonics, 2022, 16, 134–141.
342. P. Vergyris, C. Babin, R. Nold, E. Gouzien, H. Herrmann, C. Silberhorn, O. Alibart, S. Tanzilli and F. Kaiser, Appl. Phys. Lett., 2020, 117.
343. S. Atzeni, A. S. Rab, G. Corrielli, E. Polino, M. Valeri, P. Mataloni, N. Spagnolo, A. Crespi, F. Sciarrino and R. Osellame, Optica, 2018, 5, 311–314.
344. G. Corrielli, A. Crespi and R. Osellame, Nanophotonics, 2021, 10, 3789–3812.
345. M. Krecmarova, M. Gulka, T. Vandenryt, J. Hruby, L. Fekete, P. Hubik, A. Taylor, V. Mortet, R. Thoelen and E. Bourgeois, ACS Appl. Mater. Interfaces, 2021, 13, 18500–18510.
346. T. Staudacher, F. Shi, S. Pezzagna, J. Meijer, J. Du, C. A. Meriles, F. Reinhard and J. Wrachtrup, Science, 2013, 339, 561–563.
347. H. Mamin, M. Kim, M. Sherwood, C. T. Rettner, K. Ohno, D. Awschalom and D. Rugar, Science, 2013, 339, 557–560.
348. N. Arunkumar, D. B. Bucher, M. J. Turner, P. TomHon, D. Glenn, S. Lehmkuhl, M. D. Lukin, H. Park, M. S. Rosen and T. Theis, PRX Quantum, 2021, 2, 010305.
349. F. C. Ziem, N. S. Götz, A. Zappe, S. Steinert and J. R. Wrachtrup, Nano Lett., 2013, 13, 4093–4098.
350. V. Karthik, B. Karuna, P. S. Kumar, A. Saravanan and R. Hemavathy, Chemosphere, 2022, 299, 134427.
351. R. D. Allert, F. Bruckmaier, N. R. Neuling, F. A. Freire-Moschovitis, K. S. Liu, C. Schrepel, P. Schätzle, P. Knittel, M. Hermans and D. B. Bucher, Lab Chip, 2022, 22, 4831–4840.
352. N. Spagnolo, A. Lumino, E. Polino, A. S. Rab, N. Wiebe and F. Sciarrino, Machine learning for quantum metrology, in Proceedings, MDPI, 2019 Aug 23, vol. 12, no. 1, p. 28.
353. H.-K. Lo, M. Curty and K. Tamaki, Nat. Photonics, 2014, 8, 595–604.
354. N. Walenta, A. Burg, D. Caselunghe, J. Constantin, N. Gisin, O. Guinnard, R. Houlmann, P. Junod, B. Korzh and N. Kulesza, New J. Phys., 2014, 16, 013047.
355. G. Vest, M. Rau, L. Fuchs, G. Corrielli, H. Weier, S. Nauerth, A. Crespi, R. Osellame and H. Weinfurter, IEEE J. Sel. Top. Quantum Electron., 2014, 99.
356. I. Walmsley, Science, 2015, 348, 525–530.
357. U. Vazirani and T. Vidick, Commun. ACM, 2019, 62, 133.
358. T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, R. P. Mirin and T. Gerrits, New J. Phys., 2015, 17, 022002.
359. R. Liu, G. G. Rozenman, N. K. Kundu, D. Chandra and D. De, IET Quantum Commun., 2022, 3, 151–163.
360. S. Rodt and S. Reitzenstein, APL Photonics, 2021, 6, 010901.
361. P. Senellart, G. Solomon and A. White, Nat. Nanotechnol., 2017, 12, 1026–1039.
362. X. Ding, Y. He, Z.-C. Duan, N. Gregersen, M.-C. Chen, S. Unsleber, S. Maier, C. Schneider, M. Kamp and S. Höfling, Phys. Rev. Lett., 2016, 116, 020401.
363. N. Somaschi, V. Giesz, L. De Santis, J. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Anton and J. Demory, Nat. Photonics, 2016, 10, 340–345.
364. M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song and S. Stobbe, Phys. Rev. Lett., 2014, 113, 093603.
365. T. Chung, G. Juska, S. Moroni, A. Pescaglini, A. Gocalinska and E. Pelucchi, Nat. Photonics, 2016, 10, 782–787.
366. J. Liu, R. Su, Y. Wei, B. Yao, S. F. C. D. Silva, Y. Yu, J. Iles-Smith, K. Srinivasan, A. Rastelli and J. Li, Nat. Nanotechnol., 2019, 14, 586–593.
367. A. Högele, C. Galland, M. Winger and A. Imamoğlu, Phys. Rev. Lett., 2008, 100, 217401.
368. S. Castelletto, B. Johnson, V. Ivády, N. Stavrias, T. Umeda, A. Gali and T. Ohshima, Nat. Mater., 2014, 13, 151–156.
369. S. Kim, N. M. H. Duong, M. Nguyen, T. J. Lu, M. Kianinia, N. Mendelson, A. Solntsev, C. Bradac, D. R. Englund and I. Aharonovich, Adv. Opt. Mater., 2019, 7, 1901132.
370. E. Engin, D. Bonneau, C. M. Natarajan, A. S. Clark, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, K. Ohira and N. Suzuki, Opt. Express, 2013, 21, 27826–27834.
371. J. B. Spring, P. L. Mennea, B. J. Metcalf, P. C. Humphreys, J. C. Gates, H. L. Rogers, C. Söller, B. J. Smith, W. S. Kolthammer and P. G. Smith, Optica, 2017, 4, 90–96.
372. H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang and S. Zhu, Phys. Rev. Lett., 2014, 113, 103601.
373. R. Horn, P. Abolghasem, B. J. Bijlani, D. Kang, A. Helmy and G. Weihs, Phys. Rev. Lett., 2012, 108, 153605.
374. S. Saravi, T. Pertsch and F. Setzpfandt, Adv. Opt. Mater., 2021, 9, 2100789.
375. F. Kaneda and P. G. Kwiat, Sci. Adv., 2019, 5, eaaw8586.
376. M. J. Collins, C. Xiong, I. H. Rey, T. D. Vo, J. He, S. Shahnia, C. Reardon, T. F. Krauss, M. Steel and A. S. Clark, Nat. Commun., 2013, 4, 2582.
377. H. Semenenko, P. Sibson, A. Hart, M. G. Thompson, J. G. Rarity and C. J. O. Erven, Optica, 2020, 7, 238–242.
378. C. Agnesi, B. Da Lio, D. Cozzolino, L. Cardi, B. B. Bakir, K. Hassan, A. Della Frera, A. Ruggeri, A. Giudice and G. Vallone, Opt. Lett., 2019, 44, 271–274.
379. N. C. Harris, Y. Ma, J. Mower, T. Baehr-Jones, D. Englund, M. Hochberg and C. Galland, Opt. Express, 2014, 22, 10487–10493.
380. P. O. Weigel, J. Zhao, K. Fang, H. Al-Rubaye, D. Trotter, D. Hood, J. Mudrick, C. Dallo, A. T. Pomerene and A. L. Starbuck, Opt. Express, 2018, 26, 23728–23739.
381. Y. Ma, Y. Liu, H. Guan, A. Gazman, Q. Li, R. Ding, Y. Li, K. Bergman, T. Baehr-Jones and M. Hochberg, Opt. Express, 2015, 23, 16052–16062.
382. P. Xu, J. Zheng, J. K. Doylend and A. Majumdar, ACS Photonics, 2019, 6, 553–557.
383. A. Peruzzo, A. Laing, A. Politi, T. Rudolph and J. L. O’brien, Nat. Commun., 2011, 2, 224.
384. A. W. Elshaari, I. E. Zadeh, A. Fognini, M. E. Reimer, D. Dalacu, P. J. Poole, V. Zwiller and K. D. Jöns, Nat. Commun., 2017, 8, 379.
385. S. Hong, L. Zhang, Y. Wang, M. Zhang, Y. Xie and D. Dai, Photonics Res., 2022, 10, 1–7.
386. X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati and T. C. Ralph, Nat. Photonics, 2018, 12, 534–539.
387. B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys and J. C. Gates, Nat. Photonics, 2014, 8, 770–774.
388. J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska and D. Bacco, Science, 2018, 360, 285–291.
389. G. Zhang, J. Y. Haw, H. Cai, F. Xu, S. Assad, J. F. Fitzsimons, X. Zhou, Y. Zhang, S. Yu and A. Wu, Nat. Photonics, 2019, 13, 839–842.
390. H. Semenenko, P. Sibson, A. Hart, M. G. Thompson, J. G. Rarity and C. Erven, Optica, 2020, 7, 238–242.
391. K. Wei, W. Li, H. Tan, Y. Li, H. Min, W.-J. Zhang, H. Li, L. You, Z. Wang and X. Jiang, Phys. Rev. X, 2020, 10, 031030.
392. L. Cao, W. Luo, Y. Wang, J. Zou, R. Yan, H. Cai, Y. Zhang, X. Hu, C. Jiang and W. Fan, Phys. Rev. Appl., 2020, 14, 011001.
393. R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski and P. Minzioni, Photonics Res., 2019, 7, 201–239.
394. J. Cardenas, C. B. Poitras, K. Luke, L.-W. Luo, P. A. Morton and M. Lipson, IEEE Photonics Technol. Lett., 2014, 26, 2380–2382.
395. J. Wang, D. Bonneau, M. Villa, J. W. Silverstone, R. Santagati, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki and H. Terai, Optica, 2016, 3, 407–413.
396. L. Carroll, J.-S. Lee, C. Scarcella, K. Gradkowski, M. Duperron, H. Lu, Y. Zhao, C. Eason, P. Morrissey and M. Rensing, Appl. Sci., 2016, 6, 426.
397. J. S. Lee, L. Carroll, C. Scarcella, N. Pavarelli, S. Menezo, S. Bernabé, E. Temporiti and P. O'Brien, IEEE J. Sel. Top. Quantum Electron., 2016, 22, 409–417.
398. D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman and R. Baets, Jpn. J. Appl. Phys., 2006, 45, 6071.
399. L. He, M. Zhang, A. Shams-Ansari, R. Zhu, C. Wang and L. Marko, Opt. Lett., 2019, 44, 2314–2317.
400. S. F. Preble, M. L. Fanto, J. A. Steidle, C. C. Tison, G. A. Howland, Z. Wang and P. M. Alsing, Phys. Rev. Appl., 2015, 4, 021001.
401. R. Marchetti, C. Lacava, A. Khokhar, X. Chen, I. Cristiani, D. J. Richardson, G. T. Reed, P. Petropoulos and P. Minzioni, Sci. Rep., 2017, 7, 16670.
402. Y. Lin, J. C. Mak, H. Chen, X. Mu, A. Stalmashonak, Y. Jung, X. Luo, P. G.-Q. Lo, W. D. Sacher and J. K. Poon, Opt. Express, 2021, 29, 34565–34576.
403. L. Ranno, P. Gupta, K. Gradkowski, R. Bernson, D. Weninger, S. Serna, A. M. Agarwal, L. C. Kimerling, J. Hu and P. OBrien, ACS Photonics, 2022, 9, 3467–3485.
404. C. Taballione, R. van der Meer, H. J. Snijders, P. Hooijschuur, J. P. Epping, M. de Goede, B. Kassenberg, P. Venderbosch, C. Toebes and H. van den Vlekkert, Mater. Quantum Technol., 2021, 1, 035002.
405. N. C. Abrams, Q. Cheng, M. Glick, M. Jezzini, P. Morrissey, P. O'Brien and K. Bergman, J. Light Technol., 2020, 38, 3346–3357.
406. V. Sadasivan, Optical MEMS (microspheres and ring resonators): Overview of recent progress, MEMS Applications in Electronics Engineering, 2023, vol. 7.
407. Y. Yu, M. Chen, S. Zaman, S. Xing, M. Wang and H. Wang, ETransportation, 2022, 12, 100165.
408. T. K. Paraïso, I. De Marco, T. Roger, D. G. Marangon, J. F. Dynes, M. Lucamarini, Z. Yuan and A. J. Shields, Npj Quantum Inf., 2019, 5, 42.
409. C. Ma, W. D. Sacher, Z. Tang, J. C. Mikkelsen, Y. Yang, F. Xu, T. Thiessen, H.-K. Lo and J. K. Poon, Optica, 2016, 3, 1274–1278.
410. D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen and M. Grein, Phys. Rev. X, 2018, 8, 021009.
411. J. Dai, L. Zhang, X. Fu, X. Zheng and L. Yang, Opt. Lett., 2020, 45, 2014–2017.
412. Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt and L. K. Oxenløwe, Npj Quantum Inf., 2017, 3, 25.
413. X. Zheng, P. Zhang, R. Ge, L. Lu, G. He, Q. Chen, F. Qu, L. Zhang, X. Cai and Y. Lu, Adv. Photonics, 2021, 3, 055002.
414. P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner and C. M. Natarajan, Nat. Commun., 2017, 8, 13984.
415. T. K. Paraiso, T. Roger, D. G. Marangon, I. De Marco, M. Sanzaro, R. I. Woodward, J. F. Dynes, Z. Yuan and A. J. Shields, Nat. Photonics, 2021, 15, 850–856.
416. D. Orsucci, P. Kleinpaß, J. Meister, I. De Marco, S. Häusler, T. Strang, N. Walenta and F. Moll, arXiv, 2024, preprint, arXiv:.05668.
417. D. Chawla and P. S. Mehra, Internet of Things, 2023, 100950.
418. A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden and N. Gisin, Appl. Phys. Lett., 1997, 70, 793–795.
419. F. Grünenfelder, A. Boaron, D. Rusca, A. Martin and H. Zbinden, Appl. Phys. Lett., 2020, 117.
420. A. Boaron, G. Boso, D. Rusca, C. Vulliez, C. Autebert, M. Caloz, M. Perrenoud, G. Gras, F. Bussières and M.-J. Li, Phys. Rev. Lett., 2018, 121, 190502.
421. Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang and L.-X. You, Phys. Rev. X, 2016, 6, 011024.
422. C. Agnesi, M. Avesani, A. Stanco, P. Villoresi and G. Vallone, Opt. Lett., 2019, 44, 2398–2401.
423. A. Boaron, B. Korzh, R. Houlmann, G. Boso, D. Rusca, S. Gray, M.-J. Li, D. Nolan, A. Martin and H. Zbinden, Appl. Phys. Lett., 2018, 112.
424. M. Bloch, S. W. McLaughlin, J.-M. Merolla and F. Patois, Opt. Lett., 2007, 32, 301–303.
425. T. Honjo, K. Inoue and H. Takahashi, Opt. Lett., 2004, 29, 2797–2799.
426. R. J. Hughes, J. E. Nordholt, K. P. McCabe, R. T. Newell, C. G. Peterson and R. D. Somma, Network-centric quantum communications with application to critical infrastructure protection, arXiv, 2013, preprint, arXiv:1305.0305 DOI:10.48550/arXiv.1305.0305.
427. C.-X. Zhang, D. Wu, P.-W. Cui, J.-C. Ma, Y. Wang and J.-M. An, Chin. Phys. B, 2023, 32(12), 124207.
428. R. Sax, A. Boaron, G. Boso, S. Atzeni, A. Crespi, F. Grünenfelder, D. Rusca, A. Al-Saadi, D. Bronzi and S. Kupijai, Photon. Res., 2023, 11, 1007–1014.
429. G. Vest, P. Freiwang, J. Luhn, T. Vogl, M. Rau, L. Knips, W. Rosenfeld and H. Weinfurter, Phys. Rev. Appl., 2022, 18, 024067.
430. M. Avesani, L. Calderaro, M. Schiavon, A. Stanco, C. Agnesi, A. Santamato, M. Zahidy, A. Scriminich, G. Foletto and G. Contestabile, Npj Quantum Inf., 2021, 7, 93.
431. W. Geng, C. Zhang, Y. Zheng, J. He, C. Zhou and Y. Kong, Opt. Express, 2019, 27, 29045–29054.
432. P. Sibson, J. E. Kennard, S. Stanisic, C. Erven, J. L. O’Brien and M. G. Thompson, Optica, 2017, 4, 172–177.
433. M. F. Ramos, A. N. Pinto and N. A. Silva, Sci. Rep., 2022, 12, 6135.
434. Q. Liu, Y. Huang, Y. Du, Z. Zhao, M. Geng, Z. Zhang and K. Wei, Entropy, 2022, 24, 1334.
435. F. Beutel, H. Gehring, M. A. Wolff, C. Schuck and W. Pernice, Npj Quantum Inf., 2021, 7, 40.
436. A. Martin, B. Sanguinetti, C. C. W. Lim, R. Houlmann and H. Zbinden, J. Light Technol., 2015, 33, 2855–2859.
437. F. Honz, N. Vokić, M. Hentschel, P. Walther, H. Hübel and B. Schrenk, Towards an All-Silicon QKD Transmitter Sourced by a Ge-on-Si Light Emitter, IEEE Journal of Selected Topics in Quantum Electronics, 30, no. 1: Single-Photon Technologies and Applications, 2023, 1–9 DOI:10.1109/JSTQE.2023.3315584.
438. J. A. Dolphin, T. K. Paraïso, H. Du, R. I. Woodward, D. G. Marangon and A. J. Shields, Npj Quantum Inf., 2023, 9, 84.
439. V. Ansari, J. M. Donohue, B. Brecht and C. Silberhorn, Optica, 2018, 5, 534–550.
440. K. Tanizawa, K. Kato and F. Futami, J. Light Technol., 2024, 42, 1209–1214.
441. M. Borghi, N. Tagliavacche, F. A. Sabattoli, H. E. Dirani, L. Youssef, C. Petit-Etienne, E. Pargon, J. Sipe, M. Liscidini and C. Sciancalepore, Phys. Rev. Appl., 2023, 19, 064026.
442. M. Clementi, F. A. Sabattoli, M. Borghi, L. Gianini, N. Tagliavacche, H. El Dirani, L. Youssef, N. Bergamasco, C. Petit-Etienne and E. Pargon, Nat. Commun., 2023, 14, 176.
443. H. Mahmudlu, R. Johanning, A. Van Rees, A. Khodadad Kashi, J. P. Epping, R. Haldar, K.-J. Boller and M. Kues, Nat. Photonics, 2023, 17, 518–524.
444. N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison and P. M. Alsing, Optica, 2018, 5, 1623–1631.
445. F. Raffaelli, P. Sibson, J. E. Kennard, D. H. Mahler, M. G. Thompson and J. C. F. Matthews, Opt. Express, 2018, 26, 19730–19741.
446. B. Bai, J. Huang, G.-R. Qiao, Y.-Q. Nie, W. Tang, T. Chu, J. Zhang and J.-W. Pan, Appl. Phys. Lett., 2021, 118, 264001.
447. A. Politi, J. C. Matthews, M. G. Thompson and J. L. O'Brien, IEEE J. Sel. Top. Quantum Electron., 2009, 15, 1673–1684.
448. A. F. Abouraddy, M. B. Nasr, B. E. Saleh, A. V. Sergienko and M. C. Teich, Phys. Rev. A:At., Mol., Opt. Phys., 2002, 65, 053817.
449. H. Liu, B. Pan, Y. Huang, J. He, M. Zhang, Z. Yu, L. Liu, Y. Shi and D. Dai, Light: Adv. Manuf., 2023, 4, 133–142.
450. S. Kurimura, Y. Kato, M. Maruyama, Y. Usui and H. Nakajima, Appl. Phys. Lett., 2006, 89, 191123.
451. J. Aldama, S. Sarmiento, I. H. L. Grande, S. Signorini, L. T. Vidarte and V. Pruneri, J. Light Technol., 2022, 40, 7498–7517.
452. H. Cai, C. M. Long, C. T. DeRose, N. Boynton, J. Urayama, R. Camacho, A. Pomerene, A. L. Starbuck, D. C. Trotter and P. S. Davids, Opt. Express, 2017, 25, 12282–12294.
453. H. Semenenko, P. Sibson, M. G. Thompson and C. Erven, Opt. Lett., 2019, 44, 275–278.
454. J. Zhang, X. Wang, F. Xia, S. Yu and Z. Chen, Phys. Rev. A, 2024, 109, 052429.
455. M. Casariego, E. Z. Cruzeiro, S. Gherardini, T. Gonzalez-Raya, R. André, G. Frazão, G. Catto, M. Möttönen, D. Datta and K. Viisanen, Quantum Sci. Technol., 2023, 8, 023001.
456. F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson and J. C. Matthews, Quantum Sci. Technol., 2018, 3, 025003.
457. C. Ekici, E. Semenova, D. Bacco and Y. Ding, Photonic Quantum Technologies: Science Applications, 2023, vol. 2, pp. 599–650.
458. J. F. Tasker, J. Frazer, G. Ferranti, E. J. Allen, L. F. Brunel, S. Tanzilli, V. D’Auria and J. C. Matthews, Nat. Photonics, 2021, 15, 11–15.
459. D. Cozzolino, B. Da Lio, D. Bacco and L. K. Oxenløwe, Adv. Quantum Technol., 2019, 2, 1900038.
460. M. Epping, H. Kampermann and D. Bruß, New J. Phys., 2017, 19, 093012.
461. V. Giovannetti, S. Lloyd and L. Maccone, Science, 2004, 306, 1330–1336.
462. X. Zhu, C.-H. Chang, C. González-Arciniegas, A. Pe’er, J. Higgins and O. Pfister, Optica, 2021, 8, 281–290.
463. M. A. Nielsen, Rep. Math. Phys., 2006, 57, 147–161.
464. F. Lenzini, J. Janousek, O. Thearle, M. Villa, B. Haylock, S. Kasture, L. Cui, H.-P. Phan, D. V. Dao and H. Yonezawa, Sci. Adv., 2018, 4, eaat9331.
465. N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. Wong, T. Baehr-Jones and M. Hochberg, Nat. Photonics, 2017, 11, 447–452.
466. R. J. Hughes, J. E. Nordholt, K. P. McCabe, R. T. Newell, C. G. Peterson and R. D. Somma, arXiv, 2013, preprint.
467. G. Maltese, M. Amanti, F. Appas, G. Sinnl, A. Lemaître, P. Milman, F. Baboux and S. Ducci, Npj Quantum Inf., 2020, 6, 13.
468. Z.-Q. Jiao, J. Gao, W.-H. Zhou, X.-W. Wang, R.-J. Ren, X.-Y. Xu, L.-F. Qiao, Y. Wang and X.-M. Jin, Optica, 2021, 8, 1129–1135.
469. Y. Chi, J. Huang, Z. Zhang, J. Mao, Z. Zhou, X. Chen, C. Zhai, J. Bao, T. Dai and H. Yuan, Nat. Commun., 2022, 13, 1166.
470. M. A. Guidry, D. M. Lukin, K. Y. Yang, R. Trivedi and J. Vučković, Nat. Photonics, 2022, 16, 52–58.
471. Y. Zhao, Y. Okawachi, J. K. Jang, X. Ji, M. Lipson and A. L. Gaeta, Phys. Rev. Lett., 2020, 124, 193601.
472. V. D. Vaidya, B. Morrison, L. Helt, R. Shahrokshahi, D. Mahler, M. Collins, K. Tan, J. Lavoie, A. Repingon and M. Menotti, Sci. Adv., 2020, 6, eaba9186.
473. M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu and B. E. Little, Nature, 2017, 546, 622–626.
474. Z. Yang, M. Jahanbozorgi, D. Jeong, S. Sun, O. Pfister, H. Lee and X. Yi, Nat. Commun., 2021, 12, 4781.
475. J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z.-Q. Jiang, M. Li, J.-J. Jia, G. Ren, D. He, Y.-L. Zhou, X.-X. Zhang, N. Wang, X. Chang, Z.-C. Zhu, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang and J.-W. Pan, Sci. Adv., 2017, 356, 1140–1144.
476. S.-K. Liao, W.-Q. Cai, J. Handsteiner, B. Liu, J. Yin, L. Zhang, D. Rauch, M. Fink, J.-G. Ren, W.-Y. Liu, Y. Li, Q. Shen, Y. Cao, F.-Z. Li, J.-F. Wang, Y.-M. Huang, L. Deng, T. Xi, L. Ma, T. Hu, L. Li, N.-L. Liu, F. Koidl, P. Wang, Y.-A. Chen, X.-B. Wang, M. Steindorfer, G. Kirchner, C.-Y. Lu, R. Shu, R. Ursin, T. Scheidl, C.-Z. Peng, J.-Y. Wang, A. Zeilinger and J.-W. Pan, Phys. Rev. Lett., 2018, 120, 030501.
477. W.-Q. Cai, Y. Li, B. Li, J.-G. Ren, S.-K. Liao, Y. Cao, L. Zhang, M. Yang, J.-C. Wu, Y.-H. Li, W.-Y. Liu, J. Yin, C.-Z. Wang, W.-B. Luo, B. Jin, C.-L. Lv, H. Li, L. You, R. Shu, G.-S. Pan, Q. Zhang, N.-L. Liu, X.-B. Wang, J.-Y. Wang, C.-Z. Peng and J.-W. Pan, Optica, 2024, 11, 647–652.
478. C.-Y. Lu, Y. Cao, C.-Z. Peng and J.-W. Pan, Rev. Mod. Phys., 2022, 94, 035001.
479. A. V. Miller, L. V. Pismeniuk, A. V. Duplinsky, V. E. Merzlinkin, A. A. Plukchi, K. A. Tikhonova, I. S. Nesterov, D. O. Sevryukov, S. D. Levashov, V. V. Fetisov, S. V. Krasnopejev and R. M. Bakhshaliev, EPJ Quantum Technol., 2023, 10, 52.
480. F. Beutel, F. Brückerhoff-Plückelmann, H. Gehring, V. Kovalyuk, P. Zolotov, G. Goltsman and W. H. P. Pernice, Optica, 2022, 9, 1121–1130.
481. L. Mascaretti, Y. Chen, O. Henrotte, O. Yesilyurt, V. M. Shalaev, A. Naldoni and A. Boltasseva, ACS Photonics, 2023, 10, 4079–4103.
482. A. I. Kuznetsov, B. Luk’yanchuk, A. Y. Zhu, N. Engheta and P. Genevet, Nanophotonics, 2017, 6(2) DOI:10.1515/nanoph-2016-0032.
483. Y. Bao, Q. Lin, R. Su, Z.-K. Zhou, J. Song, J. Li and X.-H. Wang, Sci. Adv., 2020, 6, eaba8761.
484. A. Vaskin, R. Kolkowski, A. Koenderink and I. Staude, Nanophotonics, 2019, 8(7), 1151–1198.
485. A. N. Abramov, I. Y. Chestnov, E. S. Alimova, T. Ivanova, I. S. Mukhin, D. N. Krizhanovskii, I. A. Shelykh, I. V. Iorsh and V. Kravtsov, Nat. Commun., 2023, 14, 5737.
486. Z. Zheng, D. Rocco, H. Ren, O. Sergaeva, Y. Zhang, K. B. Whaley, C. Ying, D. de Ceglia, C. De-Angelis and M. Rahmani, Nanophotonics, 2023, 12, 4255–4281.
487. J. Ma, J. Zhang, J. Horder, A. A. Sukhorukov, M. Toth, D. N. Neshev and I. Aharonovich, Adv. Mater., 2024, 36, 2313589.
488. A. Vaskin, R. Kolkowski, A. F. Koenderink and I. Staude, Nanophotonics, 2019, 8, 1151–1198.
489. J. Zheng, Y. Xiao, M. Hu, Y. Zhao, H. Li, L. You, X. Feng, F. Liu, K. Cui and Y. Huang, Photonics Res., 2023, 11, 234–244.
490. Y. Xiao, S. Wei, J. Xu, R. Ma, X. Liu, X. Zhang, T. H. Tao, H. Li, Z. Wang and L. You, ACS Photonics, 2022, 9, 3450–3456.
491. Z. Hu, C. Jiang, J. Zhu, Z. Qiao, T. Xie, C. Wang, Y. Yuan, Z. Ye and Y. Wang, Opt. Express, 2022, 30, 41658–41670.
492. W. Chen, P. Chen, H. Zhang, Y. He, J. Tang and S. Wu, Intell. Marine Technol. Syst., 2023, 1, 10.
493. Y. Guan, H. Li, L. Xue, R. Yin, L. Zhang, H. Wang, G. Zhu, L. Kang, J. Chen and P. Wu, Opt. Lasers Eng., 2022, 156, 107102.
494. R. H. Hadfield, J. Leach, F. Fleming, D. J. Paul, C. H. Tan, J. S. Ng, R. K. Henderson and G. S. Buller, Optica, 2023, 10, 1124–1141.
495. S. Jiang, K. Huang, T. Yu, J. Fang, B. Sun, Y. Liang, Q. Hao, E. Wu, M. Yan and H. Zeng, Photonics Res., 2024, 12, 1294–1302.
496. J. A. Lau, V. B. Verma, D. Schwarzer and A. M. Wodtke, Chem. Soc. Rev., 2023, 52, 921–941.
497. J. Chang, J. Gao, I. Esmaeil Zadeh, A. W. Elshaari and V. Zwiller, Nanophotonics, 2023, 12, 339–358.
498. S. Renukaradhya, R. Bhagawati and T. Subramanian, Artificial Intelligence, Machine Learning and Blockchain in Quantum Satellite, Drone and Network, CRC Press, 2022, pp. 15–34.
499. B. Radisavljevic, M. B. Whitwick and A. Kis, ACS Nano, 2011, 5, 9934–9938.
500. X. Qiang, Y. Wang, S. Xue, R. Ge, L. Chen, Y. Liu, A. Huang, X. Fu, P. Xu, T. Yi, F. Xu, M. Deng, J. B. Wang, J. D. A. Meinecke, J. C. F. Matthews, X. Cai, X. Yang and J. Wu, Sci. Adv., 2021, 7, eabb8375.
501. A. Peruzzo, M. Lobino, J. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M. Thompson and J. Obrien, Science, 2010, 329, 1500–1503.
502. J. Chang, J. Gao, I. E. Zadeh, A. W. Elshaari and V. Zwiller, Nanophotonics, 2023, 12, 339–358.
503. N. Jain, B. Stiller, I. Khan, D. Elser, C. Marquardt and G. Leuchs, Contemp. Phys., 2016, 57, 366–387.
504. M. Lucamarini, Z. L. Yuan, J. F. Dynes and A. J. Shields, Nature, 2018, 557, 400–403.
505. M. Pereira, G. Kato, A. Mizutani, M. Curty and K. Tamaki, Sci. Adv., 2020, 6, eaaz4487.
506. V. Zapatero, T. van Leent, R. Arnon-Friedman, W.-Z. Liu, Q. Zhang, H. Weinfurter and M. Curty, Npj Quantum Inf., 2023, 9, 10.
507. J. You, Y. Luo, J. Yang, J. Zhang, K. Yin, K. Wei, X. Zheng and T. Jiang, Laser Photonics Rev., 2020, 14, 2000239.
508. H. Wang, Q. Zeng, H. Ma and Z. Yuan, Adv. Dev. Instrum., 2024, 5, 0032.
509. H.-S. Zhong, H. Wang, Y.-H. Deng, M.-C. Chen, L.-C. Peng, Y.-H. Luo, J. Qin, D. Wu, X. Ding, Y. Hu, P. Hu, X.-Y. Yang, W.-J. Zhang, H. Li, Y. Li, X. Jiang, L. Gan, G. Yang, L. You, Z. Wang, L. Li, N.-L. Liu, C.-Y. Lu and J.-W. Pan, Science, 2020, 370, 1460–1463.
510. J. Pan, K. L. Low, J. Ghosh, S. Jayavelu, M. M. Ferdaus, S. Y. Lim, E. Zamburg, Y. Li, B. Tang and X. Wang, ACS Appl. Nano Mater., 2021, 4, 6903–6915.
511. K. Rogdakis, G. Psaltakis, G. Fagas, A. Quinn, R. Martins and E. Kymakis, Discover Mater., 2024, 4, 4.
512. R. Zhao, Z. Yang, H. Zheng, Y. Wu, F. Liu, Z. Wu, L. Li, F. Chen, S. Song and J. Zhu, Nat. Commun., 2022, 13, 3427.
513. M. Pagani, D. Marpaung, D.-Y. Choi, S. J. Madden, B. Luther-Davies and B. J. Eggleton, Opt. Express, 2014, 22, 28810–28818.
514. Y. Zheng, X. Song, Z. Fredj, S. Bian and M. Sawan, Anal. Chim. Acta, 2023, 1244, 340860.
515. S.-L. Liu, Z.-G. Wang, H.-Y. Xie, A.-A. Liu, D. C. Lamb and D.-W. Pang, Chem. Rev., 2020, 120, 1936–1979.
516. G. Kabay, J. DeCastro, A. Altay, K. Smith, H. W. Lu, A. M. Capossela, M. Moarefian, K. Aran and C. Dincer, Adv. Mater., 2022, 34, 2201085.
517. Y. Xu, X. Zhang, Y. Fu and Y. Liu, Photonics Res., 2021, 9, B135–B152.
518. B. J. Shastri, A. N. Tait, T. Ferreira de Lima, W. H. Pernice, H. Bhaskaran, C. D. Wright and P. R. Prucnal, Nat. Photonics, 2021, 15, 102–114.

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