Haonan
Chang
ab and
Jun
Zhang
*ab
aState Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China. E-mail: zhangjwill@semi.ac.cn
bCenter of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
First published on 23rd September 2022
Cavity optomechanical coupling based on radiation pressure, photothermal forces and the photoelastic effect has been investigated widely over the past few decades, including optical measurements of mechanical vibration, dynamic backaction damping and amplification, nonlinear dynamics, quantum state transfer and so on. However, the delicate cavity operation, including cavity stabilization, fine detuning, tapered fibre access etc., limits the integration of cavity optomechanical devices. Dynamic backaction damping and amplification based on cavity-less exciton optomechanical coupling in III–V semiconductor nanomechanical systems, semiconductor nanoribbons and monolayer transition metal dichalcogenides have been demonstrated in recent years. The cavity-less exciton optomechanical systems interconnect photons, phonons and excitons in a highly integrable platform, opening up the development of integrable optomechanics. Furthermore, the highly tunable exciton resonance enables the exciton optomechanical coupling strength to be tuned. In this review, the mechanisms of cavity optomechanical coupling, the principles of exciton optomechanical coupling and the recent progress of cavity-less exciton optomechanics are reviewed. Moreover, the perspectives for exciton optomechanical devices are described.
In recent years, cavity optomechanics has attracted extensive attention, and has played an important role in a broad range of applications, such as phonon lasing7–12 and damping,5,13–20 telecommunications,21–25 quantum information processing,21,22,24,26 precise measurement and so on.27–29 In the field of fundamental science, quantum effects of macroscopic objects can be observed through strong cavity optomechanical coupling21–23,27,29–32 and cavity optomechanical systems are also an excellent platform for detecting gravitational waves.33 In cavity optomechanical systems, various phenomena can be observed when the pump laser frequency is red-detuned or blue-detuned from the cavity resonance frequency. On the “heating” regime, i.e., blue-detuning regime, where the pump laser frequency is lower than the cavity resonance frequency, coherent mechanical vibrations are excited through optical pumping, where phonon lasing and nonlinear optical effects, such as chaos,34,35 solitons,36 and surface acoustic wave frequency combs,37,38 can be observed. On the “cooling” regime, i.e., red-detuning regime, where the pump laser frequency is higher than the cavity resonance frequency, laser cooling18–20 and state exchange between two resonant oscillators21,39 can occur, which provides a toolbox for quantum communication protocols. Although the field of cavity optomechanics is prosperous, the abovementioned applications all require a delicate cavity operation, which is like the “sword of Damocles” for the integrated applications of optomechanics. Hence, alternative approaches are required in order to practically apply the optical control capability to integrated optomechanical systems. The “cavity-less” scheme is strongly desired to be developed.42
In recent years, some research groups have begun to explore the field of cavity-less optomechanics, such as exciton optomechanics. Yeo et al. and Montinaro et al. have reported the coupling of exciton and mechanical motion in quantum dot-nanowire hybrid systems.40,41 Hajime Okamoto and his colleagues have reported exciton optomechanical coupling in III–V semiconductor heterojunction systems.42,43 Jun Zhang et al. have reported laser cooling specific phonon modes in ZnTe nanoribbons via exciton optomechanical coupling.44 H. Xie et al. have reported highly tunable exciton optomechanical coupling in the suspended monolayer MoSe2.45 Excitons are neutral quasiparticles, which are bound states of electrons and holes formed by Coulomb interactions.46 The presence of strong exciton resonances in some semiconductors strongly interacts with incident pump lasers and presents an interesting platform to explore optomechanical effects without the need for an optical cavity.45,47 To our knowledge, cavity-less exciton optomechanics has advantages as follows. First, cavity-less exciton optomechanics interconnects photons, phonons and excitons, which provides a new platform for fundamental studies in new regimes, where simultaneously strong optical and mechanical nonlinearity can be achieved.45 Second, the optomechanical coupling rate is gate-tunable based on photothermal backaction in exciton optomechanical systems composed of two-dimensional semiconductor materials.45 Third, the opto-piezoelectric backaction from the bound electron–hole pair enables us to probe excitonic transition simply with a sub-nanowatt power of light, realizing high-sensitivity optomechanical spectroscopy,42 which would provide a novel way to improve the sensitivity of optomechanical sensing. Fourth, the exciton optomechanical system is a platform for ultrahigh-frequency mechanical resonators. The mechanical vibration in ref. 44 could reach 6.23 THz. Hence, cavity-less exciton optomechanics is a promising research field.
In this review, we will review the field of cavity optomechanics and cavity-less exciton optomechanics. In section 2, we will first introduce several mechanisms of cavity optomechanical coupling and the new research progress in cavity optomechanics based on the corresponding mechanisms. In section 3 we will introduce the fundamental principles involved in cavity-less exciton optomechanics, such as the excitation of excitons, exciton-mediated optomechanical forces, and the effect of strain on exciton resonance. In section 4, we will introduce the latest progress in the field of cavity-less exciton optomechanics and propose the future development direction of cavity-less exciton optomechanics.
Fig. 1 Cavity optomechanical coupling via radiation pressure. (a) Schematic of the cavity optomechanical system, with a Fabry–Perot cavity of length L, with one mirror fixed and the other mounted on a spring. (b) Schematic of the gravitational wave detector LIGO. Reprinted with permission from ref. 33. Copyright 2018, American Physical Society. (c) Average phonon occupation number versus cooling drive-laser power. The bottom inset is the optomechanical device. Reprinted with permission from ref. 51. Copyright 2011, Nature. (d) A single swapping interaction shows phonon Rabi oscillations. The inset is an optical cavity coupled with two mechanical resonators. Reprinted with permission from ref. 52. Copyright 2017, Nature. (e) Experimental set-up for discovering optomechanical dissipative solitons. (f) Power spectrum of the mechanical mode in the solitons regime. Reprinted with permission from ref. 36. Copyright 2021, Nature. |
The detuning frequency Δ is defined by Δ = ω0 − ωcav and many different physical phenomena can be realized by changing the sign of Δ in the optomechanical system. In the resonant regime, i.e., Δ = 0, the cavity can be operated as an interferometer. The gravitational wave detector LIGO is shown in Fig. 1(b), which is a typical example although LIGO is dedicated to the detection of gravitational waves and not the investigation of optomechanics specifically.33 The combination of the input and end test mass comprises Fabry–Perot cavities which can bounce the light between them many times (typically several hundred times) to increase the gravitational wave-induced sidebands by the number of bounces before returning the light to the beam splitter, which greatly improved measurement accuracy. In the red-detuning regime, i.e., Δ < 0, optomechanical laser cooling and state exchange between two resonant oscillators can occur. As shown in Fig. 1(c), J. Chan et al. reported that they used radiation pressure from a red-detuned laser (Δ = −ωm), where ωm is the frequency of the mechanical resonator, to cool the mechanical motion down to its quantum ground state based on a coupled, nanoscale optical and mechanical resonator formed in a silicon microchip.51 In this strong coupling regime, two resonant oscillators can exchange state between each other. As shown in Fig. 1(d), an optical cavity couples with two mechanical resonators and two incident laser beams are red-detuned from the cavity resonance frequency.52 Optomechanical efficient coherent state swapping between two spatially and frequency separated mechanical resonators can be realized, which gives inspiration to investigate the quantum effects of many resonators. In blue-detuning regime, i.e., Δ > 0, phonon lasing and nonlinear optomechanical effects can be realized. Jing Zhang et al. discovered dissipative solitons in the whispering-gallery cavity optomechanical systems. The experimental setup is shown in Fig. 1(e); when the phonon gain compensates the mechanical loss and optomechanical nonlinearity is balanced, stable localized mechanical wave packets coexisting with mechanical solitons can be realized (Fig. 1(f)), which provides a new toolbox for optomechanical applications.36 In a word, cavity optomechanical system coupling via radiation pressure force is a promising platform for quantum coherent optomechanics.
(1) |
Fig. 2 Cavity optomechanical coupling via photothermal forces. (a) Schematic diagram of optomechanical coupling mechanisms based on photothermal forces and radiation pressure. Reprinted with permission from ref. 55. Copyright 2021, American Institute of Physics. (b) Experimental set-up of optomechanical devices based on graphene. (c) Photothermal self-oscillation of a graphene resonator. Reprinted with permission from ref. 70. Copyright 2012, American Chemical Society. (d) Schematic of the plasmomechanical Fano resonance device. The power of the incident laser beam is Pin, and Pout is the power of reflected light after interaction with the optomechanical device. (e) Plasmomechanical coupling. Left: Fano resonance of the optomechanical system. τm, period of mechanical resonance. δA, the optical absorption coefficient modulation. Right: Schematic of the bending of the bilayer membrane changing resonance frequency. Reprinted with permission from ref. 77. Copyright 2016, Nature. |
The modulation of mechanical oscillators, including the cooling or amplification of mechanical resonators in various optomechanical systems, can be realized by time-delayed forces induced by a finite thermal and response time. Graphene is a two-dimensional material with low mass and stiffness, large thermal conductivity and high light absorption coefficient.56–62 Due to the virtue of its low mass and stiffness,63 which could improve the sensitivity of the optomechanical systems to the forces of light, it is an attractive candidate for mechanical resonators.57,64–66 Besides, the large thermal conductivity67 and light absorption coefficient of graphene68 demonstrate that graphene resonators are advantageous platforms to realize photothermal backaction and then enable laser cooling resonators to the quantum ground state.69 A graphene-based cavity optomechanical structure is shown in Fig. 2(b).70 The resonators are suspended monolayer graphene clamped on all sides to a silicon dioxide substrate with a source, drain, and gate electrodes, and the low finesse Fabry–Perot cavity consists of a graphene layer and platinum backplane. The voltage Vg is modulated for measurements of driven motion and tuning of the optical properties of the cavity. The vibration of graphene is actuated by voltage Vg between the graphene and the backplane. The displacement between the graphene and backplane could change the reflectivity R due to the change of optical cavity length. The feedback of this system comes from the fact that the motion of the membrane induces a force parallel to the velocity acting on the resonator with some time delay. Two possible candidates are photothermal forces and radiation pressure forces. According to the theoretical prediction, the photothermal gradient force ∇Fpth is given by
(2) |
Photonic metamaterials are artificial optical materials that can convert optical energy to heat energy efficiently.73–76 Hai Zhu et al. presented a plasmonic metamaterial absorber in a cavity optomechanical system.77 The cavity optomechanical system consists of a 25 mm gold layer with cross-shaped plasmonic nanoslot antennas and a SiN layer on a metal back-reflector (Fig. 2(d)). The gold–SiN bilayer membrane forms a Fabry–Perot cavity. The hybridization of the cavity mode and plasmonic metamaterial resonance contributes to an optical Fano resonance, and the frequency of Fano resonance can be tuned by voltage VDC. When incident light is absorbed by the gold nanoantenna layer, a strain is imposed on the bilayer membrane due to a thermoelastic process. Because of the different thermal expansion coefficient of gold and SiN, the bilayer membrane is bent by an out-of-plane displacement of δx and Fano resonance absorption is mechanically modulated by δA. They revealed that parameter δA/δx is positive when the pump laser is red-detuned from Fano resonance and is negative when the pump laser is blue-detuned from Fano resonance. Due to the mechanical delayed response from the thermal heat flow, a force F = −(δA/δx)v(t) is imposed on the mechanical resonator, where v(t) is the speed of out-plane motion. When δA/δx is positive, a mechanical resonance damping can be realized, i.e., cooling a mechanical resonator. When δA/δx is negative, mechanical vibration is amplified, which is an attractive candidate for a phonon laser.78 This work paves a novel path to modifying the properties of optical cavities in cavity optomechanics via optical metamaterials.
The photoelastic cavity optomechanical coupling in whispering-gallery resonators via a Brillouin scattering process is shown in Fig. 3(a).6 The Brillouin optomechanical process involves two optical whispering-gallery modes (OWGM), separated in the frequency space by the frequency of the acoustic whispering-gallery mode (AWGM) of interest. The model introduced is a forward scattering stimulated Brillouin scattering (SBS) setup, where the acoustic modes are low frequencies due to momentum conservation. The SBS process can be described as follows: the pump optical OWGM generates an AWGM via electrostrictive stress. The AWGM writes a traveling photoelastic grating that scatters light from the pump OWGM to the Stokes OWGM via a Brillouin scattering process.83 At the same time, the electrostrictive interference pattern generated by the two OWGMs amplifies the acoustic WGM, which leads to positive feedback. The experimental setup on a silica microsphere resonator is shown in Fig. 3(b). A tapered optical fiber is employed to evanescently couple light into the pump OWGM. The pump OWGM is scattered by the AWGM and generates a Stokes OWGM. This scattered light and pump light also evanescently couple out to the tapered optical fiber and propagate to a photodetector at the opposite end of the fiber. The output pump laser and Stokes laser signals are shown in Fig. 3(c). The electrical beat signal (Fig. 3(d)) obtained from the photodetector provides the signature of the AWGM.
Fig. 3 Cavity optomechanical coupling via photoelastic interaction. (a) Optical whispering-gallery modes couple with acoustic whispering-gallery modes by a Brillouin scattering process. (b) Experimental setup. (c) Pump and Stokes laser at output. (d) An electrical beat signal provides acoustic eigenfrequency. Reprinted with permission from ref. 84. Copyright 2014, Springer. (e) Brillouin cooling (left panel) and heating (right panel) in whispering-gallery optomechanical devices. Reprinted with permission from ref. 6. Copyright 2012, Nature. (f) Ultrahigh-frequency cavity optomechanical devices with strong optomechanical coupling made of a GaAs/AlAs microcavity (up panel) and mechanical and optical eigenmodes (bottom panel). Reprinted with permission from ref. 89. Copyright 2012, American Physical Society. (g) Microcavity optomechanical coupling enhanced by exciton resonance. |
There are two scattering mechanisms in Brillouin optomechanics: forward scattering and backward scattering. The backward Brillouin scattering is associated with large phonon momenta and therefore typically occurs with multi-GHz frequency acoustic waves. The forward Brillouin scattering in microcavities has allowed access to low-frequency acoustical modes where mechanical dissipation is lower than optical dissipation, in accordance with the requirements for cooling.84 G. Bahl and his colleagues first observed a spontaneous Brillouin cooling low-frequency acoustic mode in the forward scattering whispering-gallery optomechanical system.6 They broke the balance between the Stokes scattering and anti-Stokes scattering by optical resonance in the WGM, leading to a net absorption or generation of phonons by photons via photoelastic coupling. If the Stokes scattering is suppressed, cooling the acoustic mode would be realized (left panel in Fig. 3(e)). If anti-Stokes is suppressed, heating the acoustic mode would be realized (right panel in Fig. 3(e)). In this experiment, the photoelastic coefficient of the materials for photoelastic cavity optomechanical coupling is important. For some semiconductor materials, such as gallium arsenide,85 the photoelastic coefficients are relatively larger than the photoelastic coefficients of silica,86 and thus it is used as optomechanical resonators broadly.
Microcavity optomechanical devices based on a GaAs/AlAs structure are an outstanding candidate for ultrahigh-frequency optomechanical devices.87,88,134 Because of a “double magic coincidence” of AlxGa1−xAs,89 the ratio between their acoustic and optical impedances as well as between their longitudinal acoustic phonon and photon propagation velocities are almost the same and independent of the composition x. The AlxGa1−xAs microcavity could confine photon and acoustic phonons of the same wavelength with a comparable quality factor Q. In 2013, A. Fainstein et al. reported that distributed Bragg reflector GaAs/AlAs vertical cavities could confine photons and phonons of the same wavelength and quality factor Q and realized strong optomechanical coupling, shown in Fig. 3(f).89 Moreover, numerous pieces of literature have demonstrated a huge enhancement of optomechanical coupling between photons and GHz phonons in AlGaAs-based microcavities due to excitons (Fig. 3(g)).127–130 The exciton is a neutral bound state of a hole and electron, which will be elaborated on in section 3.1. Alexander S. Kuznetsov and his colleagues introduced a novel platform for electrically driven exciton–polariton optomechanics at 20 GHz based on the coupling of polaritons and electrically generated bulk acoustic waves (BAWs) confined in an AlGaAs microcavity with QWs, in which the values of the Qf product of the BAWs exceed 1014 Hz and the effective optomechanical coupling coefficient geff is around 50 THz nm−1.128 N. Carlon Zambon et al. theoretically investigated the case where the microcavity exciton optomechanical system operates in the strong exciton–photon coupling regime.131 The optical and excitonic resonances are parametrically modulated by the interaction with a mechanical mode and polariton–phonon interactions would enhance optomechanical coupling by two orders of magnitude. Besides, they analyzed that polariton nonlinearities affect dynamical back-action, modifying the capability to cool or amplify the mechanical motion.
Fig. 4 Cavity optomechanical coupling between plasmon and molecular vibration. (a) Schematic diagram of a plasmonic hot spot hosting a molecule with a vibrational mode. (b) The molecule vibration leads to a change of molecule polarizability, which brings about the change of plasmonic resonance frequency. This is the origin of the parametric optomechanical coupling. (c) Schematic diagram of optomechanical feedback. Variables (fluctuations from average) are indicated along the arrows, and boxes represent transfer functions. δap is the plasmonic field. δFp and δFth are the plasmonic force and thermal force, respectively. δxv is the molecule displacement. δα is the change of polarizability. Reprinted with permission from ref. 90. Copyright 2016, Nature. (d) Experimental setup of a nanoparticle-on-mirror geometry. (e) Raman spectra at a time when additional picocavity-induced lines are present. The same lines on the Stokes and anti-Stokes sides are identified by colours, with vibrational eigenmodes and effective temperatures shown. (f) The laser power dependence of anti-Stokes scattering intensity and average phonon population for different measurements on the same picocavity. (g) The average phonon population for different vibrational modes versus different powers in the same picocavity. Reprinted with permission from ref. 96. Copyright 2016, American Association for the Advancement of Science. |
In recent years, a number of molecule cavity optomechanical experiments have been reported.96–99 The volume of the cavity which confines light is decreasing and overcomes the diffraction limit. Felix Benz and his colleagues found that individual atomic features inside the gap of a plasmonic nanoassembly115 can localize light to volumes well below 1 cubic nanometre (“picocavities”), enabling optical experiments on the atomic scale.96 The experimental setup is shown in Fig. 4(d). Individual gold nanoparticles are spaced above a planar gold substrate by a nanometre-thick self-assembled monolayer (SAM) of biphenyl-4-thiol. All measurements are implemented at cryogenic temperatures using a modified dark-field microscope and laser pumping at 633 nm. According to low-temperature SERS, prominent anti-Stokes SERS lines which are blue-shifted from the laser (Fig. 4(e)) appear always and only when the additional fluctuating Stokes lines are present. The effective temperatures of eigenmodes are shown in Fig. 4(e). The effective temperatures are different for each scattering line and increase with increasing vibrational energy, which provides clear proof that the vibrational populations are nonthermal and that the pumping contribution to the phonon population cannot be ignored. A quadratic power dependence of the anti-Stokes signal and a linear power dependence for the anti-Stokes/Stokes ratio (phonon population) on different nanoparticles at different times are shown in Fig. 4(f), which provides evidence for the presence of vibrational pumping. The phonon population of different modes which linearly change with increasing laser power are shown in Fig. 4(g). However, the slope of these linear fits differed for different nanoparticles, which suggests that the slope is a measure of picocavity geometry and different optomechanical coupling strengths. In a word, the authors used laser irradiation to move atoms in the nanoparticle and produced a “picocavity” that was stable at cryogenic temperatures, which enables cavity optomechanical experiments on the atomic scale. Their work set the foundation for experiment on nonlinear quantum optics at the single-molecule nanoscale.
(3) |
(4) |
Fig. 5 Schematic diagram of Wannier excitons. (a) The generation of excitons in a semiconductor. hν denotes incident photons and FCoulomb is the Coulomb interaction. (b) Energy levels of a Wannier exciton from the bound states (n = 1, 2, and 3) to the continuum states. R* is the Rydberg constant and Eg is the bandgap. (c) Dispersion curves of an exciton–polariton (solid curves labeled I and II). The curves labeled I and II are usually referred to as the “upper” and “lower” branches of the polariton. The dashed curves denote the dispersion curves of a “bare” exciton and a “bare” photon. Reprinted with permission from ref. 82. Copyright 2010, Springer. |
The electric dipole moments of the excitons induce a polarization wave in the medium. The exciton polarized wave is formed with two branches, ωT, and ωL. The polarization wave coupling with the electromagnetic wave forms a “coupled state”, which is called an exciton–polariton.82,100,135 The dispersion curves of an exciton–polariton are shown in Fig. 5(c). As excitons travel in the medium, they radiate electromagnetic waves. Conversely, the electromagnetic wave can excite excitons in the semiconductor. In this picture, energy is converted between excitons and photons.
Edp = −BdEg/dp | (5) |
Andreas Barg et al. investigated carrier-mediated optomechanical forces in semiconductor nanomembranes with coupled quantum wells.101 The free-free nanomembranes with embedded CQWs are shown in Fig. 6(a and b). They used long-lived indirect exciton states in the CQWs as frequency-matched mediators of optomechanical forces. The lifetime of indirect exciton states is tunable over two orders of magnitudes via the bias voltage Vb. Based on the properties of indirect excitons, they simulated modulated acceleration aeh(Ωm) for piezoelectric and deformation-potential coupling using finite-element methods. As shown in Fig. 6(c and d), they obtain the calculated amplitude and phase of aeh(Ωm) as a function of the exciton lifetime in two different crystallographic orientations, [10] and [010] (Miller indices). According to the related results, if the long edges of the rectangular membrane are parallel to [10], the piezoelectric force dominates. If the long edges of the rectangular membrane are parallel to [010], the membrane is driven by the deformation-potential. As shown in Fig. 6(e and f), they concluded that the exciton-mediated forces studied here are significantly stronger than the radiation pressure and the optomechanical forces form a deformation-potential, and the piezoelectric effect can be tuned by the bias voltage Vb. Their work paves a way for us to understand the source of optomechanical forces in the cavity-less exciton optomechanical systems.
Fig. 6 Exciton-mediated optomechanical forces. (a) False-color SEM image of free–free nanomembranes with embedded CQWs. (b) Close-up of the vertical position of the CQWs. (c, d) Simulation of the amplitude (I, II) and phase (III, IV) of the acceleration aeh(Ωm) mediated by piezoelectricity and the deformation potential in crystallographic directions [10] and [010] for different bias voltages, here 0 V (blue curves) and −1 V (red curves). (e, f) The rms amplitude A (I) and phase Φ (III) of the symmetric bending mode as a function of the modulation frequency. Normalized peak rms amplitude A0/Q (II) and phase Φ0 (IV) versus bias voltage Vb as measured for two different membrane orientations, [10] (blue circles) and [010] (purple squares). The solid lines are fitting lines. Reprinted with permission from ref. 101. Copyright 2011, American Physical Society. |
The experimental setup is shown in Fig. 7(a). A flexible and transparent PMMA substrate was used to apply controllable and reproducible strains on the MoS2 samples. A layered MoS2 sample was deposited on the PMMA by mechanical exfoliation of bulk MoS2 crystals. The layer numbers of the MoS2 sample can be identified by their optical contrast. In the cantilever setup, strain of a certain direction can be applied on the MoS2 sample by bending the flexible substrate in zigzag or armchair directions because of the van der Waals coupling at the sample–substrate interface. The absorption spectrum of atomically thin MoS2 samples was measured to determine the exciton resonance energy. The photoluminescence spectroscopy (PL) was measured to determine the indirect gap transitions due to weak absorption. The absorption spectrum of the MoS2 monolayer under 0.4% strain along the armchair and zigzag directions is shown in Fig. 7(b). Compared with the absorption spectrum under no strain, both the A and B exciton features exhibit a redshift and no difference is observed for the two distinct strain directions, which indicated that the exciton resonance shift is independent of the strain direction.
Fig. 7 Exciton resonance tuning via strain in atomically thin MoS2. (a) Schematic diagram of a cantilever used in the experiment. The length L and thickness t of the square-shaped PMMA substrate are 9.5 cm and 0.245 cm, respectively. Mechanically exfoliated MoS2 samples were deposited near a corner of the substrate. Strain was applied on the samples by clamping one edge (gray) and bending the opposite edge of the substrate. The left inset is the atomic structure of monolayer MoS2. The right inset is the optical image of one sample with both a monolayer (1L) and bilayer (2L). (b) Absorption spectrum of a monolayer MoS2 sample for strain (0.4%) applied along the armchair and zigzag direction. (c) Absorption and PL spectrum of a monolayer MoS2 sample under tensile strains up to 0.52% along the zigzag direction. The black dashed line at 1.96 eV is the PMMA Raman line at 2954 cm−1, which is independent of strain. (d) Strain dependence of the absorption peak A, B and PL peak A. Reprinted with permission from ref. 110. Copyright 2013, American Chemical Society. |
The absorption spectrum and PL spectrum of monolayer MoS2 under strain along the zigzag direction are shown in Fig. 7(c). The PL spectra are normalized to the A exciton peak. Both the A and B exciton absorption peaks redshift with increasing strain. As shown in Fig. 7(d), a linear dependence is observed for the relatively small strains investigated here. The A exciton PL peak shows a similar strain dependence and a redshift rate compared with the A exciton absorption peak, which demonstrates that the Stokes shift in this sample is largely strain independent. However, the Stokes shift of the A exciton PL is strain dependent for the bilayer MoS2 sample, likely due to strain-induced defects. Their work demonstrates that strain can tune exciton resonance energy in two-dimensional materials, which opens a new opportunity for applications of 2D crystals in exciton optomechanics and provides a toolbox to understand feedback in exciton optomechanical systems.
Fig. 8 Resolved-sideband Raman cooling LOP with exciton resonance. (a) Schematic diagram of the vibrational normal mode of the LOP in ZnTe. (b) Polaron: a new quasiparticle of the exciton–LOP coupling. (c) Principle and detection method of red-detuned laser cooling in the semiconductor. (d) With increasing cooling laser power, the LOP's phonon occupation number decreases and its damping rate increases. (e, f) Principle and detection method of blue-detuned laser amplification in the semiconductor. (g) Occupation number and temperature of the LOP versus cooling laser power. (h) The measured experimental spectra of exciton transition. The red curves are the Stokes spectra of an LOP with red-detuned laser. The blue curves are the anti-Stokes spectra of an LOP with blue-detuned laser. (i) Occupation number and temperature of an LOP versus heating laser power. Reprinted with permission from ref. 44. Copyright 2016, Nature. |
The basic principle and experimental set-up of resolved sideband cooling and heating are shown in Fig. 8(c–f). The detuned frequency between the laser and exciton is defined such that Δ = ωlaser − ωexciton, where ωlaser is the frequency of the laser and ωexciton is the frequency of exciton resonance. The cooling experimental setup is shown in Fig. 8(c). The red-detuned laser beam (Δ = −ΩLO) was used to pump the system, where ΩLO is the frequency of the LOP. The anti-Stokes scattering process is enhanced by the exciton resonance, and thus the thermal vibration quanta of the LOP from the ZnTe can be cooled down. The blue-detuned laser beam (Δ = ΩLO) was used to probe the cooling behaviour of the LOP by monitoring its Stokes components. As shown in Fig. 8(d), a red-detuned driving laser will add extra damping, Γnet, into the intrinsic LOP damping, Γ0, and decrease its occupation number LO. The corresponding experimental results are shown as red curves in Fig. 8(h), in which the Stokes scattering is suppressed and anti-Stokes scattering is enhanced. The cooling results are shown in Fig. 8(g). With increasing the cooling pumping power from 0 to 1.1 mW, the occupation number LO decreases from 0.36 to 0.19 with an increase corresponding to the ground-state occupation possibility from ∼73.5 to 84.0% and an effective temperature decrease from 225 to 165 K. The heating experimental set-up is shown in Fig. 8(e). The blue-detuned laser beam (Δ = ΩLO) was used to pump the exciton optomechanical system. The Stokes scattering process is enhanced and anti-Stokes scattering process is suppressed, as shown in the blue curves in Fig. 8(h). Hence, the thermal vibration quanta of the LOP can be amplified (Fig. 8(f)) and the linewidth of the LOP decreases. The heating results are shown in Fig. 8(i). The occupation number and effective temperature of the LOP changed linearly with the heating pumping power, which suggests LOP lasing was not observed in the experiment. LOP lasing in the order of terahertz frequency is important for terahertz applications. One possible solution is increasing the power of the pump laser, because the pump laser power in the experiment may not reach the threshold of LOP lasing. Another possible solution is fabricating a cavity composed of this ZnTe nanostructure or putting ZnTe gain materials into another optical cavity. This work realized strong coupling between photons and LOPs by exploiting the strong exciton resonance in the ZnTe semiconductor, which leads to Raman cooling of LOPs. This result provides a possible experimental method to achieve a net Raman cooling of solids.
However, due to the very large exciton linewidth in this experiment, the resolved sideband Raman cooling is only limited to high-frequency optical phonons and is not feasible for low-frequency acoustic phonons because in the sideband-resolved regime, the optical decay should be smaller than the mechanical frequency i.e., κ0 < Ωm. Hence, semiconductor materials with narrower exciton linewidths are feasible to achieve resolved sideband cooling acoustic phonons. This work was implemented based on ZnTe nanobelts. However, for practical tasks, it is desirable to cool larger volumes, and that is hard to achieve because of inherently weak Raman processes and inevitable heating.132 Recently, Jia-Min Lai et al. reported laser cooling of optical phonons in a van der Waals semiconductor cavity-less exciton optomechanical system,133 which is progress in achieving laser cooling in larger volumes than reported previously.
Fig. 9 Exciton optomechanics in semiconductor heterostructures. (a) Schematic diagram of the opto-piezoelectric effect mediated by excitons. (b) Frequency response of the cantilever when the photons’ energy tuned to the exciton resonance (Ee = 1.5152 eV). (c) Schematic diagram of the strain-modulated exciton resonance and the strain-dependent opto-piezoelectric backaction for red and blue detuning. (d) Photon-energy dependence of the frequency response under modulated illumination. (e) Photoluminescence excitation (PLE) spectrum, and a sharp exciton resonance at 1.5152 eV. Noise power spectrum for photon energy (1.5145 eV) red (f) and blue (g) detuned from exciton resonance for different laser powers. Reprinted with permission from ref. 42. Copyright 2015, Nature. |
The cavity-less exciton optomechanical coupling driven by the opto-piezoelectric effects follows the following mechanism: electrons and holes excited by photo in the GaAs layer are separated by the built-in electric field along the thickness direction, which generates a dipole moment. It leads to a piezoelectric bending moment as if the cantilever is driven by a vertical backaction force Fp (Fig. 9(a)). The vibration amplitude of the cantilever is sensitive to photon energy (Fig. 9(d)) because Fp is proportional to the number of excitons contributing to the opto-piezoelectric backaction. This provides a novel mechanical method of probing the optical transitions.
As shown in Fig. 9(c), the exciton resonance in this optomechanical system can be modulated by strain via the deformation potential.111 The exciton resonance red shifts (blue shifts) when the cantilever bends upwards (downwards). Hence, when the incident photon energy red-detunes from exciton resonance, the upwards bending increases the dipole moment with an increase of absorption, leading to an increase in the backaction force (Fp + δFp), while downwards bending decreases the dipole moment with a decrease of absorption, leading to a decrease in the backaction force (Fp − δFp). In the red-detuned regime, the sign of the force gradient ∂Fp/∂z is negative, where z is the displacement of the cantilever. The negative ∂Fp/∂z and the time delay τ ∼ ω0−1 coming from the spatial separation of electrons and holes in the cantilever lead to an amplification of the mechanical vibration, where ω0 is the frequency of mechanical vibration. The Brownian displacement noise power spectrum of the cantilever when the photon energy is red detuned (1.5145 eV) is shown in Fig. 9(f). With the increasing laser power, the vibration amplitude increases and the linewidth of the resonance becomes narrow. In the blue-detuned regime, the positive ∂Fp/∂z and time delay lead to damping. As shown in Fig. 9(g), with the increasing laser power, the vibration amplitude decreases and the linewidth of the resonance becomes wide, indicating cooling of the mechanical mode. The process above is opposite to sideband amplification/damping. In this cavity-less exciton optomechanical system, the polarity of the feedback is determined by the sign of the slope in the PLE spectrum and the sign of the piezoelectric coefficient. The backforce in this exciton optomechanical system is not caused by phonon–exciton parametric coupling, but by carries-induced piezoelectric force. Besides, the retarded backaction contributed to the cooling as well as amplification of the mechanical mode without any optical cavities. Besides, the gain of the opto-piezoelectric self-feedback depends on the mechanical quality factor Qm and it is important to design higher Qm resonators in order to improve the feedback efficiency. This work is a significant progress in cavity-less exciton optomechanics. It developed a more scalable ‘cavity-less’ optomechanical scheme that also allows free-space optical access and achieved highly tunable vibration control of nanomechanical resonators.
Fig. 10 Gate tunable exciton-optomechanical coupling. (a) Schematic diagram of monolayer MoS2 optomechanical devices. (b) Reflection contrast spectrum of suspended monolayer MoSe2 at different gate voltages. The solid line in the bottom panel is the expected dependence of the exciton resonance energy. (c) Gate voltage dependence of the mechanical resonance frequency. (d) The peak response of the fractional change in reflection contrast as a function of the probe photon energy detuning from the exciton resonance. The red curve is the energy derivative of the normalized reflection contrast spectrum with Vg = 40 V multiplied by the dynamic exciton displacement with a peak-to-peak amplitude of δEX ≈ 67 μeV. The inset is a schematic diagram of the dynamic shift in exciton resonance. (e) The gate voltage dependence of δEX extracted from a similar measurement as in (d) at different gate voltages. The red curve is the expected dependence (dEX/dVg)δVg extracted from the solid line in (b) at δVg = 200 mV. The mechanical linewidth (f) and resonance frequency (g) as a function of incident photon energy detuning from exciton resonance. The blue- and red-shaded regions correspond to blue and red energy detuning, respectively. (h) The backaction-induced change in mechanical line width as a function of the energy detuning at selected gate voltages. Reprinted with permission from ref. 45. Copyright 2021, American Chemical Society. |
In this work, reflection contrast spectra were measured to detect the exciton resonance. The reflection contrast spectra were obtained by normalizing the reflected light intensity from the suspended MoSe2 region to that from a bare circular trench without MoSe2. The reflection contrast spectra of the sample at varying gate voltages (0–40 V) are shown in Fig. 10(b). The exciton resonance red shifts with increasing gate voltage because of the in-plane strain at the sample. The vibration of the membrane was measured by a network analyser. The gate voltage dependence of the fundamental mechanical mode in a contour plot was shown in Fig. 10(c). The mechanical resonance frequency slightly decreases at first and increases then with increasing gate voltages, which can be explained by gate modulation of the effective spring constant of the device (solid fit line in Fig. 10(c)).
The exciton optomechanical coupling was investigated by detecting the spectral dependence of the mechanical response. They varied the photon energy near the exciton resonance energy and obtained the fractional change in reflectivity dR/R (peak to peak value) at Vg = 40 V. The peak response versus photon energy detuning (ΔE ≡ E − Ex) from exciton resonance energy is shown in Fig. 10(d), where E is the incident photon energy, and Ex is the resonance energy. They studied energy detuning ΔE instead of the absolute photon energy E in order to rule out the red shifts of the exciton resonance caused by laser heating. The spectral response can be understood as that a dynamical shift in the exciton resonance (δEx) was induced by strain in the monolayer (as shown in the inset in Fig. 10(d)). This provides a relationship between the fractional change in reflectivity and mechanical resonance:
(6) |
The quantity (dE/dR)/R can be calculated from the measured reflection contrast spectrum in Fig. 10(b). To match the calculated red curve with data points (dR/R), δEx is treated as a variable and δEx ≈ 67 μeV approximately at Vg = 40 V. The same analysis is performed at each voltage Vg as shown in Fig. 10(e). The result confirms the picture of dynamical exciton spectral shift and shows a monotonic increase in the exciton-mechanical coupling strength with Vg.
The dynamic feedback was studied by optical detection in fundamental mechanical mode at varying incident photon energies (Vg = 40 V). The incident power is increased from 1 μW to 10 μW in order to amplify the dynamical backaction. The shift in the mechanical resonance (frequency and linewidth) is asymmetric with photon energy detuning (Fig. 10(f and g)). For large detuning from the exciton resonance, the fundamental mechanical mode is largely unperturbed by the incident light. However, the mechanical resonance red shifts and the linewidth broadens with asymmetric detuning dependences. The phenomena can be understood in a model based on photothermal backaction and gate-induced mirror symmetry breaking in the mechanical device. The MoSe2 membrane is pulled down by the electrostatic force from the back gate, which breaks the out-of-plane mirror symmetry of the device. The strain induced by mechanical vibration leads to an exciton resonance shift. The dynamical shift in turn periodically modulates the photothermal force Fph produced by laser illumination near the exciton resonance. The magnitude and phase of Fph depend on the detuning ΔE from the exciton resonance. The detuning dependences of the antisymmetric contribution of the mechanical line width at varying Vg are shown in Fig. 9(h). The amplitude of the antisymmetric contribution (half of the peak-to peak height in the detuning dependences) increases quickly with Vg, which also demonstrates gate-tunable exciton-optomechanical coupling strength.
In this work, the authors demonstrated dynamical light control of the mechanical motion of suspended monolayer MoSe2 through the strong excitonic resonance of the TMDs. The gate-tunable exciton optomechanical coupling can be realized by detuning the exciton resonance energy δEx based on photothermal backaction. Keliang He et al. demonstrated that exciton resonance detuning in monolayer and bilayer TMD (MoS2) under strain is different.110 Hence, the layer number of the two-dimensional materials may have an effect on the exciton optomechanical coupling, which requires our further research.
The experimental setup is shown in Fig. 11(a). The superlattice grown on a GaAs substrate consists of 30 periods of GaAs and AlAs layers with thicknesses of 12 nm and 14.2 nm, respectively. The resonance energy (ħω0) of the polariton is 1.55 eV (Fig. 11(b)). The aluminium films deposited on the GaAs substrate backside. When the film is excited using the pump laser pulses, a wave packet of coherent acoustic phonons is generated and propagates through the GaAs substrate with the velocity of longitudinal sound ν = 4800 m s−1. The coherent phonons are detected in the superlattice by measuring the reflectivity changes ΔR(t) of an optical probe pulse. The detected transient signal around the polariton resonance is shown in Fig. 11(c). When −150 ps ≤ t ≤ 150 ps, the wave pocket of the coherent phonons propagates through the superlattice toward the free surface. To study the effect of the superlattice polariton resonance on the TDBS signal, the authors measured the TDBS signal ΔR(t) for different central photon energies ħω. The value of ħω is varied between 1.544 and 1.556 eV, which is in the vicinity of the polariton resonance. It is seen that the amplitude of the oscillations strongly depends on the probe pulse photon energy (Fig. 11(d)). As shown in Fig. 11(e), the dependences are symmetric for amplitude (AB) and decay rates (τB−1) and antisymmetric for frequency (fB) and phase (pB) relative to ħω0, which means that the TDBS signals are governed by the polariton resonance when probing with ħω close to ħω0. The relative changes ΔR/R0 are ∼10−2 for the used pump fluence J ∼ 0.1 mJ m−2, which is three orders of magnitude higher than that previously reported.119,120 This result means that their experiments reveal a giant photoelasticity of polaritons and extremely high sensitivity to detecting coherent phonons.
In a word, their work demonstrated that 42 GHz coherent phonons can be detected with extremely high sensitivity in the cavity-less exciton optomechanical system composed of the semiconductor superlattice. Moreover, coherent acoustic phonons are suggested to become a logistic element in quantum computer networks121–123 and have been demonstrated to be promising in quantum technologies and nanophononics.124–126 Hence, their work provides a method to generate and detect high-frequency acoustic phonons in optomechanical systems without an optical resonant cavity, and a new toolbox for quantum technologies based on phonons.
Cavity-less exciton optomechanics is still a new field of optomechanical research and it has not attracted as much attention as cavity optomechanics. The on-chip cavity-less exciton optomechanical system is an optomechanical system with the advantages of easy integration, strong optomechanical coupling, and highly tunable mechanical vibrations compared with cavity optomechanical systems. The simultaneously strong optical and mechanical nonlinearity in the TMDs cavity-less exciton optomechanical devices would be a new platform for fundamental studies and applications, such as chaos, optomechanical solitons and so on. Besides, the band engineering may provide a method to alert the optomechanical coupling in exciton optomechanical devices composed of 2D semiconductor materials. The ultrahigh-frequency (∼terahertz) exciton optomechanical systems could reach a quantum ground state at high temperature, which will pave the way to a robust quantum control of phonons and provide the implementation of efficient ultrafast quantum information protocols. However, for cavity optomechanics, reaching a terahertz frequency is very difficult. Hence, cavity-less exciton optomechanical systems are a very promising platform for realizing sensing, signal processing and other functions in integrated optomechanical devices. Cavity-less exciton optomechanics will be a promising research field in the future.
This journal is © The Royal Society of Chemistry 2022 |