A 3D-assembled endohedral nitrogen fullerene in a metal–organic framework toward spin qubit and quantum sensors

Abstract

To realize quantum information processing, quantum bits are required to have considerable quantum coherence, addressability, and scalability. Arranging and stacking the high-dimensional quantum bits with superior coherence is an important approach to realizing the scalability of quantum systems. Endohedral nitrogen fullerene is a promising molecule-based quantum material with a long quantum coherence time, which is expected to be applied to the construction of high-dimensional quantum bit arrays for quantum information processing. In this work, endohedral nitrogen fullerene molecules were embedded in a 3D metal–organic framework yielding N@C₆₀@MOF-177. X-band electron paramagnetic characterization of the energy levels and spin dynamics shows that this system can be used as a spin qubit. The magnitude of the zero-field splitting of the system at low temperatures was properly resolved. Furthermore, the influencing factors on the spin coherence time at low temperatures were investigated by spin dynamic characterization, and the presence of the proton in the environment was detected by ESEEM experiments, which further reveals the feasibility of N@C₆₀ as a spin quantum sensor.

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Introduction

The development of quantum information processing (QIP), including quantum computation, quantum communication, quantum metrology and quantum sensing, is highly dependent on the development of quantum bits (qubits).¹ Quantum sensing utilizes the sensitivity of qubits to detect weak environmental fluctuations to obtain information about external stimuli.² In recent years, quantum sensing has developed rapidly in different fields and made impressive discoveries. In molecular biology, it has been applied in the detection of biological structures and dynamic processes,³ including single protein molecule spectroscopic detection^4,5 and high-resolution magnetic imaging of living cells.^6,7 In physics, quantum sensing yields a huge boost to the study of graviton,⁸ axion,⁹etc. As a transformative tool, quantum sensors would fuel future discoveries in fields as diverse as materials science, chemistry, biology, and physics.¹⁰

Two prerequisites should be satisfied for a spin qubit to be a quantum sensor.² Firstly, it should be able to initialize to a specific quantum state. Secondly, it should have a sufficiently long quantum coherence time to accumulate the signals in its surroundings and obtain high-fidelity readout. The presence of intrinsic unpaired electron spins in magnetic molecules has the potential to develop candidates for quantum sensors.¹ The magnetic molecules can be chemically modified to modulate the energy level structures,^11–13 selectively manipulated by microwave pulses in nanosecond scales^14,15 and initialized by light or magnetic field.^16,17 By assembling the molecular quantum sensor into a metal–organic framework (MOF) with a 3D organized structure and large numbers of sensor sites, the sensing of the absorbed gas inside the pores of MOF can be achieved.¹⁸ However, the current approaches of using molecule-based electron spin systems for quantum sensing are mainly achieved by the measurement of continuous-wave electron paramagnetic resonance (cw-EPR), which may only differentiate the type of the absorbed gases by experiential intensity variations.

Our work is based on the molecular spin system of N@C₆₀, which has three unpaired electrons on the 2p orbitals of the nitrogen atom encapsulated in the carbon cage.¹⁹ The electron spin (S = 3/2) coupled with the spin (I = 1) of the nitrogen nucleus forms twelve energy levels, which can be further used for the demonstration of quantum information.^14,20 Herein, we constructed a 3D-qubit array of N@C₆₀@MOF-177 via host–guest interactions between the fullerene and MOF and attained a spin quantum sensor candidate based on N@C₆₀ molecules to detect the spin dynamics behavior, which directly reflects the species of nuclear spins in the surrounding environment. Through the π–π interactions,^21,22 building blocks of long-coherent N@C₆₀ are able to bond with the porous MOF-177 of suitable size (pore diameter of 10.8 Å). Moreover, the host–guest interaction between N@C₆₀ and MOF-177 breaks the symmetry of the N@C₆₀ molecule and produces zero-field splitting, which leads to the further degeneracy of the four-level system in the ground state.¹⁵ Additionally, the quantum coherence time of N@C₆₀@MOF-177 powder is relatively long at 100 K and below, which suggests that the dispersion of the electron spins by the pores of MOF-177 could effectively reduce the dipole–dipole interactions, thus extending the quantum coherence of the electron spin centers.²² Therefore, the influence of the hydrogen nucleus on the spin center can still be detected by electron spin echo envelope modulation (ESEEM), which enables the N@C₆₀ to be a molecular probe that can sense the surrounding nuclear spins.

Experimental section

Sample preparation

Crude N@C₆₀ was synthesized by bombarding the C₆₀ molecules with N atoms using ion implantation.²³ Then, the crude product can be purified by high-performance liquid chromatography (HPLC), because C₆₀ and N@C₆₀ have slightly different retention times.^24,25 The spin number and fullerene amount were measured by quantitative cw-EPR, and ultraviolet-visible (UV-Vis) spectroscopy, respectively. The molar ratio in the final enriched N@C₆₀/C₆₀ was 1 : 1000. MOF-177 crystals were immersed in a 1000 ppm N@C₆₀ solution of toluene and left for more than a week to allow N@C₆₀ to be completely adsorbed into the pores of MOF-177 and obtained N@C₆₀@MOF-177 (Fig. 1). N@C₆₀@MOF-177 crystals were dried in a dark vacuum oven for 15 h at 40 °C, and then ground to prepare a powder sample.

Fig. 1 N@C₆₀ embedded in MOF-177.

EPR measurements

Both the cw- and pulsed-EPR data were measured on an X-band Chinainstru and Quantumtech (Hefei) EPR100 spectrometer with a pulse-probe cavity (9.56 GHz). The low-temperature environment was achieved using liquid helium cryostats. The signal of the pulsed-EPR experiments was collected by integrating the Hahn-echo (π/2-τ-π-τ-echo) with τ = 400 ns. The T₁ values were measured by the inversion recovery method (π-T-π/2-τ-π-τ-echo) with 2-step phase cycling. T_m values were obtained using the Hahn-echo sequence with 2-step phase cycling. The Rabi oscillations were obtained by nutation sequence (t_p-T-π/2-τ-π-τ-echo), where t_p is the duration time of the nutation pulse and T is longer than 5T_m. Two-pulse (2p-) and three-pulse (3p-) electron spin echo envelope modulation (ESEEM) experiments were carried out with the standard sequences (π/2-τ-π-τ-echo) and (π/2-τ-π/2-T-π/2-τ-echo). The π/2 and π pulse lengths in EDFS, T₁, and T_m measurements were 120 and 240 ns with 18 dB attenuation of the microwave power 450 W, respectively. In nutation experiments, the π/2 pulse lengths were adjusted to 20, 40, 80, 160, 320 ns by 0, 6, 12, 18, and 24 dB attenuation. In 2p- and 3p-ESEEM experiments, the π/2 pulse lengths were set to 20 ns by 0 dB attenuation to collect the clear modulation signal of the ¹H nuclear spin.

Results and discussion

CW-EPR characterization

Compared to the isotropic N@C₆₀ powder sample at 140 K (Fig. 2a), weak zero-field splitting peaks caused by the anisotropy of the MOF were observed at both 3401.5 G and 3436.5 G in the cw-EPR spectra of N@C₆₀@MOF-177 at the same temperature (Fig. 2b). The intensity of the zero-field splitting peaks cannot be simulated by using a single-system model and a double-system model was applied to properly simulate the cw-EPR spectra (all the spectra are simulated with EasySpin²⁶). Here, the system I is anisotropic (|D| = 15.5 MHz and E = 0.5 MHz) while the system II is isotropic (Fig. 1). The weight ratio of the system I to the system II is 0.3. It means that most of the N@C₆₀ molecules in the MOF-177 still remained isotropic at 140 K, while the symmetry of the remnant N@C₆₀ molecules was broken, resulting in zero-field splitting. This broken symmetry might be due to the mobility restriction of the N@C₆₀ in MOF-177 and the π–π interactions^21,22 between the aromatic skeleton of MOF-177 and fullerene, because several possible fullerene localizations in MOF-177 have been theoretically evaluated previously.²⁷ Upon the increment of the temperature, the proportion of N@C₆₀ molecules with an anisotropic environment gradually decreases (Fig. 2c). At 140 K, the N@C₆₀ with an anisotropic environment accounts for 23.1% of the total number of N@C₆₀ molecules, while at a higher temperature of 290 K, the proportion decreases to 9.9%. This might be attributed to the weakened host–guest interactions caused by the dilatation of the MOF pores²⁸ and the enhanced kinetics of the N@C₆₀ molecules upon warming (Fig. 2d).

Fig. 2 (a) cw-EPR spectrum of N@C₆₀ powder and (b) N@C₆₀@MOF-177 at 140 K, where |A| = 15.85 MHz. (c) Temperature-dependent cw-EPR spectrum of N@C₆₀@MOF-177 powders. (d) Temperature dependence of the proportion of anisotropic N@C₆₀ molecules in N@C₆₀@MOF-177 (all cw-EPR experiments were performed with 9.565 GHz frequency, 0.0005 mW microwave power, 0.1 G modulation amplitude, and 100 kHz modulation frequency).

Quantum coherent behaviour

The spin relaxation properties of the N@C₆₀@MOF-177 powder sample are investigated by the pulsed-EPR experiments at the central peak. The relaxation time of a spin qubit can be categorized into two types: the spin–lattice relaxation time (T₁) and the phase memory time (T_m). T₁ represents the ability of the system to maintain spin polarization and T_m represents the duration of the quantum superposition state. The inversion recovery sequence (π-T-π/2-τ-π-τ-echo) and the Hahn-echo sequence (π/2-τ-π-τ-echo) were utilized to characterize the T₁ and T_m. All echo attenuation data were fitted with a mono-exponential attenuation function as shown in the ESI eqn (S1).†

The T₁ value, which determines the upper limit of T_m (T_m ≤ 2T₁)²⁹ is relatively long (Fig. 3a) in N@C₆₀@MOF-177 powder (1.101(19) ms at 100 K) compared to the other 3D-qubit arrays.^30–32 It might be attributed to the quenched spin–orbital coupling in N@C₆₀ that limits the disturbances from the polarity of the MOF-177 environment. Also, the rigid carbon cage of N@C₆₀ might suppress the external thermal perturbation, resulting in a further extension of T₁. Furthermore, T₁ has significant temperature dependence, which becomes longer upon cooling (22(1) ms at 10 K, Fig. 3a). This indicates that the thermal processes prominent spin–lattice relaxation mechanism of the system.

Fig. 3 (a) T₁ and (b) T_m measurements of N@C₆₀@MOF-177 powder at 100 K and 10 K.

T _m measurements of N@C₆₀@MOF-177 powder at 100 K and 10 K are shown in Fig. 3b. The main factors affecting quantum decoherence are described by eqn (1),^11,33

where the three terms represent the interaction of spin-phonon coupling, electron–electron spin coupling and electron-nuclear spin coupling, respectively. In N@C₆₀@MOF-177, firstly, the T₁ is about three orders of magnitude larger than T_m at the measured temperature, so the effect of spin-phonon coupling is not a dominant factor affecting T_m. Secondly, the concentration of N@C₆₀ (1000 ppm) is low enough and the N@C₆₀ molecules are further diluted by the pores of MOF-177, thus the electron–electron spin coupling is largely suppressed. Therefore, it can be inferred that the electron-nuclear spin coupling is the main factor affecting T_m. Fortunately, benefitting from the suppressing effect of the first two mechanisms, T_m of N@C₆₀@MOF-177 powder (3.507(1) μs) is sufficiently long for sensing the nuclear spin even in 100 K and extended to 5.09(12) μs at 10 K. Therefore, it is expected that a spin probe material can be prepared with high sensitivity that can be used in quantum sensing.

Rabi oscillations and ESEEM

Rabi oscillations of N@C₆₀@MOF-177 were obtained by the nutation sequence (t_p-T-π/2-τ-π-τ-echo), where t_p is the duration time of the nutation pulse. In order to dephase the spin after the nutation pulse, T should be longer than 5T_m. We performed the nutation experiments at different microwave powers to confirm the possibility of preparing the spin into arbitrary coherent superposition states. As a result, the Rabi oscillations of N@C₆₀@MOF-177 were clearly observed at both 100 K (Fig. 4a) and room temperature (ESI Fig. S9†). Consistent with previous proposals,^30–32 these experiments proved that this 3D-MOF could be another competitive candidate for a spin qubit array. The Rabi frequencies were obtained after the fast Fourier transform (FFT) and are linearly correlated with the B₁ field (Fig. 4b). Notably, a low amplitude oscillation at high microwave power (0 dB) is observed (Fig. 4a), which is assigned to the ¹H nuclear spin Larmor precession frequency. It indicates that the N@C₆₀ can be used for nuclear spin detection.

Fig. 4 (a) Rabi oscillations of N@C₆₀@MOF-177 powder at 100 K with different microwave powers. (b) The FFT of Rabi oscillations and the linear relationship between the Rabi frequencies and the intensity of microwave B₁ field. (c) 2p-ESEEM and (d) 3p-ESEEM experiments of N@C₆₀@MOF-177 powder at 100 K, extracting the ¹H nuclear Larmor precession frequency in the modulation signals by FFT.

To further confirm the ability to sense the ¹H nuclear spin, ESEEM experiments were carried out. ESEEM is a method of quantum sensing that detects the magnetic nuclei around the electron spin center utilizing the modulation of the echo intensity by the nuclear spin.³⁴ The observation of ESEEM in the arrayed 2D polymers has been reported recently.³⁵ Here, we performed two-pulse ESEEM (2p-ESEEM) and three-pulse ESEEM (3p-ESEEM) experiments at high microwave power (0 dB) to probe the ¹H nuclei of the spin system. The wide excitation bandwidth at high microwave power excites all the transitions and allows the Larmor progression of the ¹H nucleus to be detected. 2p-ESEEM (π/2-τ-π-τ-echo) detects the variation of the echo intensity upon the increment of τ to obtain the modulation envelope, and 3p-ESEEM (π/2-τ-π/2-T-π/2-τ-echo) detects the echo intensity by gradually increasing the interval T between the second and the third pulse to obtain the modulation envelope with a constant τ at the hydrogen-enhanced position. As shown in Fig. 4c and d, the periodic oscillations in 2p- and 3p-ESEEM experiments are observed. After assigning the peak in the FFT diagram of the modulation signals of 2p- and 3p-ESEEM experiments, the frequencies are properly matched with the Larmor frequency of the ¹H nuclear spin, indicating that N@C₆₀ is capable of sensing the nuclear spins of the surroundings. It suggests that the N@C₆₀ molecule has the potential to be applied in differenciating the types of the adsorbed gases via their nuclear spins.

Conclusions

In conclusion, we prepared an endohedral nitrogen fullerene embedded in a 3D metal–organic framework (N@C₆₀@MOF-177). The continuous-wave EPR spectra suggested that some of the N@C₆₀ molecules generate zero-field splitting due to the host–guest interaction with MOF-177, and this interaction will be enhanced upon cooling. The study of spin dynamics reveals that though the skeleton of MOF-177 contains substantial protons, the coherence of N@C₆₀@MOF-177 is still sufficiently long. Preparation and manipulation of arbitrary coherent superposition states can be demonstrated by Rabi oscillation experiments. These facts suggest that N@C₆₀@MOF-177 is a potential candidate for a spin qubit. Furthermore, we observed significant modulation of signals through the electron spin echo envelope modulation experiments and confirmed that these oscillations originate from the ¹H nuclei by fast Fourier transform. It demonstrates that N@C₆₀ has high sensitivity in sensing nuclear spins in external environments, which is promising for probing nuclear spins of gases adsorbed within the porous organic frameworks and improving the identification of gas species. Our results provide a path towards the application of molecular qubits to quantum sensors and open up the possibility of sensing the magnetic properties of nanoscale magnets on a single-spin scale.³⁶

Data availability

The data supporting this article have been included as part of the ESI.†

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The research is supported by the Natural Science Foundation of China (22271311, 22325503, 22250001, U20A6002 and 222203033), Natural Science Foundation of Hunan Province of China (2023JJ20049), National University of Defense Technology.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4qi01782j

‡ These authors contributed equally to this work.

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