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arXiv:2502.01769 · Physical Review Letters

Cavity-Enhanced Solid-State Nuclear Spin Gyroscope

Hanfeng Wang, Shuang Wu, Kurt A. Jacobs, Yuqin Duan, Dirk Englund, Matthew E. Trusheim

Published May 9, 2025• 6 citations
arXivHTMLPDF

Abstract

Solid-state quantum sensors based on ensembles of nitrogen-vacancy (NV) centers in diamond have emerged as powerful tools for precise sensing applications. Nuclear spin sensors are particularly well suited for applications requiring long coherence times, such as inertial sensing, but remain underexplored due to control complexity and limited optical readout efficiency. In this work, we propose cooperative cavity quantum electrodynamic (cQED) coupling to achieve efficient nuclear spin readout. Unlike previous cQED methods used to enhance electron spin readout, here we employ two-field interference in the NV hyperfine subspace to directly probe the nuclear spin transitions. We model the nuclear spin NV-cQED system (nNV-cQED) and observe several distinct regimes, including electromagnetically induced transparency, masing without inversion, and oscillatory behavior. We then evaluate the nNV-cQED system as an inertial sensor, indicating a rotation sensitivity improved by 3 orders of magnitude compared to previous solid-state spin demonstrations. Furthermore, we show that the NV electron spin can be simultaneously used as a comagnetometer, and the four crystallographic axes of NVs can be employed for vector resolution in a single nNV-cQED system. These results showcase the applications of two-field interference using the nNV-cQED platform, providing critical insights into the manipulation and control of quantum states in hybrid NV systems and unlocking new possibilities for high-performance quantum sensing.

DOI
10.1103/physrevlett.134.183603

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Solid-state quantum sensors based on ensembles of nitrogen-vacancy (NV) centers in diamond have emerged as powerful tools for precise sensing applications. Nuclear spin sensors are particularly well suited for applications requiring long coherence times, such as inertial sensing, but remain underexplored due to control complexity and limited optical readout efficiency. In this work, we propose cooperative cavity quantum electrodynamic (cQED) coupling to achieve efficient nuclear spin readout. Unlike previous cQED methods used to enhance electron spin readout, here we employ two-field interference in the NV hyperfine subspace to directly probe the nuclear spin transitions. We model the nuclear spin NV-cQED system (nNV-cQED) and observe several distinct regimes, including electromagnetically induced transparency, masing without inversion, and oscillatory behavior. We then evaluate the nNV-cQED system as an inertial sensor, indicating a rotation sensitivity improved by 3 orders of magnitude compared to previous solid-state spin demonstrations. Furthermore, we show that the NV electron spin can be simultaneously used as a comagnetometer, and the four crystallographic axes of NVs can be employed for vector resolution in a single nNV-cQED system. These results showcase the applications of two-field interference using the nNV-cQED platform, providing critical insights into the manipulation and control of quantum states in hybrid NV systems and unlocking new possibilities for high-performance quantum sensing.
Quantum sensing has witnessed rapid development and transition from laboratories to practical applications in the past decade. Applications of quantum sensors, ranging from nanotechnologies to biosensing, are expected to benefit from quantum sensors' unprecedented spatial resolution and sensitivity. Solid-state spin systems are particularly attractive platforms for quantum sensing technologies because room temperature operation is viable while reaching the quantum limits of sensitivity. Among various solid-state spin systems, nitrogen-vacancy (NV) centers in diamond demonstrated high-fidelity initialization, coherent control, and high contrast readout of the electron spin state. However, electron spin coherence due to noise from the surrounding spin bath and this environment effect limits the sensitivity of NV centers. Thus, a critical task in NV center-based quantum sensing is sensitivity enhancement through coherence protection. Several strategies, such as dynamical decoupling techniques, feedback control, and nuclear spin-assisted sensing protocols, have been developed and realized for this task. Among these strategies, nuclear spin-assisted protocols have demonstrated greater enhancement of electron spin coherence. In addition, the electron and nuclear spin pair of an NV center in diamond naturally allows the application of the nuclear spin-assisted sensitivity enhancement protocol. Owing to long nuclear coherence times, further enhancement of sensitivity can be achieved by exploiting active nuclear spins (e.g., 14N, 13C) in the proximity of an NV center as memory ancillas when coupled with the NV center. Here, we review the spin properties of NV centers, mechanisms of the nuclear spin-assisted protocol and its gate variation, and the status of quantum sensing applications in high-resolution nuclear spin spectroscopy, atomic imaging, and magnetic field sensing. We discuss the potential for commercialization, current challenges in sensitivity enhancement, and conclude with future research directions for promoting the development of nuclear spin-assisted protocol and its integration into industrial applications.
Gyroscopes find wide applications in everyday life from navigation and inertial sensing to rotation sensors in hand-held devices and automobiles. Current devices, based on either atomic or solid-state systems, impose a choice between long-time stability and high sensitivity in a miniaturized system. Here, we introduce a quantum sensor that overcomes these limitations by providing a sensitive and stable three-axis gyroscope in the solid state. We achieve high sensitivity by exploiting the long coherence time of the 14{}^{14}14N nuclear spin associated with the nitrogen-vacancy center in diamond, combined with the efficient polarization and measurement of its electronic spin. Although the gyroscope is based on a simple Ramsey interferometry scheme, we use coherent control of the quantum sensor to improve its coherence time and robustness against long-time drifts. Such a sensor can achieve a sensitivity of $\ensuremath{\eta}\ensuremath{\sim}0.5\phantom{\rule{0.28em}{0ex}}(\mathrm{mdeg}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1})/\sqrt{\mathrm{Hz}\phantom{\rule{0.16em}{0ex}}{\mathrm{mm}}^{3}}$ while offering enhanced stability in a small footprint. In addition, we exploit the four axes of delocalization of the nitrogen-vacancy center to measure not only the rate of rotation, but also its direction, thus obtaining a compact three-axis gyroscope.
Solid-state quantum sensors based on ensembles of nitrogen-vacancy (NV) centers in diamond have emerged as powerful platforms for high-precision metrology. Coupling the NV ensemble to a microwave cavity mode in a cavity quantum electrodynamics (cQED) configuration enables spin readout that surpasses the limitations of conventional optical detection, achieving sub-picotesla magnetic sensitivities. However, existing continuous-wave cQED approaches remain far from the intrinsic spin-projection-noise limit due to spin saturation and power broadening. Here, we introduce a dispersive cQED readout technique to overcome these fundamental limitations in NV ensemble sensing. We develop a comprehensive theoretical framework describing the dispersive interaction and analyze the time-domain dynamics of a strongly-coupled NV-cavity system. Our results indicate near-unity inverse readout fidelity and femtotesla-level sensitivity using a commercially available diamond NV ensemble. Importantly, the dispersive readout exhibits a distinct sensitivity scaling that improves as 1/N with increasing number of spins N, providing a practical pathway toward approaching the standard quantum limit for solid-state spin-ensemble sensors.
Abstract Quantum sensors based on solid-state defects, in particular nitrogen-vacancy (NV) centers in diamond, enable precise measurement of magnetic fields, temperature, rotation, and electric fields. Cavity quantum electrodynamic (cQED) readout, in which an NV ensemble is hybridized with a microwave mode, can overcome limitations in optical spin detection and has resulted in leading magnetic sensitivities at the pT-level. This approach, however, remains far from the intrinsic spin-projection noise limit due to thermal Johnson-Nyquist noise and spin saturation effects. Here we tackle these challenges by combining recently demonstrated spin refrigeration techniques with comprehensive nonlinear modeling of the cQED sensor operation. We demonstrate that the optically-polarized NV ensemble simultaneously provides magnetic sensitivity and acts as a heat sink for the deleterious thermal microwave noise background, even when actively probed by a microwave field. Optimizing the NV-cQED system, we demonstrate a broadband sensitivity of 576 ± 6 fT/ Hz\sqrt{{{{\rm{Hz}}}}}Hz​ Hz around 15 kHz in ambient conditions. We then discuss the implications of this approach for the design of future magnetometers, including near-projection-limited devices approaching 3 fT/ Hz\sqrt{{{{\rm{Hz}}}}}Hz​ Hz sensitivity enabled by spin refrigeration.
Nuclear spins in certain solids couple weakly to their environment, making them attractive candidates for quantum information processing and inertial sensing. When coupled to the spin of an optically active electron, nuclear spins can be rapidly polarized, controlled, and read via lasers and radio-frequency (rf) fields. Possessing typical coherence times of several milliseconds at room temperature, nuclear spins hosted by a nitrogen-vacancy center in diamond are thus intriguing systems to observe how classical physical rotation at quantum timescales affects a quantum system. In this work, we demonstrate optical nuclear-spin polarization and rapid quantum control of nuclear spins in a diamond physically rotating at 1kHz1\phantom{\rule{0.16em}{0ex}}\mathrm{kHz}1kHz, faster than the nuclear-spin coherence time. Free from the need to maintain strict field alignment, we are able to measure and control nuclear spins in the presence of a large, time-varying magnetic field that makes an angle of more than ${100}^{\ensuremath{\circ}}$ to the nitrogen-lattice vacancy axis. The field induces spin mixing between the electron and nuclear states of the qubits, decoupling them from oscillating rf fields. We are able to demonstrate that coherent spin state control is possible at any point of the rotation. We combine continuous dynamical decoupling with feed-forward control to eliminate decoherence induced by imperfect mechanical rotation. Our work liberates a previously inaccessible degree of freedom of the NV nuclear spin, unlocking new approaches to quantum control and rotation sensing.