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arXiv:2404.10628 · Nature Communications

A spin-refrigerated cavity quantum electrodynamic sensor

Hanfeng Wang, Kunal L. Tiwari, Kurt A. Jacobs, Michael W. Judy, Xin Zhang, Dirk Englund, Matthew E. Trusheim

Published Nov 28, 2024• 19 citations
arXivHTMLPDF

Abstract

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/ $$\sqrt{{{{\rm{Hz}}}}}$$ 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/ $$\sqrt{{{{\rm{Hz}}}}}$$ Hz sensitivity enabled by spin refrigeration.

DOI
10.1038/s41467-024-54333-8

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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.

arXiv:2502.01769•Physical Review Letters•May 9, 2025•6 citations
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.
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.
Overcoming poor readout is an increasingly urgent challenge for devices based on solid-state spin defects, particularly given their rapid adoption in quantum sensing, quantum information, and tests of fundamental physics. However, in spite of experimental progress in specific systems, solid-state spin sensors still lack a universal, high-fidelity readout technique. Here we demonstrate high-fidelity, room-temperature readout of an ensemble of nitrogen-vacancy centers via strong coupling to a dielectric microwave cavity, building on similar techniques commonly applied in cryogenic circuit cavity quantum electrodynamics. This strong collective interaction allows the spin ensemble's microwave transition to be probed directly, thereby overcoming the optical photon shot noise limitations of conventional fluorescence readout. Applying this technique to magnetometry, we show magnetic sensitivity approaching the Johnson-Nyquist noise limit of the system. Our results pave a clear path to achieve unity readout fidelity of solid-state spin sensors through increased ensemble size, reduced spin-resonance linewidth, or improved cavity quality factor.
A fundamental result of quantum mechanics is that the fluctuations of a bosonic field are given by its temperature TTT. An electromagnetic mode with frequency ωωω in the microwave band has a significant thermal photon occupation at room temperature according to the Bose-Einstein distribution nˉ=kBT/ℏω\bar{n} = k_BT / \hbarωnˉ=kB​T/ℏω. The room temperature thermal state of a 3 GHz mode, for example, is characterized by a mean photon number nˉ∼2000\bar{n} \sim 2000nˉ∼2000 and variance Δn2≈nˉ2Δn^2 \approx \bar{n}^2Δn2≈nˉ2. This thermal variance sets the measurement noise floor in applications ranging from wireless communications to positioning, navigation, and timing to magnetic resonance imaging. We overcome this barrier in continuously cooling a ∼3{\sim} 3∼3 GHz cavity mode by coupling it to an ensemble of optically spin-polarized nitrogen-vacancy (NV) centers in a room-temperature diamond. The NV spins are pumped into a low entropy state via a green laser and act as a heat sink to the microwave mode through their collective interaction with microwave photons. Using a simple detection circuit we report a peak noise reduction of −2.3±0.1 dB-2.3 \pm 0.1 \, \textrm{dB}−2.3±0.1dB and minimum cavity mode temperature of 150±5K150 \pm 5 \textrm{K}150±5K. We present also a linearized model to identify the important features of the cooling, and demonstrate its validity through magnetically tuned, spectrally resolved measurements. The realization of efficient mode cooling at ambient temperature opens the door to applications in precision measurement and communication, with the potential to scale towards fundamental quantum limits.
We demonstrate 4π4π4π-steradian vector magnetic field sensing using an ensemble of nitrogen-vacancy (NV) centers in a single-crystal diamond coupled to a microwave (MW) cavity. The MW cavity enhances the spin-photon coupling which enables efficient, high-contrast spin-state readout via MW interrogation and removes the need for bulky optical collection components. An applied AC bias magnetic field lifts the zero-field degeneracy of the four crystallographic NV orientations, allowing each orientation to be individually addressed and used for vector reconstruction of the magnetic field. The resulting magnetometer has a 40\% contrast (20x higher than typical for optical spin-ensemble readout) and achieves a single-axis sensitivity of 250 pT/Hz\sqrt{\mathrm{Hz}}Hz​ which is flat from DC to 1 kHz. Noise models of the composite spin-cavity system establish MW amplitude noise as the dominant noise source and predict a thermal noise limit of 2 pT/Hz\sqrt{\mathrm{Hz}}Hz​.
Nitrogen-vacancy (NV) centre ensembles are leading room-temperature magnetometers, but their sensitivity is usually extracted from a single resonance and relies on external microwave and bias-field hardware. This work proposes a chip-scale NV magnetometer built around a one-dimensional YIG/CoFeB magnonic crystal, in which a single structural defect forms a passive magnonic cavity and integrated permanent magnets supply the bias field. Micromagnetic simulations show a defect-localised spin-wave mode at 2.910 GHz inside the 2.5-3.0 GHz magnonic band gap, 40 MHz from the NV zero-field splitting, with a band structure that matches an independent plane-wave calculation. A Tavis-Cummings/Lindblad model in which the microwave reaches the NV ensemble through this mode predicts a hyperfine-resolved optically detected magnetic resonance spectrum that is strong only within the mode linewidth, and a dispersive homodyne response with one steep edge per 14^{14}14N hyperfine line. The master-equation solutions agree with the closed-form homodyne steady state (R2>0.9999R^2 > 0.9999R2>0.9999) and with an approximate analytic ODMR theory (peak positions within 0.012 MHz). For a critically coupled readout with room-temperature electronics, combining the three edges gives a projected sensitivity of 93 pT/Hz\sqrt{\rm Hz}Hz​, a 3\sqrt{3}3​-fold gain over the best single edge. Mapping the sensitivity against the NV-magnon coupling reveals an optimum near gens/2π≈0.2g_{\rm ens}/2π\approx 0.2gens​/2π≈0.2-0.40.40.4 MHz, where it reaches 72 pT/Hz\sqrt{\rm Hz}Hz​ for a 0.64 MHz spin linewidth and 19 pT/Hz\sqrt{\rm Hz}Hz​ for 0.17 MHz, with thermal limits of 6.6 and 1.7 pT/Hz\sqrt{\rm Hz}Hz​. The antenna-mode coupling, the NV-magnon coupling and the spin linewidth are therefore the main design levers.
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.