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. 2024 Nov 28;15(1):10320.
doi: 10.1038/s41467-024-54333-8.

A spin-refrigerated cavity quantum electrodynamic sensor

Affiliations

A spin-refrigerated cavity quantum electrodynamic sensor

Hanfeng Wang et al. Nat Commun. .

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 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 sensitivity enabled by spin refrigeration.

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Conflict of interest statement

Competing interests: The authors declare no competing interests.

Figures

Fig. 1
Fig. 1. Hybrid NV-cavity system.
a A diamond containing an NV ensemble is located at the mode maximum of the TE01δ mode of a dielectric resonator. A green laser is applied to continuously polarize the NV spins to the ms=0 electronic ground state, and a detection loop is incorporated to electrically probe the system. The cavity field is denoted as α, the input drive field as βin, detected output field as βout, the NV-cavity coupling rate g, NV decoherence rate γ, cavity intrinsic loss rate as κc and cavity-drive coupling κc1. b NV-cavity energy level structure. The NV electron spin ms = 0 to ms = 1 transition, cavity, and drive fields have frequencies ωs, ωc, and ωd respectively, resulting in spin-cavity detuning Δs = ωc − ωs and drive-cavity detuning Δ = ωc − ωd. The NV spin transition frequency is tuned with an external magnetic field B, has an inhomogeneous width Γ, and is optically polarized at a rate γp. c Reflection ∣r2 as a function of spin-cavity and drive-cavity detuning. Three avoided crossings, labeled 1+, 2+, and 3+, indicate strong coupling to each of the three NV sub-ensembles shifted by 14N hyperfine coupling.
Fig. 2
Fig. 2. cQED sensor nonlinear model.
a Power reflection coefficient ∣r2 (blue) and reflected power P0 (red) with resonant tuning (Δ = Δs = 0). Circles are experimental data, solid lines are model results using parameters κc1 = 2π × 125 kHz, κc = 2π × 130 kHz, Γ = 2π × 330 kHz, γ0 = 2π × 26 kHz, g = 2π × 190 kHz, L = 0.53. The optical excitation rate, I, is related to the effective longitudinal relaxation, γp and the equilibrium polarization, P¯, through the expressions given in Supplementary Note IID. The dashed line shows the model result assuming zero inhomogeneous broadening. The saturation power Ps is plotted with the dash-dotted lines in abd. b Experimental imaginary component of the cavity reflection coefficient as a function of probe (Δ) and atom-cavity (Δs) detunings for microwave input powers P = − 50 dBm,  − 18 dBm, and  − 8 dBm. c Device signal S as a function of input microwave power at fixed optical polarization rate γp = 2π × 1.36 kHz. Blue dots: experimental data. Red line: theoretical plot from nonlinear theory using the parameters given above. Green dotted line: the signal S predicted by the spectroscopic signature model presented in. The indicated points 1, 2, 3 correspond to the spectra shown in b. d Device signal S as a function of input microwave power and optical polarization rate. The operating point that maximizes signal S is indicated with the blue dot e, S as a function of optical polarization rate at microwave power P = − 22 dBm. The nonlinear model is the red curve and experimental measurements are blue points. The errorbar is smaller than the marker.
Fig. 3
Fig. 3. Spin refrigeration.
a Noise reduction with different microwave driving powers P. Blue (red) dots show the noise in 1 Hz bandwidth at 15 kHz offset in two regimes of spin-cavity detuning Δs ≠ 0 (Δs = 0). The left axis shows the relative change in power spectral density compared to a 50 Ω reference measurement, and the right axis shows the voltage amplitude spectral density. All measurements were taken with a power gain of 36.5 dB and the values are doubled-sided. The blue curve shows the noise model considering thermal and phase noises. The red curve shows the noise model with linear steady-state cooling (See Methods). The green curve is the contribution of mode cooling alone, without thermal or phase noises. Inset: frequency-resolved noise reduction with P = − 58 dBm and Δs = 0. b Sensitivity η at 15 kHz offset with different microwave power (blue dots). The blue curve shows the sensitivity corresponding to the room temperature limit η0. The red dots show the sensitivity difference Δη/η = (η − η0)/η0. We observe sub-thermal sensitivity with P < − 18 dBm. The errorbar is smaller than the marker.
Fig. 4
Fig. 4. Broadband magnetometry.
Sensitivity of the cQED sensor as a function of magnetic field frequency derived from the voltage noise floor of the device. Red: The magnetic-field-equivalent noise floor of the microwave circuitry, including low noise amplifier, circulator, and mixer, measured by replacing the cQED sensor with a 50 Ω terminator. Green: The field-equivalent noise floor of the cQED sensor with NV spins detuned (Δs = 5 MHz). Blue: Magnetic field sensitivity at the optimized operating point. Inset: the magnetic field sensitivity is around 20 kHz showing the mode cooling effect. We achieve a sub-room-temperature Johnson-Nyquist limit sensitivity of η = 576 ± 6 fT/Hz.
Fig. 5
Fig. 5. Cavity and spin optimization predicted by the nonlinear model.
a Magnetic field sensitivity with different diamond volumes Vd and NV density ρ. The diamond volume is normalized by the cavity mode volume (V = 1.7 cm3). Three dotted lines show the contour of the sensitivity η=5fT/Hz, 50fT/Hz, and 500fT/Hz. The blue dot shows the current device and the green dot shows the best sensitivity achievable from an optimized diamond using the cavity shown in this work. The black dotted line shows the optical polarization limit. b Magnetic field sensitivity with different unloaded quality factors Q and single coupling strength gs. The red dots show cavity design for stripline cavities or superconducting circuits. Blue dots various three-dimensional cavity designs from. The current device is shown as a yellow cylinder.

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