Demonstration of diamond nuclear spin gyroscope

Abstract

We demonstrate the operation of a rotation sensor based on the nitrogen-14 (¹⁴N) nuclear spins intrinsic to nitrogen-vacancy (NV) color centers in diamond. The sensor uses optical polarization and readout of the nuclei and a radio-frequency double-quantum pulse protocol that monitors ¹⁴N nuclear spin precession. This measurement protocol suppresses the sensitivity to temperature variations in the ¹⁴N quadrupole splitting, and it does not require microwave pulses resonant with the NV electron spin transitions. The device was tested on a rotation platform and demonstrated a sensitivity of 4.7°/$\sqrt{\mathrm{s}}$ (13 mHz/$\sqrt{\text{Hz}}$), with a bias stability of 0.4 °/s (1.1 mHz).

Fig. 1.. Experimental setup.

Electrical connections for the laser and the photodetector are wired to the rotating platform through slip-ring lines. RF signals are delivered to the platform via a single-channel RF rotary joint. NA, numerical aperture. ND, neutral density.

Fig. 2.. DQ measurement protocol using ¹⁴N nuclear spins in diamond.

(A) Energy-level diagram of the NV center ground state with and without a magnetic field B applied along the NV axis. The inset depicts the ¹⁴N nuclear spin levels, where the splitting between the ∣m_I = ±1⟩ sublevels depends on the applied field and on the rotation of the sample around the NV axis. Rotation sensing is based on the measurement of this interval. (B) DQ nuclear Ramsey pulse sequence. Inset: 4-Ramsey phase cycling measurement scheme. (C) DQ nuclear Ramsey fringes (R1, R2, R3, and R4) obtained by sequentially alternating phases of the last double quantum pulse as depicted in the inset of (B). The frequency-domain spectrum shows the square of the absolute value of the Fourier transform, which reveals DQ signal at f_DQ frequency and residual single-quantum (SQ) signals at f₁ and f₂ frequencies. Bottom left: DQ nuclear 4-Ramsey fringes obtained by combining four DQ sequential Ramsey measurements R = R1 − R2 + R3 − R4 to cancel residual SQ signals. (D) DQ nuclear 4-Ramsey fringes. Symbols represent experimental data, while the solid line is an exponentially decaying sine wave fit. The oscillation frequency of the signal corresponds to the f_DQ, while an exponential decay time corresponds to the nuclear DQ spin coherence time $T_2^{*}$= 1.95(5) ms. Inset: Zoomed plot of DQ 4-Ramsey fringes near the working point; rotation measurements were performed at a fixed free precession time τ ≈ 1.4 ms by monitoring changes in the fluorescence signal.

Fig. 3.. Diamond gyroscope: Rotation sensing.

(A) Diamond gyroscope fluorescence signal R measured as a function of the rotation rate of the platform (average of 15 traces; 200 s per trace). The calibration coefficient α is determined from the linear fit. Inset: Time stability of α. Fractional change in α is measured over several hours. (B) The rotation rates both measured by the diamond gyroscope and reported by the rate table are averaged over each second and then plotted together as a function of time. The time dependence is programmed to trace “NV.”

Fig. 4.. Diamond gyroscope: Allan deviation.

Diamond gyroscope noise measurement as a function of averaging time. The diagonal dash-dotted line shows a $1/\sqrt{t}$ dependence consistent with a white frequency noise.