Stability improvement of nuclear magnetic resonance gyroscope with self-calibrating parametric magnetometer

In this paper, we study the stability of nuclear magnetic resonance gyroscope (NMRG), which employs Xe nuclear spins to measure inertial rotation rate. The Xe spin polarization is sensed by an in situ Rb magnetometer. The Rb magnetometer works in a parametric oscillation mode (henceforth referred to as the Rb parametric magnetometer, or Rb PM), in which the Larmor frequency of the Rb spins is modulated and the transverse components of Xe nuclear spin polarization are measured. As the measurement output of the Rb PM, the phase of the Xe nuclear spin precession is eventually converted to the Xe nuclear magnetic resonance (NMR) frequencies and the inertial rotation rate. Here we provide a comprehensive study of the NMR phase measured by the Rb PM, and analyze the influence of various control parameters, including the dc magnetic field, the frequency and phase of the modulation field, and the Rb resonance linewidth, on the stability of the NMR phase. Based on these analyses, we propose and implement a self-calibrating method to compensate the NMR phase drift during the Rb-PM measurement. With the self-calibrating Rb PM, we improve the bias instability of the NMRG from 1 to 0.2 deg/hr for datasets of 8 h, or to 0.02 deg/hr for the best approximately 5000 s dataset.