Analysis and suppression of the Rb resonance frequency error in NMR angular velocity sensor

The nuclear magnetic resonance (NMR) angular velocity sensor has the potential for high precision measurement in small volumes, which measures the ¹²⁹Xe and ¹³¹Xe precession frequencies to obtain the angular velocity with respect to an inertial reference frame. One of the key challenges in frequency measurement is the long-term stability of the measured signal phase. The measured signal is acquired by applying a carrier magnetic field along the z-axis and demodulating the carrier signal at its frequency, which is typically fixed. However, fluctuations in light shifts and static magnetic fields can lead to instabilities in the Rb resonance frequency, consequently impacting the measurements of phase and precession frequencies of ¹²⁹Xe and ¹³¹Xe. To address this issue, an analysis of the Rb resonance frequency error is conducted, and a suppression scheme based on carrier frequency correction is provided. This scheme can mitigate the effect of Rb resonance frequency fluctuations without further suppressing fluctuations of light shifts and static magnetic fields. The experiment demonstrates a 53.5 % reduction in the precession frequency error between ¹²⁹Xe and ¹³¹Xe and a 59.0 % decrease in bias instability. This scheme can improve the long-term stability of ¹²⁹Xe and ¹³¹Xe precession frequency measurements, thereby enhancing the performance of the NMR angular velocity sensor.