Analysis on the power error for the optical pumping system in the atomic spin comagnetometer

The atomic spin comagnetometer based on the Spin Exchange Relaxation-Free (SERF) regime boasts ultra-high sensitivity for rotation rate measurement and excellent suppression of magnetic field disturbances, making it a promising tool for long-term navigation applications. Additionally, SERF comagnetometers have applications in geophysics and geological exploration, providing reliable tools for precision measurements. They have been widely used in Lorentz and CPT tests. However, the power error from the optical pumping system limits the performance of SERF comagnetometers in two key areas: the scale factor and zero-bias stability. Current analyses of power errors in SERF comagnetometers primarily focus on the scale factor, with a notable lack of analysis regarding zero-bias stability. To address the impact of power errors on the system's zero-bias stability, the nonlinear dynamics of the K-Rb-21Ne comagnetometer have been simplified into a linear time-invariant system using Taylor expansion. This paper derives the frequency response model of the optical pumping system's power for the K-Rb-21Ne comagnetometer based on the state space method. To validate the frequency response model, a sinusoidal wave with a peak power of 2 milliwatts was superimposed on a base pumping power of 35 milliwatts. The amplitude-frequency response and phase-frequency response of the SERF comagnetometer output were then recorded to fit the theoretical frequency response model. The theoretical model fits the test results well, demonstrating its credibility. From the amplitude-frequency response results, it can be concluded that when the frequency of the optical pumping power error is very low, the output of the SERF comagnetometer is directly proportional to changes in the pumping light power. Therefore, slow drifts in the pumping power will directly impact the long-term stability of the SERF comagnetometer. When the frequency of the power error is lower than the electron Larmor frequency, the response amplitude decreases due to the slower response of the noble gas, which can suppress a certain amount of the power error effects. However, this suppression effect is quite limited. In summary, both theoretical and experimental results indicate that the magneto-optical non-orthogonality of the comagnetometer introduces a differential component into the power transfer function. This results in the comagnetometer's output signal being approximately proportional to the pumping power within its operational bandwidth. The study provides an accurate model for analyzing inertial measurement errors caused by fluctuations in the pumping power within the SERF comagnetometer. Additionally, it offers theoretical support for subsequent efforts aimed at suppressing power errors from the optical pumping system.