Analyzing power errors in the optical pumping system of atomic spin comagnetometers

The spin exchange relaxation-free (SERF) atomic comagnetometer is a highly sensitive device designed to measure rotation rates with extreme precision. The ability of the proposed method to suppress disturbances from external magnetic fields makes it ideal for various applications, particularly in long-term navigation systems where accuracy and stability are paramount. Beyond navigation, SERF comagnetometers are valuable tools for geophysics and geological exploration, offering reliable tools for high-precision measurements. They also play a crucial role in fundamental physics research, including testing Lorentz symmetry and charge–parity–time (CPT) symmetry, which are essential for understanding potential deviations from standard physical theories. A significant challenge in the SERF comagnetometers performance is power errors in optical pumping systems, which affect two critical operational aspects: scale factor and zero-bias stability. The scale factor determines the relationship between the input signal and the comagnetometer output, whereas zero-bias stability refers to the system’s long-term stability in the absence of an input signal. Although previous research has focused primarily on how power errors affect the scale factor, their effect on zero-bias stability remains underexplored, yet it is crucial for applications that require sustained precision. To address this gap, this study simplified the nonlinear dynamics of the K–Rb–21Ne SERF comagnetometer into a linear time-invariant system using Taylor expansion. This simplification helps analyze the system response to power errors. The study then develops a frequency response model of the optical pumping system’s power utilizing the state space method to predict how power fluctuations affect the system output. This model is an important step toward understanding how power errors propagate within a comagnetometer. An experiment was conducted to validate the derived frequency response model, where a sinusoidal wave with a peak power of 2 milliwatts was superimposed on a base pumping power of 35 milliwatts. This setup was designed to simulate real-world fluctuations in the pumping power that may occur during the comagnetometer operation. The amplitude–frequency and phase–frequency responses of the SERF comagnetometer’s output were recorded and compared with the theoretical predictions. The experimental results aligned well with the theoretical model, demonstrating the model’s accuracy in predicting the system’s response to power errors. From the amplitude–frequency response, it was found that at very low frequencies of the optical pumping power error, the output of the SERF comagnetometer is directly proportional to the changes in the pumping light power. This implies that slow drifts or fluctuations in pumping power can directly affect the long-term stability of the comagnetometer, which is critical for applications requiring minimal drift over time. However, when the power error frequency is lower than the electron Larmor frequency, the response amplitude decreases because of the slower response time of the noble gas atoms, which partially suppresses the impact of the power error. Nevertheless, this suppression is not sufficient to eliminate the power error’s influence. The study concludes that the magneto-optical nonorthogonality of the comagnetometer introduces a differential component into the power transfer function. As a result, within the device’s operational bandwidth, the output signal is approximately proportional to the pumping power. This finding reveals that fluctuations in optical pumping power can significantly affect the system’s measurement accuracy and stability, particularly over long periods.