Zero-Position Closed-Loop Control of Nuclear Spin in a K-Rb- 21 Ne $^{21}{\rm Ne}$ Comagnetometer

In SERF (spin-exchange relaxation-free) comagnetometers, the fluctuation of the atomic ensemble's polarization significantly impacts the long-term stability of the output signal. A real-time closed-loop control method for the nuclear spin polarization is proposed, and the measurement model is established using Kalman state observer. Furthermore, magnetic field control signals are generated using a proportional-integral-derivative (PID) strategy, which is then applied to the atomic ensemble to dynamically adjust the nuclear spin polarization. Finally, closed-loop control of nuclear spin polarization is achieved through continuous feedback and control. Moreover, experiments have demonstrated that implementing a closed-loop system for nuclear spin zero-position is conducive to reducing the sensitivity of the output signal to fluctuations in the external environment. The experimental results show that the Allan deviation at 100 s is reduced by $44.3\%$, and the sensitivity of inertial rotation measurement is significantly improved, that is, the noise level at 1 Hz is suppressed by approximately $60\%$.