Optimization and arbitrary frequency stabilization of probe laser based on a transfer cavity in SERF Co-Magnetometer

We demonstrate an arbitrary frequency stabilization technology that can ensure both the frequency stability and tunability of the probe laser in a spin-exchange relaxation-free (SERF) atomic co-magnetometer at the frequencies far from the atomic resonance line. In theory, the non-negligible coupling between the cavity length locking and the locked laser frequency is identified and a transfer function model for the frequency stabilization system is established. The modulation multiplexing cavity length locking method and dual-phase modulation sideband locking method are designed to overcome the limitations of traditional transfer cavity method, including noise coupling and insufficient frequency tunability. Experimental results show that at a frequency far from the atomic resonance line, the Allan deviation after the frequency locking reached 8.223 × 10⁻¹¹ for an averaging time of 10³ s, which is lower by approximately two orders of magnitude than the frequency instability of free running laser. The research work is of great significance to improve the frequency stability, frequency tunability, cost-effectiveness, and compactness of the far-detuned probe laser in a SERF atomic co-magnetometer.