Enhancing Faraday rotation effect in SERF Co-Magnetometers using Multi-Reflection cavities

Enhancing the interaction strength between light and atoms amplifies the Faraday rotation effect, thereby improving the measurement sensitivity of optical rotation detection. This work integrates a multi-reflection cavity into the vapor cell of the SERF co-magnetometer for the first time, increasing the interaction strength between light and atoms. However, the multi-reflection cavity causes the issue of biaxial coupling of the output signal. Additionally, the high operating temperature and high-atomic-density conditions of the SERF co-magnetometer result in complex cavity reflection modes, necessitating an accurate assessment of the completeness of the reflection modes within the cavity. To address the above issues, we first establish a response model that accounts for light propagation in multiple directions, clarifying the impact of the sensitive-axis component on the output signal and improving the system's measurement accuracy. Subsequently, we propose the reflection mode integrity validation method, which ensures the stable and effective operation of the multi-reflection cavity in the SERF co-magnetometer. Experimental results show that the Faraday rotation effect is enhanced by a factor of 13.6 compared to single-pass, which closely matches the designed 14 reflections, thereby verifying the accuracy of the response model and the reflection count measurement. This paper offers a new approach to enhancing the sensitivity of SERF co-magnetometers and offers guidance for the integration of optical cavities into such systems.