In situ real-time measurement for electron spin polarization in atomic spin gyroscopes

Atomic spin gyroscopes (ASGs) based on spin-exchange relaxation-free (SERF) co-magnetometers represent a new generation of ultra-high-precision inertial sensors. However, their long-term stability is significantly constrained by the stability of electron spin polarization. Despite its critical importance, current research lacks effective methods for in situ and real-time measurement of electron spin polarization. This paper addresses this gap by developing a model for pump laser propagation within the vapor cell and proposing an Euler-particle swarm optimization (PSO) algorithm to estimate the model's unknown parameters. By utilizing artificial neural networks, we derive an output equation for electron spin polarization, using transmitted laser power and cell temperature as independent variables. Comparative experiments validate the accuracy of the proposed method, and perturbation experiments demonstrate its real-time capability. The proposed in situ real-time measurement method for electron spin polarization lays a solid foundation for improving closed-loop control and enhancing the long-term stability of ASGs.