Atomic density disturbance rejection in atomic gyroscopes via faraday polarimetric decoupling

Atomic spin gyroscopes are promising candidates for next-generation inertial navigation due to extremely high theoretical precision, relatively small size among atomic gyroscopes, and promising potential for miniaturization. In particular, the spin-exchange relaxation-free (SERF) atomic gyroscope relies on optical pumping to polarize atoms, enabling rotation sensing through the Faraday optical rotation angle (FORA). However, fluctuations in atomic density introduce systematic errors in FORA measurements, limiting long-term stability. We present a data-driven decoupling method that isolates atomic density fluctuations from the FORA signal by modeling spatially resolved light absorption in the vapor cell. The model accounts for the spatial distribution of spin polarization in the pump-light interaction volume, density-dependent relaxation rates, wall-induced relaxation, and polarization diffusion, and is implemented within a finite-element framework. Compared to the conventional Lambert-Beer law, which assumes one-dimensional homogeneity, our approach captures the full three-dimensional density and polarization distribution, significantly improving the accuracy of light absorption modeling. The resulting absorption-density maps are used to train a feedforward neural network, yielding a high-precision estimator for atomic density fluctuations. This estimator enables the construction of a decoupling equation that separates the density contribution from the FORA signal. Experimental validation shows that this method improves the bias instability at σ (100 s) of the gyroscope was improved by 73.1% compared to traditional platinum-resistance-based stabilization. The proposed framework is general and can be extended to other optical pumping-based sensors, such as optically pumped magnetometers.