Physics-informed Neural-network Calibration of Pump-Probe Nonorthogonality in SERF Co-magnetometers

Abstract Pump--probe nonorthogonality causes readout bias in spin-exchange relaxation-free (SERF) co-magnetometers through longitudinal leakage into the Faraday detection channel. This paper develops a pump-power-scan calibration method and a physics-informed neural network (PINN) inverse estimator for determining the pump--probe nonorthogonality angle. The method exploits pump-power-induced changes in the longitudinal polarization, transverse response, and steady readout signal. The actual pump beam defines the experimental z-axis, and the actual probe direction is represented in this pump-fixed frame by an out-of-plane nonorthogonality angle and an in-plane skew angle. The proposed PINN embeds the pump-power-dependent optical response and the measured readout into the inverse estimation loss, enabling angle recovery from experimentally recorded scans with independent transverse-response information. An experimental dual-axis scan with calibrated detection gain recovers both probe-direction angles, with the estimates reported at a conservative precision of 0.05 mrad. A second scan covering the 14-point pump-power grid returns out-of-plane and in-plane skew estimates of 1.35 mrad and -1.65 mrad, consistent with the reference settings within a ±0.05 mrad repeatability band. Transverse-response checks are consistent with the sign reversal of the in-plane skew pathway and the stability of the two recovered angles. A linearized effective pump-power fit on the same 14-point grid achieves an RMSE of 0.0295 a.u. and a coefficient of determination of 0.9981. These results show that pump-power modulation provides an experimentally accessible response path for PINN-based pump--probe nonorthogonality calibration in SERF co-magnetometers.