Model Predictive Control for Real-Time Stabilization of Magnetic Field Using NMOR Atomic Magnetometers

Accurate calibration of atomic magnetometers and the detection of weak magnetic signals in applications such as biomagnetism and fundamental physics experiments are hindered by low-frequency environmental disturbances that mask useful signals. To address this, we implement a magnetic field reference source system that integrates a nonlinear magneto-optical rotation (NMOR) atomic magnetometer with a predictive-control-based active compensation loop. The system establishes a quiet and stable magnetic environment, supporting both magnetometer calibration and weak-field measurements. By modeling the NMOR response, the relation between field variation and demodulated phase is derived and used as a robust error signal for stabilization. Under a 10 000-nT bias field, the system suppresses low-frequency noise by 42.6 dB compared with passive shielding and achieves residual levels of 264 fT/(Hz)^1/2 at 0.1 Hz. Allan deviation analysis further verifies improved long-term stability, enabling accurate biomagnetic and low-field NMR studies as well as performance evaluation of precision magnetometers.