A Multilevel Optical Bloch Framework for Saturated Absorption Spectroscopy in the Hyperfine Paschen–Back Regime

High magnetic fields are often encountered in applications such as medical imaging, plasma science, and fusion research, where accurate field determination is essential for quantitative interpretation. In these environments, conventional sensors can be difficult to deploy, susceptible to electromagnetic interference, or lacking in intrinsic calibration. Atomic magnetometry offers an alternative approach, as magnetic-field information is directly encoded in atomic energy levels defined by fundamental constants. In strong magnetic fields, alkali atoms enter the hyperfine Paschen-Back regime, producing strongly field-dependent transitions that can be exploited for magnetometry using saturated absorption spectroscopy (SAS).

Here we present a comprehensive optical Bloch equation framework for modeling pump-probe SAS of ⁸⁷Rb in magnetic fields extending into the hyperfine Paschen--Back regime, with experimental validation in a vapor cell at 0.2 - 0.4 T. Our approach explicitly incorporates a multilevel structure and velocity averaging, enabling the simulation of realistic sub-Doppler spectra under strong-field conditions. The calculated fluorescence-based spectra are consistent with experimental measurements.

This framework provides a physics-based interpretation of saturated absorption spectra in strong magnetic fields and can be used to generate high-fidelity synthetic datasets for machine learning. We will present progress towards demonstrating autonomous magnetometry in the high-field regime.