A saturation-absorption rubidium magnetometer with multilevel optical Bloch-equation modeling for intermediate-to-high fields

TL;DR

This paper introduces a high-field rubidium magnetometer that uses advanced modeling of atomic spectra to accurately measure magnetic fields in the intermediate-to-high regime, enabling applications like MRI and fusion research.

Contribution

The work develops a multilevel optical Bloch-equation model for high-field rubidium spectra and demonstrates precise magnetic field measurement up to 0.4 T, advancing atomic magnetometry techniques.

Findings

Achieved magnetic field measurement with ±0.0017 T precision from 0.2 T to 0.4 T

Developed a comprehensive spectral model that matches experimental data in high magnetic fields

Established a foundation for machine learning-based autonomous magnetometry

Abstract

We present SASHMAG (Saturated Absorption Spectroscopy High-field MAGnetometer), an atomic sensor designed for precision magnetic-field measurements in the intermediate-to-high field regime ($>0.2\,\text{T}$) using Rubidium-87 ($^{87}Rb$). The sensor operates in the hyperfine Paschen-Back regime, where the hyperfine and Zeeman interactions decouple, and utilizes counter-propagating pump-probe configuration in Faraday geometry to resolve isolated, Doppler-free Zeeman transitions. To interpret the resulting spectra in this strongly field-dependent regime, we developed a comprehensive multilevel optical Bloch-equation model solved explicitly in the uncoupled $\ket{m_I, m_J}$ basis, capturing state mixing and nonlinear saturation dynamics. This model reproduces measured spectra at sub-Doppler resolution and is consistent with analytical expectations for power broadening and thermal Doppler scaling. Magnetic field estimation is performed using a physics-constrained optimization routine that infers the magnetic field by minimizing the residual between experimentally extracted line centers and calculated transition frequencies from the field-dependent Hamiltonian. We demonstrate magnetic field retrieval from $0.2\,\text{T}$ to $0.4\,\text{T}$ with a precision of $\pm 0.0017 \,\text{T}$). Furthermore, the validated simulation establishes a foundation for generating synthetic training datasets, paving the way for autonomous, Machine Learning-enhanced magnetometry in applications ranging from MRI to fusion reactors.