Magneto-optical rotation: Accurate approximated analytical solutions for single probe atomic magnetometers

TL;DR

This paper develops an accurate approximate analytical solution for single-probe atomic magnetometers, improving understanding and potential design of these devices by providing solutions where none previously existed.

Contribution

It introduces the first approximated analytical solution for a four-state atomic magnetometer, extending to three-state systems, with high accuracy across broad parameters.

Findings

Excellent agreement with numerical solutions

Applicable across broad probe power and detuning ranges

Enables analytical insights into atomic magnetometer behavior

Abstract

We report an approximated analytical solution for a single-probe four-state atomic magnetometer where no analytical solution exists. This approximated analytical solution demonstrates excellent accuracy in broad probe power and detuning ranges when compared with the numerical solution obtained using a 4th order Runge-Kutta differential equation solver on MATLAB. The theoretical framework and results also encompass widely applied single-probe three-state atomic magnetometers for which no analytical solution, even approximated, is available to date in small detuning regions.