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

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