Effects of Zeeman degeneracy on the steady-state properties of an atom interacting with a near-resonant laser field: Analytic results

The analytic solution of the steady-state density matrix is presented for a closed two-level atom with an arbitrary ground-state angular momentum ${\mathit{J}}_{\mathit{g}}$ and an excited-state angular momentum ${\mathit{J}}_{\mathit{e}}$ interacting with a linearly polarized laser field. From this solution, analytic formulas for the total rate of laser-atom scattering, the rate of coherent scattering, and radiative forces are derived. Interestingly, it is found that population inversion in true atomic states, as opposed to the population inversion in the dressed states, can occur under certain conditions. A method is proposed to take advantage of this inversion for light amplification. The mathematical formulation is built around the concept of the resolvent operator in Liouville space, with some conclusions that are generally applicable to any system with a unique steady state.