Effective two-level approximation of a multilevel system driven by coherent and incoherent fields

The numerical simulation of multiple scattering in dense ensembles is the mostly adopted solution to predict their complex optical response. While the scalar- and vectorial-light-mediated interactions are accurately taken into account, the computational complexity still limits current simulations to the low saturation regime and ignores the internal structure of atoms. Here, we propose to go beyond these restrictions, at constant computational cost, by describing a multilevel system by an effective two-level system that best reproduces the coherent and total scattering properties in any saturation regime. The correspondence of our model is evaluated for different experimentally realistic conditions such as the modification of the driving field polarization, the presence of stray magnetic fields, or an incoherent resonant electromagnetic field background. The trust interval of the model is quantified for the D-2 line of( 87)Rb atoms, but it could be generalized to any closed transition of a multilevel quantum system.