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

Abstract

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 multi-level system (MLS) by an effective two-level system (TLS) 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 D2-line of 87 Rb atoms but it could be generalized to any closed transition of a multi-level quantum system.

Quantitative absorption imaging of optically dense effective two-level systems

“…As shown in [5], the coherent scattering properties of a TLS probed by circularly polarized light are almost insensitive at first order to experimental imperfections such as magnetic bias orientation or incident polarization. Nevertheless, in the same paper, it was shown that the presence of an incoherent electromagnetic background will influence the coherent response of atoms.…”

“…where I sat is the saturation intensity which is related to the cross section by σ 0 = ωΓ/(2I sat ). For a multi-level system, it can be shown [5] that the coherent scattering rate is reduced and takes the form…”

“…The electromagnetic field and intensity therefore only depend on z. For a resonant σ polarized probe, the scattering properties of an atom embedded in an incoherent electromagnetic background are well described [5] by an effective TLS. Its coherent and total scattering rates, as deduced from the density matrix calculation, are given by :…”

“…To get rid of the former constraint, the BLL can be easily modified and yields a decay of the light intensity following Lambert W function [2]. This solution is exact in a dilute medium of two-level atoms and was used to develop absorption imaging technics and derivatives [3] Including the full multi-level nature of an atomic system is straightforward under perfectly polarized probing, as it is only a matter of computing the effective dipole strength [4,5]. To modify minimally the BLL, Reinaudi et al [6] originally proposed to reduce the saturation intensity with a single parameter α, globally encapsulating any deviation from the idealized BLL.…”

“…We recently demonstrated [5] by solving the multilevel Optical Bloch Equations in the single atom picture that stray magnetic fields or an imperfect probe polarization have little influence on α, although an incoherent pumping dramatically increases its value.…”