Electromagnetically induced transparency in the multiple scattering regime

Here we present a microscopic model that describes the Electromagnetically Induced Transparency (EIT) phenomenon in the multiple scattering regime. We consider an ensembles of cold three-level atoms, in a $Lambda$ configuration, scattering a probe and a control field to the vacuum modes of the electromagnetic field. By first considering a scalar description of the scattering, we show that the light-mediated long-range interactions that emerge between the dipoles narrow the EIT transparency window for increasing densities and sample sizes. For a vectorial description, we demonstrate that near-field interacting terms can critically affect the atomic population transfer in the Stimulated Raman Adiabatic Passage (STIRAP). This result points out that standard STIRAP-based quantum memories in dense and cold atomic ensembles would not reach efficiency high enough for quantum information processing applications.