Optical nonlinearity of a cold atomic ensemble driven by a strong coherent field in a saturation regime

We present a microscopic analysis and evaluation of the dielectric susceptibility of a dielectric medium consisting of vector-type two-energy-level atoms, responding to a weak probe mode, when the atoms are driven by a strong coherent field. Each atom, in an environment of others, exists as a quasiparticle, further structuring the bulk medium. In a limit of dilute atomic gas, the dynamics of each atom follows the Mollow-type nonlinear excitation regime, and the medium susceptibility collectivizes the individual atomic responses to the probe mode. We outline how the collective dynamics can be interpolated up to a dense medium, and we argue from general positions that in such a medium, the optical nonlinearity and, in particular, its parametric part could be significantly magnified by manipulating both the coherent pump and the sample density. This indicates certain limitations for potential capabilities of quantum communication protocols utilizing entangled photons created by a parametric process as a main resource of quantum correlations.