Parametric matter in semiconductor microcavities

Recent theoretical results are presented for the non-linear dynamics of resonantly excited semiconductor microcavities in the strong exciton-photon coupling regime. Treating the microcavity polaritons as a system of interacting bosons, the model describes the very efficient polariton parametric amplification observed experimentally, including the role of multiple scattering. The theoretical analysis is also extended to account for the spontaneous scattering that determines the parametric luminescence occurring when no seeding probe is applied. The theory shows the coupled dynamics of polariton population and parametric correlation between polariton pairs. The pump-pump scattering spontaneously generates the parametric correlation which drives the build-up of the polariton population. In addition to the spontaneous generation rate, the parametric correlation is found to be stimulated by the polariton population. Concerning the spectral features of the emission, the parametric correlation produces collective modes with energy dispersion which can be dramatically off the usual polariton branch and with pronounced negative mass.