Statistics of microcavity polaritons under non-resonant excitation

A model describing amplification and quantum statistics of the exciton polaritons with k=0 in a non-resonantly excited semiconductor quantum well embedded in a microcavity is presented. Exploiting the bottleneck effect for exciton polaritons, it is assumed that the polaritons with k different from 0 act as a reservoir. The time evolution of the k=0 polaritons is described by a master equation, in which two- and one-polariton transitions between the mode with k=0 and the reservoir are accounted for. The k=0 mode exhibits a threshold depending on the material parameters and on the injected exciton density. Below threshold the quantum statistics of the emission is characteristic of an incoherent process, while above threshold it approaches that of a laser.