Exciton-exciton scattering dynamics in a semiconductor microcavity and stimulated scattering into polaritons

We study the polariton dynamics in a semiconductor microcavity for small temperatures and zero exciton-cavity detuning, including the exciton-exciton and exciton-phonon scatterings. A bottleneck in the relaxation of excitons into lower polariton is found, which persists up to high densities. We then consider injection of large populations of lower polaritons with an external pump. All scatterings featuring the lower polariton as the final state become stimulated. In particular, scattering of two excitons into both lower and upper polaritons shows direct evidence of stimulation. Within the rate equation approach, we also predict sizable saturation effects due to the stimulated emission.