Dynamics-Controlled Truncation Scheme for Nonlinear Dynamics in Semiconductor Microcavities

Abstract

We present a systematic theory of Coulomb-induced correlation effects in the nonlinear optical processes within the strong-coupling regime. In this paper we shall set a dynamics controlled truncation scheme \cite{Axt Stahl} microscopic treatment of nonlinear parametric processes in SMCs including the electromagnetic field quantization. It represents the starting point for the microscopic approach to quantum optics experiments in the strong coupling regime without any assumption on the quantum statistics of electronic excitations (excitons) involved. We exploit a previous technique, used in the semiclassical context, which, once applied to four-wave mixing in quantum wells, allowed to understand a wide range of observed phenomena \cite{Sham PRL95}. We end up with dynamical equations for exciton and photon operators which extend the usual semiclassical description of Coulomb interaction effects, in terms of a mean-field term plus a genuine non-instantaneous four-particle correlation, to quantum optical effects.