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We present a systematic theory of Coulomb-induced correlation effects in thenonlinear optical processes within the strong-coupling regime. In this paper weshall set a dynamics controlled truncation scheme \cite{Axt Stahl} microscopictreatment of nonlinear parametric processes in SMCs including theelectromagnetic field quantization. It represents the starting point for themicroscopic approach to quantum optics experiments in the strong couplingregime without any assumption on the quantum statistics of electronicexcitations (excitons) involved. We exploit a previous technique, used in thesemiclassical context, which, once applied to four-wave mixing in quantumwells, allowed to understand a wide range of observed phenomena \cite{ShamPRL95}. We end up with dynamical equations for exciton and photon operatorswhich extend the usual semiclassical description of Coulomb interactioneffects, in terms of a mean-field term plus a genuine non-instantaneousfour-particle correlation, to quantum optical effects.

Dynamics-Controlled Truncation Scheme for Nonlinear Dynamics in Semiconductor Microcavities