Theory of exciton-exciton correlation in nonlinear optical response

Abstract

We present a systematic theory of Coulomb interaction effects in the nonlinear optical processes in semiconductors using a perturbation series in the exciting laser field. The third-order dynamical response consists of a phase-space filling correction, a mean-field exciton-exciton interaction, and two-exciton correlation effects expressed as a force-force correlation function. The theory provides a unified description of effects of bound and unbound biexcitons, including memory effects beyond the Markovian approximation. In the degenerate four-wave-mixing experiments, correlation effects are shown leading to polarization mixing, ringing, etc. The strong interaction, a nonperturbative theory of the correlation function, is numerically evaluated for a one-dimensional model. Approximations for the correlation function are presented.