Exciton-Exciton Correlation in the Nonlinear Optical Regime

We present a theory of the time development of the nonlinear optical excitations in a semiconductor in which the correlated part of the many-body problem is expressed in terms of the exact $N$-exciton eigenstates and is decoupled from the optical excitation process. A first-principles exact numerical solution for the four-wave mixing in a one-dimensional model demonstrates the role of two-exciton correlation in polarization mixing and, in particular, shows a ringing of the polarization with the frequency given by the binding energy of the biexciton.