Two-Exciton States and Coherent Third-Order Response from Semiconductor Quantum Wells

We present a microscopic description of the coherent third-order response from a quantum well, treated as a quasi-two-dimensional semiconductor, in the exciton representation. We establish a closed system of dynamic equations including those for coherent spin-polarized photons and excitons and for correlated two-exciton structures, called molecules. We employ such a system of equations as a starting point for calculating all third-order contributions to the semiconductor coherent polarization in the case where the eigenenergies and eigenfunctions of the molecules are available. Considering the molecular problem, we calculate the interaction potential between excitons in molecules for quantum-well samples in the limit of small exciton momentum taking place in the close-to-normal-incidence excitation geometry. The potential computed allows an approximate explicit determination of the molecular eigenenergies and eigenfunctions in the slow scattering limit. The criterion for a coherent pump-probe experiment to support the limit is pointed out.