Optical Bloch equations with dual photon excitation explain the polarization dependence of four wave mixing quantum beats

We explain the polarization dependence of four wave mixing (FWM) quantum beats for semiconductors as essentially due to the spin phase correlations of photo-excited electrons, rather than to Coulomb interaction between the electrons. A theoretical analysis is given within the framework of optical Bloch equations for the light-semiconductor interactions and the Luttinger-Kohn model for the band structure. Residual Coulomb interactions between charge carriers are ignored. The results suggest that the polarization dependence of FWM quantum beats is a purely coherent effect of dual photon excitations, rather than, e.g., exciton-exciton Coulomb interaction. We show that the coherence transfer between the excited states is responsible for the FWM in a configuration with orthogonally polarized pump and probe.