Exciton-boson formalism for laser-excited semiconductors and its application in coherent four-wave mixing spectroscopy

Exciton-boson formalism approach to the description of two-pair correlations in the electron-hole system in laser-excited direct semiconductors is proposed. The spin of quasiparticles is properly included by group-theoretical rules. On the example of the system of heavy hole excitons in quantum wells it is shown that two-pair Coulomb correlations consist of two components: effective repusion between excitons with nonzero total spin and attraction between excitons with zero total spin. The latter component is behind the biexciton formation and its coupling to excitons. In application to the study of coherent four-wave-mixing (FWM) it is established that the two components generate FWM respectively in the co-circular and cross-linear polarizations, and jointly in the collinear polarization. General expressions are derived for the amplitude of the FWM signal in the polarization configurations yielding analytical results in the ultrashort pulses limit. Refined by computations taking pulses temporal evolution into consideration, these results provide an adequate description of biexciton effects and the polarization dependence of coherent FWM in quantum wells.