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Journal of Russian Laser Research 25, 412-439 (2004)


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

H. N. Cam

By the use of a bosonization transformation and group-theoretical arguments, the Hamiltonian of an electron-hole-photon system in a laser-excited direct two-band semiconductor is transcribed into that of an exciton-photon system with the particle spins rigorously, taken into consideration. It is shown that the third-order optical nonlinearities in the spectral region below the band edge have their microscopic origin in two-exciton correlations, which are expressed in terms of the effective exciton-exciton and anharmonic exciton-photon interactions. The dependence of the interparticle interactions on the spin states of quasiparticles is behind the polarization dependence of the semiconductor nonlinear optical response. On the example of the system of heavy hole excitons in quantum wells, grown from compounds with the zinc blende type of symmetry, it is demonstrated that the effective exciton-exciton interaction in two-exciton states with nonzero total spin is repulsive, while in zero-spin states it is attractive, which may result in the biexciton formation. The derived Heisenberg equations of motion for the exciton and biexciton operators form the basis for a theoretical study of the coherent four-wave-mixing in GaAs and ZnSe quantum wells. It is readily apparent from the equations that in different polarization configurations the coherent four-wave-mixing is generated by different ingredients of two-exciton Coulomb correlations: in the co-circular configuration, it is the interexciton repulsion, in the cross-linear configuration, the formation of the biexciton and its coupling to excitons, and in the collinear configuration, both of them jointly. The obtained expressions for the time-resolved and frequency-resolved four-wave-mixing signals adequately describe the main characteristics and various details of wave mixing phenomena, including a biexciton signature in the appropriate polarization configurations. Results of the work clarify the microscopic mechanism of the polarization dependence in coherent four-wave-mixing spectroscopy in semiconductor quantum wells.