Quasibosonic exciton dynamics near the semiconductor band edge

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Abstract
We develop a heirarchy of equations that describes the electrodynamics of the semiconductor band edge. An exciton basis that incorporates intrapair Coulomb interaction is used. The excitons are treated as quasibosons that satisfy commutation relations intermediate between bosonic and fermionic. Their nonlinear dynamics are a consequence of phase-space filling and an effective exciton-exciton interaction that depends only on their center-of-mass wave vectors and internal quantum numbers. The resulting expansion in powers of the optical field is analogous to Axt and Stahl’s dynamically controlled truncation, but takes a simpler form. If damping is omitted or if all interband and intraband dephasing time constants are the same, we find a set of relationships among the interband and intraband correlation functions which in the free pair basis give the semiconductor Bloch equations.