Abstract
An effective boson Hamiltonian of 1s excitons with “spin” degrees of freedom is derived through a projection procedure. This procedure yields renormalization effect, resulting in the emergence of the interaction between excitons with opposite spins. The procedure also renormalizes the scattering amplitude between excitons with the same spins. The relevant interactions for the formation of bi-excitons are identified. The present theory gives the microscopic foundation of the phenomenology that was previously introduced for analyzing a four-wave mixing experiment in a GaAs quantum well in a high-Q microcavity.
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