Coherent effects in the physics of composite excitons
Résumé
Up to now, the many-body theory for composite excitons we have constructed has applied to excitons made of electrons and holes having all the same spins. The fact that excitons are not elementary quantum particles is even more important when various spins are present, because the Pauli scatterings of two bright excitons with opposite spins generate two dark excitons. We show how to extend our theory to ``coherent composite excitons'' which are linear combinations of excitons having different spins, as the ones coupled to linearly polarized photons. This extension is indeed necessary to possibly predict the nontrivial polarization effects which can take place in these coherent systems. We calculate two important quantities of the exciton many-body physics: namely, the normalization factor of N coherent composite excitons coupled to photons having an arbitrary polarization and the expectation value of the system Hamiltonian in this N-exciton state. We show that the possible escape of bright excitons into dark states resulting from their Pauli scatterings makes a decrease of the exchange part of these quantities by a factor (cos(2n) theta+sin(2n) theta), where theta is the ellipticity of the coherent composite excitons while n is the number of excitons involved in the exchange process at hand. The Shiva diagrams for N-body exchanges we have recently introduced make transparent the origin of this nontrivial coherence effect.