Faraday rotation in photoexcited semiconductors: A composite-exciton many-body effect

Abstract

We assign Faraday rotation in a photoexcited semiconductor with bright excitons all having the same spin, to the exciton composite nature through the ``Pauli interactions,'' i.e., carrier exchanges, between the real excitons present in the sample and the virtual excitons coupled to the ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ parts of the linearly polarized probe beam. While direct Coulomb interactions scatter bright excitons into bright excitons whatever their spins are, Pauli interactions scatter bright excitons into bright excitons if they have the same spin only. This makes Pauli interactions entirely responsible for the Faraday rotation: Indeed, the refractive index differenc between ${\ensuremath{\sigma}}_{+}$ and ${\ensuremath{\sigma}}_{\ensuremath{-}}$ photons comes from processes in which the virtual bright exciton, which is created by the unabsorbed probe photon, and the one which recombines to regenerate this probe photon, have zero or one common carrier. The new many-body theory for interacting composite excitons we have constructed provides quite appropriate tools to write this difference in terms of the physical parameters of the problem, namely, the photon detuning and the density of the excitons present in the sample. The multiarm ``Shiva'' diagrams that we have recently introduced to visualize $N$-body exchanges between composite excitons, make transparent the physics involved in the various terms. This work also shows the interesting link that exists between Faraday rotation and the exciton optical Stark effect we studied long ago.