Microscopic description of exciton polaritons in direct two-band semiconductors

Based on a quantum electrodynamical formulation, a microscopic description of exciton polaritons in a two-band semiconductor is presented. We show tha t the interband exchange Coulomb interaction, responsible for the coupling of the exciton with the longitudinal part of the induced field, should be t reated on equal footing together with the coupling to the transverse part o f the induced field (the photon field). The constitutive relation is establ ished to connect the current density with the total electric field of polar itons. The classical Maxwell equations are derived from the quantum represe ntation of photons to get a closed system of equations. The temporal evolut ion for an initial excited exciton state is studied in detail and an anisot ropic polariton vacuum Rabi splitting is shown to occur. A number of up-to- now unresolved discrepancies in the literature are clarified.