Quantum-wire excitons: Polaritons and exchange effects

Exciton-polariton dispersion and long-range exchange energy in quantum wires are obtained by a Green’s-function approach. The quasi-one-dimensional generalization of the longitudinal-transverse splitting (long-range exchange interaction) is shown to be a consequence of the completeness relation satisfied by the set of optical modes. Exchange splittings of 0.3 meV are predicted for state-of-the-art GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wires, while polariton splittings are expected to be smaller. The effects on the polariton dispersion and long-range exchange splittings of embedding the quantum wire in an optical microcavity are discussed.