Polarisation properties of exciton-polaritons in semiconductor microcavities

Abstract

Interactions of exciton-polaritons in semiconductor microcavities and the resulting polarisation dynamics are investigated theoretically. Within the coboson framework of polariton-polariton scattering, it is shown that the matrix element of direct Coulomb scattering is proportional to the transferred momentum, q, cubed in the limit of small q. In the same limit, the magnitude of superexchange/exchange interactions can be considered constant. These results are applied to the elastic circle geometry, where a system of equations describing the steady-state pseudospin components is derived. It is shown, that for this geometry, polariton-polariton scattering can account for the generation of circularly/linearly polarised final states from linearly/circularly polarised initial states, depolarisation and the generation of spin currents. In the low density regime polaritons are good bosons and the dynamics of polariton Bose-Einstein condensation (BEC) are investigated. A stochastic model is derived, resulting in a Langevin type equation describing the time dynamics of the condensate spinor order parameter. The build up in condensate polarisation degree is shown to evidence macroscopic ground state population, while the stochastic choice of polarisation vector evidences the symmetry breaking nature of the phase transition. The decrease of polarisation degree above threshold is demonstrated to be a consequence of polariton-polariton interactions, a result which is complemented by recent experimental work. The stochastic model is extended to include Josephson coupling of spatially separate condensates. The coupling results in polarisation and phase correlations between the condensates, explaining the polarisation locking and spatial coherence seen experimentally. Finally, the effect of polarisation pinning by local effective fields is examined.

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