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arXiv:cond-mat/0702431 · Physical Review Letters

Excitations in a Nonequilibrium Bose-Einstein Condensate of Exciton Polaritons

Michiel Wouters, Iacopo Carusotto

Published Oct 3, 2007• 653 citations
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Abstract

We develop a mean-field theory of the dynamics of a nonequilibrium Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity. The spectrum of elementary excitations around the stationary state is analytically studied by means of a generalized Gross-Pitaevskii equation. A diffusive behavior of the Goldstone mode is found in the spatially homogeneous case and new features are predicted for the Josephson effect in a two-well geometry.

DOI
10.1103/physrevlett.99.140402

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Abstract The dynamics of an exciton–polariton Bose–Einstein condensate in an optical microcavity was considered. A novel version of the stochastic Gross–Pitaevskii equation was proposed to describe the condensate evolution under the non-Markovian interaction with the environment. The proposed version was used to analyze the condensate dynamics at various temperatures. The phase transition from the homogeneous to the fragmented state of the condensate near a temperature of 15 K was detected. This phase transition is accompanied by a sharp drop in the condensate density and a decrease in the correlation length. It was found that, at a temperature of 10 K, the correlation length oscillates with time. The results obtained indicated the necessity to take into account the non-Markovianity of the condensate interaction with the excitonic reservoir.
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We study the behavior of exciton polaritons in an optical microcavity with an embedded semiconductor quantum well. We use a two-component exciton-photon approach formulated in terms of path integral formalism. In order to describe spatial distributions of the exciton and photon condensate densities, the two coupled equations of the Gross-Pitaevskii type are derived. For a homogeneous system, we find the noncondensate photon and exciton spectra, calculate the coefficients of transformation from the exciton-photon basis to the lower-upper polariton basis, and obtain the exciton and photon occupation numbers of the lower and upper polariton branches for nonzero temperatures. For an inhomogeneous system, the set of coupled equations of the Bogoliubov--de Gennes type is derived. The equations govern the spectra and spatial distributions of noncondensate photons and excitons.