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We theoretically investigate a Bose-condensed exciton gas out of equilibrium.Within the framework of the combined BCS-Leggett strong-coupling theory withthe non-equilibrium Keldysh formalism, we show how the Bose-Einsteincondensation (BEC) of excitons is suppressed to eventually disappear, when thesystem is in the non-equilibrium steady state. The supply of electrons andholes from the bath is shown to induce quasi-particle excitations, leading tothe partial occupation of the upper branch of Bogoliubov single-particleexcitation spectrum. We also discuss how this quasi-particle induction isrelated to the suppression of exciton BEC, as well as the stability of thesteady state.

Non-equilibrium properties of a pumped-decaying Bose-condensed electron-hole gas in the BCS-BEC crossover region