Optical properties of a highly-excited exciton-polariton condensate*

We theoretically investigate nonequilibrium effects on optical properties of a highly-excited exciton-polariton condensate. In this system, it has been theoretically predicted that a negative energy branch of the Bogoliubov dispersion (the so-called “ghost branch”) appear in photoluminescence, as a direct consequence of the quantum depletion of the Bose-condensate. However, in most experiments, the ghost branch is absent. In this work, by extending the combined generalized random phase approximation with the Hartree-Fock-Bogoliubov theory to the nonequilibrium Keldysh formalism, we show that nonequilibrium effects strongly suppress the visibility of the ghost branch. Our results are in qualitative agreement with experiments, where we see a blue shift of the condensate emission, appearance of the diffusive Goldstone mode, as well as the suppression of dispersive profile of the branch in the photoluminescence. Our results indicate that quantum depletion is strongly suppressed by the driven-dissipative nature of a nonequilibrium exciton-polariton condensate.