Bose glass and superfuid phases of cavity polaritons

We report the calculation of cavity exciton-polariton phase diagram which takes into account the presence of realistic structural disorder. Polaritons are modelled as weakly interacting two-dimensional bosons. We show that with increasing density polaritons first undergo a quasi-phase transition towards a Bose glass: the condensate is localized in at least one minimum of the disorder potential, depending on the value of the chemical potential of the polariton system. A further increase of the density leads to a percolation process of the polariton fluid which gives rise to a Kosterlitz-Thouless phase transition towards superfluidity. The spatial representation of the condensate wavefunction as well as the spectrum of elementary excitations are obtained from the solution of the Gross-Pitaevskii equation for all the phases.