Coherence of condensed microcavity polaritons calculated within Boltzmann-Master equations

The first-order spatial and the second-order temporal coherences of condensed microcavity polaritons are calculated in terms of Boltzmann equations for the excited states and the ground state supplemented by a Master equation for the probability to find a given number of particles in the condensate. The resulting first-order spatial coherence agrees both in its pump power dependence and in its variation with distance with the results of a recent double-slit experiment. Inserting the calculated rates between the excited states and the condensate with various saturation and depletion models, we solve for stationary situations the Master equation for the ground-state population. The resulting second-order correlations for the various models are compared with recent measurements.