Condensation and lasing of microcavity polaritons: comparison between two models

Condensation of microcavity polaritons and the substantial influence of pair-breaking disorder and decoherence leading to a laser regime has been recently considered using two different models: a model for direct two band excitons in a disordered quantum well coupled to light and a model, where the cavity mode couples instead to a medium of localised excitons, represented by two-level oscillators in the presence of dephasing processes. Even if complementary from the point of view of assumptions, the models share most of the main conclusions and show similar phase diagrams. The issue whether excitons are propagating or localised seems secondary for the polariton condensation and the way in which pair-breaking disorder and decoherence processes influence the condensation and drive the microcavity into a lasing regime is, within the approximations used in each model, generic. The reasons for the similarities between the two physical situations are analysed and explained.