Photon Bose-Einstein condensation and lasing in semiconductor cavities

Photon Bose-Einstein condensation and photon thermalisation have been largely studied with molecular gain media in optical cavities. Their observation with semiconductors has remained elusive despite a large body of experimental results and a very well established theoretical framework. We use this theoretical framework as a convenient platform to revisit photon Bose-Einstein condensation in the driven-dissipative regime and compare with the lasing regime. We discuss the thermalisation figures of merit and the different experimental procedures to asses thermalization. We compare the definitions of lasing and condensation thresholds. Finally, we explore the fluctuations of the system and their relation to the different regimes.