Gain-dependent Purcell enhancement, breakdown of Einstein's relations, and superradiance in nanolasers

Light emitters in a single-mode nanolaser interact with the same cavity field, that gives rise to polarization correlations which transform mode. Usually these are ignored, however, collective phenomena can lead distinct sub- and superradiance, whose fully quantum description is challenging. Here, we develop simple yet rigorous picture of radiative transitions nanolasers accounts for correlations. We show behavior modifies photonic density states leading gain-dependent Purcell enhancement spontaneous emission. Moreover, stimulated emission rate dependent on both photon number laser lineshape. As line narrows, becomes stronger than predicted by Einstein's relations reaches threshold earlier. Finally, provide concise, ready-to-use expressions rates seamlessly describing conventional superradiant nanolasers.