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