  It is shown that the intensity quantum noise of a single-emitter nanolaser
can be accurately computed by adopting a stochastic interpretation of the
standard rate equation model under the only assumption that the emitter
excitation and photon number are stochastic variables with integer values. This
extends the validity of rate equations beyond the mean-field limit and avoids
using the standard Langevin approach, which is shown to fail for few emitters.
The model is validated by comparison to full quantum simulations of the
relative intensity noise and second-order intensity correlation function,
g(2)({\tau} ). Surprisingly, even when the full quantum model displays vacuum
Rabi oscillations, which are not accounted for by rate equations, the intensity
quantum noise is correctly predicted by the stochastic approach. Adopting a
simple discretization of the emitter and photon populations, thus, goes a long
way in describing quantum noise in lasers. Besides providing a versatile and
easy-to-use tool for modeling a new generation of nanolasers with many possible
applications, these results provide insight into the fundamental nature of
quantum noise in lasers.
