A stochastic approach to the quantum noise of a single-emitter nanolaser

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.