Analytical results from the quantum theory of a single-emitter nanolaser. II

TL;DR

This paper analyzes the properties of a nanolaser with a single emitter using Heisenberg-Langevin and density operator methods, providing analytical results for linewidth, fluctuations, and threshold behavior in different cavity regimes.

Contribution

It offers a comparative analytical study of nanolaser properties in different regimes using two approaches, highlighting their agreement and detailed thresholdless behavior analysis.

Findings

Analytical expressions for linewidth and fluctuation spectra in good-cavity regime.

Estimation of relaxation oscillation frequency in bad-cavity regime.

Confirmation of approach agreement with numerical simulations.

Abstract

Using two equivalent approaches, Heisenberg-Langevin and density operator, we investigate the properties of nanolaser: an incoherently pumped single two-level system interacting with a single-cavity mode of finite finesse. We show that in the case of good-cavity regime the Heisenberg-Langevin approach provides the analytical results for linewidth, amplitude fluctuation spectrum, and intracavity Mandel Q-parameter. In the bad-cavity regime we estimate the frequency at which the peak of relaxation oscillations appears. With the help of the master equation for density operator written in terms of coherent states we obtain approximated expression for Glauber-Sudarshan P function. This solution can be used in the case of good-cavity regime and allows us to investigate in more detail the thresholdless behaviour of the nanolaser. All two approaches are in a very good agreement with each other and numerical simulations.