Quantum theory of a single-emitter nanolaser

摘要

Using two equivalent methods, the Heisenberg-Langevin and themaster equation, we investigate the propertiesnof a single-emitter nanolaser: an incoherently pumped single two-level system interacting with a single cavitynmode of finite finesse. We are interested in a stationary generation regime when the mean number of photonsninside the laser cavity is much larger than unity. In this case we linearize the Heisenberg-Langevin equationsnaround the stationary classical solution and obtain analytical results for the linewidth, the quadrature fluctuationnspectra, and the intracavity MandelQparameter. As the second method we use the master equation for the densitynoperator of the laser field. Using the coherent-state representation of the density matrix we obtain the stationarynsolution for the Glauber P function of the laser mode and investigate the quantum statistics of the laser field andnits threshold behavior. We compare the results of both methods with numerical simulations and find very goodnagreement. In the end we use our theoretical results for analyzing experiment with single-ion nanolasers.