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arXiv:2201.02872 · Physical Review A

Perturbation approach in Heisenberg equations for lasers

Игорь Евгеньевич Проценко, Alexander V. Uskov

Published May 19, 2022• 10 citations
arXivHTMLPDF

Abstract

Nonlinear Heisenberg-Langevin equations are solved analytically by operator Fourier expansion for the laser in the light-emitting diode (LED) regime. Fluctuations of populations of lasing levels are taken into account as perturbations. The spectra of operator products are calculated as convolutions, preserving Bose commutations for the lasing field operators. It is found that fluctuations of population significantly affect spontaneous and stimulated emissions into the lasing mode, increase the radiation rate, the number of lasing photons, and broaden the spectrum of a bad cavity threshold-less and the superradiant lasers. The method can be applied to various resonant systems in quantum optics.

DOI
10.1103/physreva.105.053713

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Using two equivalent methods, the Heisenberg-Langevin and the master equation, we investigate the properties of a single-emitter nanolaser: an incoherently pumped single two-level system interacting with a single cavity mode of finite finesse. We are interested in a stationary generation regime when the mean number of photons inside the laser cavity is much larger than unity. In this case we linearize the Heisenberg-Langevin equations around the stationary classical solution and obtain analytical results for the linewidth, the quadrature fluctuation spectra, and the intracavity Mandel QQQ parameter. As the second method we use the master equation for the density operator of the laser field. Using the coherent-state representation of the density matrix we obtain the stationary solution for the Glauber PPP function of the laser mode and investigate the quantum statistics of the laser field and its threshold behavior. We compare the results of both methods with numerical simulations and find very good agreement. In the end we use our theoretical results for analyzing experiment with single-ion nanolasers.