Perturbation approach in Heisenberg equations for lasers

TL;DR

This paper develops an analytical perturbation method to solve nonlinear Heisenberg-Langevin equations for lasers, accounting for population fluctuations and analyzing their impact on emission spectra and laser characteristics.

Contribution

It introduces a novel perturbation approach in Heisenberg equations that accurately incorporates population fluctuations in laser models.

Findings

Population fluctuations significantly influence emission spectra.

Fluctuations increase radiation rate and photon number.

Method applicable to various quantum optical systems.

Abstract

Nonlinear Heisenberg-Langevin equations are solved analytically by operator Fourier-expansion for the laser in the LED regime. Fluctuations of populations of lasing levels are taken into account as perturbations. 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 broad the spectrum of a bad cavity thresholdless and the superradiant lasers. The method can be applied to various resonant systems in quantum optics.