Basic properties of a mean field laser equation
Abstract
We study the non-linear quantum master equation describing a laser under the mean field approximation. The quantum system is formed by a single mode optical cavity and two level atoms, which interact with reservoirs. Namely, we establish the existence and uniqueness of the regular solution to the non-linear operator equation under consideration, as well as we get a probabilistic representation for this solution in terms of a mean field stochastic Schr\"ondiger equation. To this end, we find a regular solution for the non-autonomous linear quantum master equation in Gorini-Kossakowski-Sudarshan-Lindblad form, and we prove the uniqueness of the solution to the non-autonomous linear adjoint quantum master equation in Gorini-Kossakowski-Sudarshan-Lindblad form. Moreover, we obtain rigorously the Maxwell-Bloch equations from the mean field laser equation.
Cite
@article{arxiv.2006.13001,
title = {Basic properties of a mean field laser equation},
author = {Franco Fagnola and Carlos M. Mora},
journal= {arXiv preprint arXiv:2006.13001},
year = {2020}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1803.00875