Basic properties of a mean field laser equation

• URL: http://arxiv.org/abs/2006.13001v1
• Date: Fri, 19 Jun 2020 18:51:44 GMT
• Title: Basic properties of a mean field laser equation
• Authors: Franco Fagnola, Carlos M. Mora
• Abstract summary: We study the non-linear quantum master equation describing a laser under the mean field approximation. We establish the existence and uniqueness of the regular solution to the non-linear operator equation. We obtain rigorously the Maxwell-Bloch equations from the mean field laser equation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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