Solvability of the Generalized System of Stochastic Differential Equations in Driven Cavity Single Mode

TL;DR

This paper investigates the solvability of a class of stochastic differential equations relevant to quantum optics, providing explicit solutions and generalizations for systems with variable coefficients.

Contribution

It introduces a method to analyze and solve a class of stochastic differential equations in quantum optics, including cases with variable coefficients and two-photon losses.

Findings

Explicit solutions for the stochastic differential equations are derived.

The approach extends to systems with variable coefficients.

The method simplifies analysis of quantum optical models with stochastic dynamics.

Abstract

A useful approach is investigated in order to analyze a class of a stochastic differential equations that can be encountered in quantum optics problems, especially, in the case of two photon losses on the driven cavity mode. The passage to the ordinary coupled differential equations is presented and the treatment of the obtained coupled system is explored. Generalization of the problem to stimulate variable coefficients is discussed and the exact solutions are achieved in explicit forms under suitable conditions on the coefficients.