Higher order moments dynamics for some multimode quantum master equations

TL;DR

This paper derives and solves high-order moment equations for multimode quantum master equations, revealing that finite-order moments follow a finite set of linear differential equations, simplifying their analysis.

Contribution

It introduces a method to derive and solve equations for arbitrary high-order moments in multimode quantum master equations with quadratic generators.

Findings

Finite-order moments follow a finite set of linear differential equations.

The approach applies to master equations averaged over classical Poisson processes.

Provides a systematic way to analyze moments in multimode quantum systems.

Abstract

We derive Heisenberg equations for arbitrary high order moments of creation and annihilation operators in the case of the quantum master equation with a multimode generator which is quadratic in creation and annihilation operators and obtain their solutions. Based on them we also derive similar equations for the case of the quantum master equation, which occur after averaging the dynamics with a quadratic generator with respect to the classical Poisson process. This allows us to show that dynamics of arbitrary finite-order moments of creation and annihilation operators is fully defined by finite number of linear differential equations in this case.