Invariant states of linear quantum stochastic systems under Weyl perturbations of the Hamiltonian and coupling operators

TL;DR

This paper analyzes how invariant states of linear quantum stochastic systems respond to nonlinear Weyl perturbations of Hamiltonian and coupling operators, providing a framework for approximate computation and analysis.

Contribution

It introduces an infinitesimal perturbation analysis of invariant states using the Wigner-Moyal phase-space framework for systems with Weyl perturbations.

Findings

Derived correction formulas for invariant states in the frequency domain

Applicable to approximate computation of invariant states

Facilitates analysis of relaxation dynamics and non-Gaussian states

Abstract

This paper is concerned with the sensitivity of invariant states in linear quantum stochastic systems with respect to nonlinear perturbations. The system variables are governed by a Markovian Hudson-Parthasarathy quantum stochastic differential equation (QSDE) driven by quantum Wiener processes of external bosonic fields in the vacuum state. The quadratic system Hamiltonian and the linear system-field coupling operators, corresponding to a nominal open quantum harmonic oscillator, are subject to perturbations represented in a Weyl quantization form. Assuming that the nominal linear QSDE has a Hurwitz dynamics matrix and using the Wigner-Moyal phase-space framework, we carry out an infinitesimal perturbation analysis of the quasi-characteristic function for the invariant quantum state of the nonlinear perturbed system. The resulting correction of the invariant states in the spatial frequency domain may find applications to their approximate computation, analysis of relaxation dynamics and non-Gaussian state generation in nonlinear quantum stochastic systems.