Partly invariant steady state of two interacting open quantum systems

TL;DR

This paper studies conditions under which the steady state of one open quantum system remains unaffected by interactions with another system, providing theoretical insights and applications to models like optomechanical coupling.

Contribution

It introduces a class of coupled open quantum systems where one system's steady state remains invariant despite interactions, supported by a detailed proof and practical examples.

Findings

Invariant steady state in certain coupled systems

Application to optomechanical models

Theoretical framework for steady state invariance

Abstract

We investigate two interacting open quantum systems whose time evolutions are governed by Markovian master equations. We show a class of coupled systems whose interaction leaves invariant the steady state of one of the systems, i.e., only one of the reduced steady states is sensitive to the interactions. A detailed proof with the help of the Trotter product formula is presented. We apply this general statement to a few models, one of which is the optomechanical coupling model where an optical cavity is coupled to a small mechanical oscillator.