Projection based adiabatic elimination of bipartite open quantum systems

TL;DR

This paper extends an adiabatic elimination method to remove fast subsystems in bipartite open quantum systems, simplifying their dynamics, with applications demonstrated on a two-qubit system and the open Rabi model.

Contribution

It introduces a projection-based adiabatic elimination technique specifically for bipartite open quantum systems, expanding previous methods.

Findings

Effective reduction of system complexity demonstrated

Application to dispersively coupled two-qubit system

Application to open Rabi model

Abstract

Adiabatic elimination methods allow the reduction of the space dimension needed to describe systems dynamics which exhibits separation of time scale. For open quantum system, it consists in eliminating the fast part assuming it has almost instantaneously reached its steady-state and obtaining an approximation of the evolution of the slow part. These methods can be applied to eliminate a linear subspace within the system Hilbert space, or alternatively to eliminate a fast subsystems in a bipartite quantum system. In this work, we extend an adiabatic elimination method used for removing fast degrees of freedom within a open quantum system (Phys. Rev. A 2020, 101,042102) to eliminate a subsystem from an open bipartite quantum system. As an illustration, we apply our technique to a dispersively coupled two-qubit system and in the case of the open Rabi model.