Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode

TL;DR

This paper rigorously analyzes the limit where an oscillator mode mediating coupling in a quantum system can be eliminated, resulting in an effective direct system-reservoir interaction, relevant in quantum optics.

Contribution

It provides a rigorous mathematical framework for the singular perturbation limit in quantum stochastic differential equations with oscillator-mediated coupling.

Findings

Effective direct coupling derived in the strong coupling limit

Mathematically rigorous treatment of the limit process

Model includes emission, absorption, and scattering interactions

Abstract

We consider a physical system which is coupled indirectly to a Markovian resevoir through an oscillator mode. This is the case, for example, in the usual model of an atomic sample in a leaky optical cavity which is ubiquitous in quantum optics. In the strong coupling limit the oscillator can be eliminated entirely from the model, leaving an effective direct coupling between the system and the resevoir. Here we provide a mathematically rigorous treatment of this limit as a weak limit of the time evolution and observables on a suitably chosen exponential domain in Fock space. The resulting effective model may contain emission and absorption as well as scattering interactions.