Multiple-scale analysis of open quantum systems

TL;DR

This paper introduces a multiple-scale perturbation method for open quantum systems, providing a straightforward way to derive analytical approximations for their dynamics, applicable to both Markovian and non-Markovian cases.

Contribution

It presents a novel, easy-to-implement multiple-scale technique for analytical solutions of quantum master equations, applicable to various open quantum system models.

Findings

Derived approximate solutions for atom-cavity dynamics

Identified characteristic time scales in different coupling regimes

Validated method with Jaynes-Cummings model example

Abstract

In this work, we present a multiple-scale perturbation technique suitable for the study of open quantum systems, which is easy to implement and in few iterative steps allows us to find excellent approximate solutions. For any time-local quantum master equation, whether markovian or non-markovian, in Lindblad form or not, we give a general procedure to construct analytical approximations to the corresponding dynamical map and, consequently, to the temporal evolution of the density matrix. As a simple illustrative example of the implementation of the method, we study an atom-cavity system described by a dissipative Jaynes-Cummings model. Performing a multiple-scale analysis we obtain approximate analytical expressions for the strong and weak coupling regimes that allow us to identify characteristic time scales in the state of the physical system.