Coarse-Graining Can Beat the Rotating Wave Approximation in Quantum Markovian Master Equations

TL;DR

This paper introduces a coarse-graining method for deriving Markovian master equations in quantum systems that outperforms the traditional rotating wave approximation, especially in accurately capturing population dynamics.

Contribution

The authors develop a first-principles coarse-graining approach that avoids the rotating wave approximation and provides more accurate quantum master equations.

Findings

Coarse-graining approach yields better agreement with exact dynamics.

RWA misses key features in population evolution.

Optimizing coarse-graining timescale improves accuracy.

Abstract

We present a first-principles derivation of the Markovian semi-group master equation without invoking the rotating wave approximation (RWA). Instead we use a time coarse-graining approach which leaves us with a free timescale parameter, which we can optimize. Comparing this approach to the standard RWA-based Markovian master equation, we find that significantly better agreement is possible using the coarse-graining approach, for a three-level model coupled to a bath of oscillators, whose exact dynamics we can solve for at zero temperature. The model has the important feature that the RWA has a non-trivial effect on the dynamics of the populations. We show that the two different master equations can exhibit strong qualitative differences for the population of the energy eigenstates even for such a simple model. The RWA-based master equation misses an important feature which the coarse-graining based scheme does not. By optimizing the coarse-graining timescale the latter scheme can be made to approach the exact solution much more closely than the RWA-based master equation.