A general approach to quantum dynamics using a variational master equation: Application to phonon-damped Rabi rotations in quantum dots

TL;DR

This paper introduces a versatile variational master equation method for modeling the non-equilibrium dynamics of two-level quantum systems interacting with a bosonic environment, effectively capturing complex phonon effects in quantum dots.

Contribution

It presents a new general formalism that accurately describes quantum system dynamics across various regimes, including non-perturbative effects, and validates it against numerical methods.

Findings

Excellent agreement with Feynman integral results

Captures multi-phonon processes and bath-induced effects

Reliable in regimes where previous methods fail

Abstract

We develop a versatile master equation approach to describe the non-equilibrium dynamics of a two-level system in contact with a bosonic environment, which allows for the exploration of a wide range of parameter regimes within a single formalism. As an experimentally relevant example, we apply this technique to the study of excitonic Rabi rotations in a driven quantum dot, and compare its predictions to the numerical Feynman integral approach. We find excellent agreement between the two methods across a generally difficult range of parameters. In particular, the variational master equation technique captures effects usually considered to be non-perturbative, such as multi-phonon processes and bath-induced driving renormalisation, and can give reliable results even in regimes in which previous master equation approaches fail.