Simple master equations for describing driven systems subject to classical non-Markovian noise

TL;DR

This paper introduces a systematic method using generalized cumulant expansions to derive a time-local master equation for driven quantum systems with classical non-Markovian noise, capturing effects like negative dephasing rates and Hamiltonian renormalizations.

Contribution

It presents a novel, accurate approach to model driven quantum systems with classical non-Markovian noise, improving upon existing phenomenological methods.

Findings

The master equation accurately matches numerical simulations for a driven qubit with non-Markovian noise.

It reveals that non-Markovian noise can induce effective time-dependent dephasing rates, including negative values.

The approach accounts for noise-induced Hamiltonian renormalizations despite the noise being classical.

Abstract

Driven quantum systems subject to non-Markovian noise are typically difficult to model even if the noise is classical. We present a systematic method based on generalized cumulant expansions for deriving a time-local master equation for such systems. This master equation has an intuitive form that directly parallels a standard Lindblad equation, but contains several surprising features: the combination of driving and non-Markovianity results in effective time-dependent dephasing rates that can be negative, and the noise can generate Hamiltonian renormalizations even though it is classical. We analyze in detail the highly relevant case of a Rabi-driven qubit subject to various kinds of non-Markovian noise including $1/f$ fluctuations, finding an excellent agreement between our master equation and numerically-exact simulations over relevant timescales. The approach outlined here is more accurate than commonly employed phenomenological master equations which ignore the interplay between driving and noise.