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

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.

Automated summary

We propose a systematic method based on generalized cumulant expansions to derive a time-local master equation for driven quantum systems subject to non-Markovian noise. The derived master equation has an intuitive form similar to the standard Lindblad equation but exhibits several surprising features, such as time-dependent dephasing rates that can be negative due to the combination of driving and non-Markovianity, and Hamiltonian renormalizations induced by classical noise. We analyze the case of a Rabi-driven qubit under different types of non-Markovian noise including $1/f$ fluctuations, and find excellent agreement between our master equation and numerically-exact simulations within relevant timescales. Our approach provides more accurate results than commonly used phenomenological master equations that neglect the interplay between driving and noise.