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

Peter Groszkowski1,2, Alireza Seif1, Jens Koch3, and A. A. Clerk1

1Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
2National Center for Computational Sciences, Oak Ridge National Laboratory, TN 37831, USA
3Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA

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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.

Driven quantum systems subject to non-Markovian noise are typically difficult to model even if the noise is classical. In this work, we present a systematic method based on a generalized cumulant expansion for deriving a time-local master equation for such systems. Our master equation directly parallels the standard Lindblad form, 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. Although our theory is general, as an explicit example, we provide a detailed analysis of a highly relevant case consisting of a Rabi-driven qubit subject to various kinds of non-Markovian noise types, such as quasistatic, Lorentzian as well as $1/f$. We find an excellent agreement between our master equation and numerically-exact simulations over relevant timescales and show that our approach is more accurate than commonly employed phenomenological master equations which ignore the interplay between driving and noise.

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