Simple master equations for describing driven systems subject to classical non-Markovian noise
Peter Groszkowski, Alireza Seif, Jens Koch, A. A. Clerk
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo>/</mml:mo></mml:mrow><mml:mi>f</mml:mi></mml:math> 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.