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

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.

Modelling non-Markovian noise in driven superconducting qubits

“…Thus, the values obtained for the corresponding noise terms by non-linear regression should approximately be the same for all three noise models. The method for the noisy simulation of the Markovian and Qubit-TLS model is described in appendix H. Simulations for the PMME model are done by semi-analytically solving the Master equation equation (26).…”

Caracas afterlives: The city after collapse and emigration

“…The models that we consider here fit into the larger class of stochastic modeling of open systems, but do not seem to have been analyzed before. See [8] and [9] for two comprehensive treatises of open systems, and [10] for the fluctuation-dissipation relations and, [11], [12] for two recent works on the use of stochastic methods to describe quantum open systems. For a probabilistic approach of particles in random media, consider [13] and [14].…”