High-frequency expansions for time-periodic Lindblad generators

TL;DR

This paper develops a method to derive a proper Floquet Lindbladian for periodically driven open quantum systems using high-frequency expansions in a rotating frame, capturing the transition from Markovian to non-Markovian dynamics.

Contribution

It introduces a rotating frame approach to accurately obtain Floquet Lindbladians, addressing limitations of previous high-frequency expansion methods for open quantum systems.

Findings

Proper Floquet Lindbladian can be obtained in a rotating frame.

Transition from Markovian to non-Markovian dynamics explained.

Non-Markovianity linked to system micromotion.

Abstract

Floquet engineering of isolated systems is often based on the concept of the effective time-independent Floquet Hamiltonian, which describes the stroboscopic evolution of a periodically driven quantum system in steps of the driving period and which is routinely obtained analytically using high-frequency expansions. The generalization of these concepts to open quantum systems described by a Markovian master equation of Lindblad type turns out to be non-trivial: On the one hand, already for a two-level system two different phases can be distinguished, where the effective time-independent Floquet generator (describing the stroboscopic evolution) is either again Markovian and of Lindblad type or not. On the other hand, even though in the high-frequency regime a Lindbladian Floquet generator (Floquet Linbladian) is numerically found to exist, this behaviour is, curiously, not correctly reproduced within analytical high-frequency expansions. Here, we demonstrate that a proper Floquet Lindbladian can still be obtained from a high-frequency expansion, when treating the problem in a suitably chosen rotating frame. Within this approach, we can then also describe the transition to a phase at lower driving frequencies, where no Floquet Lindbladian exists, and show that the emerging non-Markovianity of the Floquet generator can entirely be attributed to the micromotion of the open driven system.