Floquet-Liouville Theory for Strongly Driven Open Quantum Systems

Abstract

Periodically driven quantum systems are commonly modeled using master equations constructed in the eigenbasis of an undriven Hamiltonian, implicitly assuming that environmental dissipation couples to static energy transitions even under strong time-periodic driving. The validity of this approximation beyond weak or near-resonant driving remains poorly understood. To address the need for a more self-consistent quantum theory approach, we formulate a nonsecular Floquet--Markov generalized master equation (F-GME) in the quasienergy basis, treating interaction-induced (internal) and drive-induced (external) nonperturbative dressing on an equal footing. We subsequently investigate dissipation in two minimal driven open quantum systems---a harmonically driven two-level system and a harmonically driven coupled-two-level-system---each weakly coupled to a Markovian bath. Comparing the F-GME to a time-independent dressed-basis master equation, we show that even for a flat-bath spectral density and weak dissipation, the two approaches can yield qualitatively different steady-state populations and emission spectra. We resolve dissipation into drive-assisted sideband processes decaying via Floquet extended-space quasienergy channels, and show these channels can hybridize through nonsecular couplings into collective Floquet--Liouville modes governing observable spectral resonances. This analysis demonstrates that time-independent dissipative descriptions can incorrectly weight multiphoton Floquet transitions by collapsing quasienergy-resolved decay pathways into static energy gaps. The F-GME framework provides a systematic diagnostic for identifying regimes where Floquet-consistent dissipation is essential and clarifies the physical origin of discrepancies between commonly used master-equation approaches.

63 pages, 9 figures, 2 tables