Periodically Driven Open Quantum Systems: Spectral Properties and Non-Equilibrium Steady States

Abstract

In this article, we investigate periodically driven open quantum systems within the framework of Floquet-Lindblad master equations. Specifically, we discuss Lindblad master equations in the presence of a coherent, time-periodic driving and establish their general spectral features. We also clarify the notions of transient and non-decaying solutions from this spectral perspective, and then prove that any physical system described by a Floquet-Lindblad equation must have at least one \textit{physical} non-equilibrium steady state (NESS), corresponding to an eigenoperator of the Floquet-Lindblad evolution superoperator ${\mathcal{U}}_F$ with unit eigenvalue. Since the Floquet-Lindblad formalism encapsulates the entire information regarding the NESS, it in principle enables us to obtain non-linear effects to all orders at once. The Floquet-Lindblad formalism thus provides a powerful tool for studying driven-dissipative solid-state systems, which we illustrate by deriving the nonlinear optical response of a simple two-band model of an insulating solid and comparing it with prior results established through Keldysh techniques.

19 pages, 2 figures

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• Non-Hermitian Floquet dynamics in absorption spectroscopy
• Topical review on acousto-optical Floquet engineering of single-photon emitters