Floquet theorem for open systems and its applications

TL;DR

This paper extends Floquet theory to open quantum systems described by Lindblad equations, providing a way to analyze periodically driven open systems and demonstrating its effectiveness through examples.

Contribution

The work generalizes Floquet theorem to open systems with Lindblad dynamics, introducing a high-frequency expansion and constructing effective time-independent Lindbladians.

Findings

Effective Lindbladian matches exact dynamics at high frequency

Open Floquet theory applies to periodically driven open systems

Examples illustrate the theory's validity and applicability

Abstract

For a closed system with periodic driving, Floquet theorem tells that the time evolution operator can be written as $ U(t,0)\equiv P(t)e^{\frac{-i}{\hbar}H_F t}$ with $P(t+T)=P(t)$, and $H_F$ is Hermitian and time-independent called Floquet Hamiltonian. In this work, we extend the Floquet theorem from closed systems to open systems described by a Lindblad master equation that is periodic in time. Lindbladian expansion in powers of $\frac 1 \omega$ is derived, where $\omega$ is the driving frequency. Two examples are presented to illustrate the theory. We find that appropriate trace preserving time-independent Lindbladian of such a periodically driven system can be constructed by the application of open system Floquet theory, and it agrees well with the exact dynamics in the high frequency limit.