Effective Floquet-Gibbs states for dissipative quantum systems

TL;DR

This paper extends the concept of Floquet-Gibbs states to dissipative quantum systems under non-adiabatic driving, demonstrating their validity beyond the rotating wave approximation with finite system-bath coupling.

Contribution

It introduces the effective Floquet-Gibbs state framework for dissipative systems beyond RWA using Magnus expansion and effective Hamiltonians.

Findings

Floquet-Gibbs states can be extended beyond RWA.

Effective Floquet Hamiltonian describes non-adiabatic regimes.

Weak system-bath coupling allows for Gibbs-like states in driven systems.

Abstract

A periodically driven quantum system, when coupled to a heat bath, relaxes to a non-equilibrium asymptotic state. In the general situation, the retrieval of this asymptotic state presents a rather non-trivial task. It was recently shown that in the limit of an infinitesimal coupling, using so-called rotating wave approximation (RWA), and under strict conditions imposed on the time-dependent system Hamiltonian, the asymptotic state can attain the Gibbs form. A Floquet-Gibbs state is characterized by a density matrix which is diagonal in the Floquet basis of the system Hamiltonian with the diagonal elements obeying a Gibbs distribution, being parametrized by the corresponding Floquet quasi-energies. Addressing the non-adiabatic driving regime, upon using the Magnus expansion, we employ the concept of a corresponding effective Floquet Hamiltonian. In doing so we go beyond the conventionally used RWA and demonstrate that the idea of Floquet-Gibbs states can be extended to the realistic case of a weak, although finite system-bath coupling, herein termed effective Floquet-Gibbs states.