Condition for emergence of the Floquet-Gibbs state in periodically driven open systems

TL;DR

This paper proves that under certain conditions, the steady state of a periodically driven open quantum system is described by a Floquet-Gibbs distribution, independent of bath details, even with strong external driving.

Contribution

It establishes conditions under which the Floquet-Gibbs state emerges in driven open quantum systems, extending understanding beyond weak driving regimes.

Findings

Steady state follows Floquet-Gibbs distribution at bath temperature.

Independence from thermal bath details under specified conditions.

Validity even with strong external driving fields.

Abstract

We study probability distribution of a steady state of a periodically driven system coupled to a thermal bath by using a quantum master equation in the weak coupling limit. It is proved that, even when the external field is strong, the probability distribution is independent of the detailed nature of the thermal bath under the following conditions: (i) the Hamiltonian of the relevant system is bounded and the period of the driving field is short, (ii) the Hamiltonians for the driving field at different times commute, and (iii) the Hamiltonians of the driving field and of the interaction between the relevant system and the thermal bath commute. It is shown that the steady state is described by the Gibbs distribution of the Floquet states of the relevant system at the temperature of the thermal bath.