Asymptotic Floquet states of open quantum systems: The role of interaction

TL;DR

This paper explores how periodically driven open quantum systems reach asymptotic states, emphasizing the influence of particle interactions and introducing the dissipative Floquet map to analyze their long-term behavior.

Contribution

It introduces the dissipative Floquet map for analyzing asymptotic states in open quantum systems and examines the impact of interactions on these states.

Findings

Particle interactions induce bifurcations in mean-field dynamics.

Dissipative Floquet maps reveal system relaxation properties.

Interactions affect the characteristics of the quantum many-body state.

Abstract

We investigate the asymptotic state of a periodically driven many-body quantum system which is weakly coupled to an environment. The combined action of the modulations and the environment steers the system towards a state being characterized by a time-periodic density operator. To resolve this asymptotic non-equilibrium state at stroboscopic instants of time, we introduce the dissipative Floquet map, evaluate the stroboscopic density operator as its eigen-element and elucidate how particle interactions affect properties of the density operator. We illustrate the idea with a periodically modulated Bose-Hubbard dimer and discuss the relations between the interaction-induced bifurcations in a mean-field dynamics and changes in the characteristics of the genuine quantum many-body state. We argue that Floquet maps provide insight into the system relaxation towards its asymptotic state and may help to understand whether it is possible (or not) to construct a stroboscopic time-independent generator mimicking the action of the original time-dependent one.