Non-equilibrium Floquet steady states of time-periodic driven Luttinger liquids

TL;DR

This paper investigates non-equilibrium steady states in a periodically driven one-dimensional quantum gas modeled as a Luttinger liquid, revealing resonant Floquet states and a transition from power-law to density wave correlations.

Contribution

It develops a novel time-periodic operator algebra and Floquet-Bogoliubov ansatz to analyze non-equilibrium steady states in strongly interacting, periodically driven Luttinger liquids.

Findings

Resonant Floquet eigenenergies occur at specific frequency conditions.

Predicted transition from power-law to density wave correlations at certain frequencies.

Analytic solutions for non-equilibrium steady states in driven Luttinger liquids.

Abstract

Time-periodic driving facilitates a wealth of novel quantum states and quantum engineering. The interplay of Floquet states and strong interactions is particularly intriguing, which we study using time-periodic fields in a one-dimensional quantum gas, modeled by a Luttinger liquid with periodically changing interactions. By developing a time-periodic operator algebra, we are able to solve and analyze the complete set of non-equilibrium steady states in terms of a Floquet-Bogoliubov ansatz and known analytic functions. Complex valued Floquet eigenenergies occur when multiples of driving frequency approximately match twice the dispersion energy, which correspond to resonant states. In experimental systems of Lieb-Liniger bosons we predict a change from powerlaw correlations to dominant collective density wave excitations at the corresponding wave numbers as the frequency is lowered below a characteristic cut-off.