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Bulletin of the American Physical Society

Non-equilibrium steady state solutions of time-periodic driven Luttinger liquids

Serena Fazzini, Piotr Chudziński, Christoph Dauer, Imke Schneider, Sebastian Eggert

Published Mar 18, 2021• 0 citations
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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 nonequilibrium steady states in terms of a Floquet-Bogoliubov ansatz and known analytic functions. Complex valued Floquet eigenenergies occur when integer multiples of the 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 power-law correlations to dominant collective density wave excitations at the corresponding wave numbers as the frequency is lowered below a characteristic cutoff.

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We propose and investigate an exactly solvable model of non-equilibrium Luttinger liquid on a star graph, modeling a multi-terminal quantum wire junction. The boundary condition at the junction is fixed by an orthogonal matrix , which describes the splitting of the electric current among the leads. The system is driven away from equilibrium by connecting the leads to heat baths at different temperatures and chemical potentials. The associated non-equilibrium steady state depends on and is explicitly constructed. In this context, we develop a non-equilibrium bosonization procedure and compute some basic correlation functions. Luttinger liquids with general anyon statistics are considered. The relative momentum distribution away from equilibrium turns out to be the convolution of equilibrium anyon distributions at different temperatures. Both the charge and heat transport are studied. The exact current–current correlation function is derived and the zero-frequency noise power is determined.
We propose and investigate an exactly solvable model of non-equilibriumLuttinger liquid on a star graph, modeling a multi-terminal quantum wirejunction. The boundary condition at the junction is fixed by an orthogonalmatrix S, which describes the splitting of the electric current among theleads. The system is driven away from equilibrium by connecting the leads toheat baths at different temperatures and chemical potentials. The associatednon-equilibrium steady state depends on S and is explicitly constructed. Inthis context we develop a non-equilibrium bosonization procedure and computesome basic correlation functions. Luttinger liquids with general anyonstatistics are considered. The relative momentum distribution away fromequilibrium turns out to be the convolution of equilibrium anyon distributionsat different temperatures. Both the charge and heat transport are studied. Theexact current-current correlation function is derived and the zero-frequencynoise power is determined.
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 nonequilibrium steady states in terms of a Floquet-Bogoliubov ansatz and known analytic functions. Complex valued Floquet eigenenergies occur when integer multiples of the 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 power-law correlations to dominant collective density wave excitations at the corresponding wave numbers as the frequency is lowered below a characteristic cutoff.