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

We study interplay of Floquet states and strong interactions using time-periodic fields in a Luttinger liquid with periodically changing interactions. By developing a time-periodic operator algebra, we are able to obtain the complete set of explicit steady state solutions of the time-dependent Schrödinger equation 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. Including damping effects we show that this resonant behavior leads to a large number of density excitations, which allow quantitative comparisons with experiments. This setup is one or the rare cases, where a complete Floquet solution can be obtained exactly for a time-periodically driven many-body system.