# Integrable Floquet Hamiltonian for a Periodically Tilted 1D Gas

## TL;DR

This paper demonstrates that a periodically driven Lieb--Liniger model with a linear potential remains integrable, allowing exact solutions for its quasi-energies and insights into its dynamics, with potential experimental realizations.

## Contribution

It shows that the Floquet Hamiltonian of an integrable 1D Bose gas under periodic linear tilt is itself integrable, enabling exact Bethe ansatz solutions.

## Key findings

- Floquet Hamiltonian remains integrable under periodic linear tilt.
- Quasi-energies can be exactly determined using Bethe ansatz.
- Proposes an experimental setup with shaken ring potential.

## Abstract

An integrable model subjected to a periodic driving gives rise generally to a non-integrable Floquet Hamiltonian. Here we show that the Floquet Hamiltonian of the integrable Lieb--Liniger model in presence of a linear potential with a periodic time--dependent strength is instead integrable and its quasi-energies can be determined using the Bethe ansatz approach. We discuss various aspects of the dynamics of the system at stroboscopic times and we also propose a possible experimental realisation of the periodically driven tilting in terms of a shaken rotated ring potential.