Seminarium Fizyki Materii Skondensowanej

After an introduction to 1D ultracold gases and their coherence properties, I discuss how to implement an integrable Floquet Hamiltonian for a periodically tilted 1D Bose gas. In general, an integrable model subjected to a periodic driving gives rise 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 realizationof the periodically driven tilting in terms of a shaken rotated ring potential. We also discuss the micro-motion operator and the expression for a generic time evolved state of the system. To conclude, a discussion of the applications to atomtronics is presented. For the seminar link contact Pawel Jakubczyk.