Floquet engineering in interacting systems of ultracold Fermions in optical lattices

Periodic modulation is a powerful tool to modify properties of a static system such as opening topological gaps or controlling magnetic order. The versatility of cold atom experiments offers the possibility to implement many of these schemes. Nonetheless, preparing a desired Floquet state in this out-of-equilibrium situation is a more difficult task, especially when the driving frequency is close to a characteristic energy scale of the system. In this work, we prepare fermionic atoms in a driven optical lattice such that the system can be described by two interacting particles on a double well potential with a periodically modulated tilt. We show how to adiabatically prepare and control individual Floquet states. This study is extended to a 3D connected lattice, implementing a driven Fermi-Hubbard model. In the off-resonant case the dynamics of the many-body system can be understood by an effective Hamiltonian which is experimentally observed by directly comparing the driven system to its static counterpart.