Synthetic gauge fields with ultracold atoms in periodically-driven lattices
Ultracold atoms in optical lattices are powerful experimental platforms to study a variety of phenomena ranging from condensed-matter to statistical physics. Recently, a promising new direction was opened by the successful realization of paradigmatic topological condensed matter models, in particular the Hofstadter and the Haldane model. I will introduce one of the most common experimental methods used to generate topological band structures in ultracold atoms, i.e., Floquet engineering, and report on recent results as well as challenges regarding its application to many-body systems. The basic idea of the method is to periodically modulate the system's parameters to emulate the properties of a non-trivial static system. Floquet engineering has further been proposed to engineer density-dependent gauge fields or even complete gauge theories, which require an interaction between matter and gauge fields. One example is the realization of Z2 lattice gauge theories, which play an important role in condensed matter physics and quantum computation. Recently, we have implemented such a model with a two-component mixture of ultracold bosons in a double-well potential - the basic building block of Z2 lattice gauge theories.