Floquet engineering is an important tool for the engineering
of novel band structures with interesting properties that go
beyond those offered by static systems. Recently, Floquet
systems have enabled the generation of Bloch bands with
non-trivial topological properties, such as the Hofstadter
and Haldane model. This led to the observation of chiral
Meissner currents and the first Chern-number measurements
with charge-neutral atoms.
Besides this success studies of many-body phases in driven
systems remains experimentally challenging in particular due
to the interplay between periodic driving an interactions.
In a driven system energy is not conserved which can lead to
severe heating. In order to find stable parameter regimes
for the generation of driven many-body phases it is
essential to develop a deeper understanding of the
Here, I briefly review recent experimental advances in the
generation of topological band structures in the
non-interacting regime using Floquet engineering and present
first studies of interacting atoms in driven 1D lattices.