The spontaneous breaking of time-translation symmetry has led to the discovery of a new
phase of matter: the discrete time crystal. Discrete time crystals exhibit rigid subharmonic …

Non-equilibrium topological phenomena can be induced in quantum many-body systems
using time-periodic fields (for example, by laser or microwave illumination). This Review …

Floquet engineering, the control of quantum systems using periodic driving, is an old
concept in condensed matter physics dating back to ideas such as the inverse Faraday …

There have been significant recent advances in realizing band structures with geometrical
and topological features in experiments on cold atomic gases. This review summarizes …

The thermalization of isolated quantum many-body systems is deeply related to fundamental
questions of quantum information theory. While integrable or many-body localized systems …

The past decade has witnessed an explosion in the field of quantum materials, headlined by
the predictions and discoveries of novel Landau-symmetry-broken phases in correlated …

Time-periodic forcing in the form of coherent radiation is a standard tool for the coherent
manipulation of small quantum systems like single atoms. In the last years, periodic driving …

Time crystals are time-periodic self-organized structures postulated by Frank Wilczek in
2012. While the original concept was strongly criticized, it stimulated at the same time an …

In Floquet engineering, periodic driving is used to realize novel phases of matter that are
inaccessible in thermal equilibrium. For this purpose, the Floquet theory provides us a recipe …

Driving a quantum system periodically in time can profoundly alter its long-time dynamics
and trigger topological order. Such schemes are particularly promising for generating …