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

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 …

We give a general overview of the high-frequency regime in periodically driven systems and
identify three distinct classes of driving protocols in which the infinite-frequency Floquet …

Artificial gauge fields are currently realized in a wide range of physical settings. This
includes solid-state devices but also engineered systems, such as photonic crystals …

We propose a realistic scheme to detect the 4D quantum Hall effect using ultracold atoms.
Based on contemporary technology, motion along a synthetic fourth dimension can be …

Extensions of Berry's phase and the quantum Hall effect have led to the discovery of new
states of matter with topological properties. Traditionally, this has been achieved using …

We explore prethermal Floquet steady states and instabilities of the weakly interacting two-
dimensional Bose-Hubbard model subject to periodic driving. We develop a description of …

Motivated by recent experimental implementations of artificial gauge fields for gases of cold
atoms, we study the scattering properties of particles that are subjected to time-periodic …

Periodic driving of optical lattices has enabled the creation of novel band structures not
realizable in static lattice systems, such as topological bands for neutral particles. However …

Quantum systems can show qualitatively new forms of behavior when they are driven by fast
time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of …