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 …

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

Photonic time crystals (PTCs), materials with a dielectric permittivity that is modulated
periodically in time, offer new concepts in light manipulation. We study theoretically the …

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 …

Floquet engineering is the concept of tailoring a system by a periodic drive, and it is
increasingly employed in many areas of physics. Ultracold atoms in optical lattices offer a …

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 …

We derive a systematic high-frequency expansion for the effective Hamiltonian and the
micromotion operator of periodically driven quantum systems. Our approach is based on the …

The physics of non-equilibrium many-body systems is a rapidly expanding area of
theoretical physics. Traditionally employed in laser physics and superconducting kinetics …

We show that two-dimensional periodically driven quantum systems with spatial disorder
admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator …

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 …