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 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 …

Coherent control via periodic modulation, also known as Floquet engineering, has emerged
as a powerful experimental method for the realization of novel quantum systems with exotic …

Topological photonics is a rapidly emerging field of research in which geometrical and
topological ideas are exploited to design and control the behavior of light. Drawing …

Integer-valued topological indices, characterizing nonlocal properties of quantum states of
matter, are known to directly predict robust physical properties of equilibrium systems. The …

Periodically driven systems have emerged as a useful technique to engineer the properties
of quantum systems, and are in the process of being developed into a standard toolbox for …

We present a topological characterization of time-periodically driven two-band models in 2+
1 dimensions as Hopf insulators. The intrinsic periodicity of the Floquet system with respect …

Landau's theory of phase transitions provides a framework for describing phases of matter in
thermodynamic equilibrium. Recently, an intriguing new class of quantum many-body …

We provide a pedagogical technical guide to many of the key theoretical tools and ideas that
underlie work in the field of Floquet engineering. We hope that this document will serve as a …

We investigate a class of periodically driven many-body systems that allows us to extend the
phenomenon of prethermalization to the vicinity of isolated intermediate-to-low drive …