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 …

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 …

The approach to thermal equilibrium, or thermalization, in isolated quantum systems is
among the most fundamental problems in statistical physics. Recent theoretical studies have …

The Haldane model on a honeycomb lattice is a paradigmatic example of a Hamiltonian
featuring topologically distinct phases of matter. It describes a mechanism through which 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 …

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 …

Gauge fields are central in our modern understanding of physics at all scales. At the highest
energy scales known, the microscopic universe is governed by particles interacting with …

Topological properties lie at the heart of many fascinating phenomena in solid-state systems
such as quantum Hall systems or Chern insulators. The topology of the bands can be …