Quantum circuits—built from local unitary gates and local measurements—are a new
playground for quantum many-body physics and a tractable setting to explore universal …

Weakly interacting quasiparticles play a central role in the low-energy description of many
phases of quantum matter. At higher energies, however, quasiparticles cease to be well …

Recent progress in utilizing ultrafast light-matter interaction to control the macroscopic
properties of quantum materials is reviewed. Particular emphasis is placed on photoinduced …

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 …

Spontaneous symmetry breaking is a fundamental concept in many areas of physics,
including cosmology, particle physics and condensed matter. An example is the breaking of …

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 …

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 …

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 emergence of statistical mechanics for isolated classical systems comes about through
chaotic dynamics and ergodicity. Here we review how similar questions can be answered in …

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 …