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

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 …

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

Strong periodic driving with light offers the potential to coherently manipulate the properties
of quantum materials on ultrafast timescales. Recently, strategies have emerged to …

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 …

In Floquet engineering, periodic driving is used to realize novel phases of matter that are
inaccessible in thermal equilibrium. For this purpose, the Floquet theory provides us a recipe …

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 …

This work explores a fundamental dynamical structure for a wide range of many-body
quantum systems under periodic driving. Generically, in the thermodynamic limit, such …