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

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 …

Low-dimensional quantum systems can host anyons, particles with exchange statistics that
are neither bosonic nor fermionic. However, the physics of anyons in one dimension …

Periodic driving of optical lattices has enabled the creation of novel band structures not
realizable in static lattice systems, such as topological bands for neutral particles. However …

We review recent work on low-frequency Floquet engineering and its application to quantum
materials driven by light, focusing on van der Waals systems hosting Moiré superlattices …

We study the dynamics and timescales of a periodically driven Fermi-Hubbard model in a
three-dimensional hexagonal lattice. The evolution of the Floquet many-body state is …

The concept of “Floquet engineering” relies on an external periodic drive to realize novel,
effectively static Hamiltonians. This technique is being explored in experimental platforms …

We develop a low-frequency perturbation theory in the extended Floquet Hilbert space of a
periodically driven quantum systems, which puts the high-and low-frequency …

Low-dimensional quantum systems can host anyons, particles with exchange statistics that
are neither bosonic nor fermionic. Despite indications of a wealth of exotic phenomena, the …

We study the low-frequency dynamics of periodically driven one-dimensional systems
hosting Floquet topological phases. We show, both analytically and numerically, in the low …