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 …

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 …

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 …

Since the discovery of topological insulators, many topological phases have been predicted
and realized in a range of different systems, providing both fascinating physics and exciting …

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 …

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 …

This is an introductory review of the physics of topological quantum matter with cold atoms.
Topological quantum phases, originally discovered and investigated in condensed matter …

In periodically driven lattice systems, the effective (Floquet) Hamiltonian can be engineered
to be topological; then, the principle of bulk-boundary correspondence guarantees the …

Topological states of matter in non-Hermitian systems have attracted a lot of attention due to
their intriguing dynamical and transport properties. In this paper, we propose a periodically …