A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

In this review recent investigations are summarized of many-body quantum systems with
long-range interactions, which are currently realized in Rydberg atom arrays, dipolar …

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 …

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

Quantum theory provides an extensive framework for the description of the equilibrium
properties of quantum matter. Yet experiments in quantum simulators have now opened up …

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 …

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 …

We overview the concept of dynamical phase transitions (DPTs) in isolated quantum
systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized …

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 …

Interactions between atoms and light in optical cavities provide a means of investigating
collective (many-body) quantum physics in controlled environments. Such ensembles of …