We review the recent developments and the current status in the field of quantum-gas cavity
QED. Since the first experimental demonstration of atomic self-ordering in a system …

After many years of development of the basic tools, quantum simulation with ultracold atoms
has now reached the level of maturity at which it can be used to investigate complex …

We use the resonant dipole-dipole interaction between Rydberg atoms and a periodic
external microwave field to engineer XXZ spin Hamiltonians with tunable anisotropies. The …

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 Berry phase provides a modern formulation of electric polarization in crystals. We
extend this concept to higher electric multipole moments and determine the necessary …

A d-dimensional second-order topological insulator (SOTI) can host topologically protected
(d-2)-dimensional gapless boundary modes. Here, we show that a 2D non-Hermitian SOTI …

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 …

During the last ten years, superconducting circuits have passed from being interesting
physical devices to becoming contenders for near-future useful and scalable quantum …

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 …

This Colloquium describes a new paradigm for creating strong quantum interactions of light
and matter by way of single atoms and photons in nanoscopic lattices. Beyond the …