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

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 …

Strongly interacting topological matter exhibits fundamentally new phenomena with potential
applications in quantum information technology,. Emblematic instances are fractional …

Atomtronics deals with matter-wave circuits of ultracold atoms manipulated through
magnetic or laser-generated guides with different shapes and intensities. In this way, new …

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 …

Gauge fields that appear in models of high-energy and condensed-matter physics are
dynamical quantum degrees of freedom due to their coupling to matter fields. Since the …

We demonstrate the experimental implementation of an optical lattice that allows for the
generation of large homogeneous and tunable artificial magnetic fields with ultracold atoms …

Topological features—global properties not discernible locally—emerge in systems ranging
from liquid crystals to magnets to fractional quantum Hall systems. A deeper understanding …

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 …

Ultracold quantum gases offer a unique setting for quantum simulation of interacting many-
body systems. The high degree of controllability, the novel detection possibilities and the …