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 …

Recent experiments have produced evidence for fractional quantum anomalous Hall
(FQAH) states at zero magnetic field in the semiconductor moiré superlattice system t MoTe …

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

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

We experimentally implement the Harper Hamiltonian for neutral particles in optical lattices
using laser-assisted tunneling and a potential energy gradient provided by gravity or …

When a neutral atom moves in a properly designed laser field, its center-of-mass motion
may mimic the dynamics of a charged particle in a magnetic field, with the emergence of a …

Topological insulators and their intriguing edge states can be understood in a single-particle
picture and can as such be exhaustively classified. Interactions significantly complicate this …

Topologically ordered phases are characterized by long-range quantum entanglement and
fractional statistics rather than by symmetry breaking. First observed in a fractionally filled …