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 phases constitute an exotic form of matter characterized by non-local properties
rather than local order parameters. The paradigmatic Haldane model on a hexagonal lattice …

Integer-valued topological indices, characterizing nonlocal properties of quantum states of
matter, are known to directly predict robust physical properties of equilibrium systems. The …

Topological quantum states are characterized by nonlocal invariants. We present a new
dynamical approach for ultracold-atom systems to uncover their band topology, and we …

Topological phase of matter is now a mainstream of research in condensed matter physics,
of which the classification, synthesis, and detection of topological states have brought …

We show how the topological number of a static Hamiltonian can be measured from a
dynamical quench process. We focus on a two-band Chern insulator in two dimension, for …

Symmetry plays a fundamental role in understanding complex quantum matter, particularly
in classifying topological quantum phases, which have attracted great interests in the recent …

We report the experimental implementation of discrete-time topological quantum walks of a
Bose-Einstein condensate in momentum space. Introducing stroboscopic driving sequences …

We introduce and study the dynamical probes of band-structure topology in the postquench
time evolution of quantum many-body systems initialized in mixed states. Our construction …