Thouless pum** provides one of the simplest manifestations of topology in quantum
systems and has attracted a lot of recent interest, both theoretically and experimentally …

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 …

Quantum gas microscopes have revolutionized quantum simulations with ultracold atoms,
allowing one to measure local observables and snapshots of quantum states. However …

Artificial gauge fields are currently realized in a wide range of physical settings. This
includes solid-state devices but also engineered systems, such as photonic crystals …

In this perspective we discuss verification of quantum devices in the context of specific
examples formulated as proposed experiments. Our first example is verification of analog …

The discovery of topological states of matter has greatly improved our understanding of
phase transitions in physical systems. Instead of being described by local order parameters …

Geometric properties of wave functions can explain the appearance of topological invariants
in many condensed-matter and quantum systems. For example, topological invariants …

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 …

We propose counterintuitive topological pumps induced by disorder in noninteracting and
interacting systems. We show an extrinsic topological pump driven by the on-site …

Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing
quantum many-body states in analog quantum simulation. We describe a protocol where …