Anyons obeying fractional exchange statistics arise naturally in two dimensions: Hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent exchange paths …
Gauge theories form the theoretical foundation of our understanding of many fields of science, in particular elementary particle physics and nuclear physics. They are, however, extremely difficult to treat with conventional methods such as analytical …
Recent advancements in fabrication techniques have enabled unprecedented clean interfaces and gate tunability in semiconductor-superconductor heterostructures. Inspired by these developments, we propose protocols to realize Thouless quantum pumping …
The topological θ-angle is central to several gauge theories in condensed-matter and high-energy physics. For example, it is responsible for the strong CP problem in quantum chromodynamics and can emerge in effective theories of electrodynamics in …
We address routing of classical and quantum information over quantum network and show how to exploit chirality (directionality) to achieve nearly optimal and robust transport. In particular, we prove how continuous-time chiral quantum walks over a …
In this Chapter, we give a brief review of the state of the art of theoretical and experimental studies of synthetic magnetic fields and quantum Hall effects in ultracold atomic gases. We focus on integer, spin, and fractional Hall effects, indicate …
The recent rapid experimental advancement in the engineering of quantum many-body systems opens the avenue to controlled studies of fundamental physics problems via digital or analog quantum simulations. Here, we systematically analyze the capability …
We propose a simple scheme for tomography of band-insulating states in one- and two-dimensional optical lattices with two sublattice states. In particular, the scheme maps out the Berry curvature in the entire Brillouin zone and extracts topological …