Interacting Topological Matter: Atomic, Molecular and Optical Systems

Coordinators: Monika Aidelsburger, Georg Bruun, Victor Gurarie, and Pietro Massignan

Topological quantum matter is a vibrant area of research of theoretical condensed matter physics. Starting with the explanation of integer and fractional quantum Hall effect, with subsequent breakthroughs of the prediction of topological insulators, classifying symmetry protected topological states starting with lower dimensional systems, and continuing with the elucidation of the concept of topological order, including the recent discovery of the fractonic topological order, the field is rapidly covering an increasingly broad ground. Many of the proposed topological states require interactions for their existence and yet so far much of the experimental progress has occurred for non-interacting topological states, such as topological insulators.

This program aims to advance the field by exploring realistic models of interacting topological quantum matter, which rely on interactions accessible with AMO tools or other engineered quantum systems. Those tools include optical lattices, interactions tunable by Feshbach resonances, low- and mixed-dimensional systems, Bose and Fermi mixtures, periodically-driven systems, systems with dissipation, local control with quantum gas microscopes, as well as optomechanical devices and other tools for engineering quantum systems. The relevant models can be addressed analytically within some corner of their phase diagram, numerically for a broader range of their parameters and conceptually by matching them against the broader classification schemes already developed or whose development is in progress. Detection and “smoking-gun” signatures of these topological states will also be explored.