Observation of a non-Abelian Yang Monopole: From New Chern Numbers to a Topological Transition

Abstract

Because global topological properties are robust against local perturbations, understanding and manipulating the topological properties of physical systems is essential in advancing quantum science and technology. For quantum computation, topologically protected qubit operations can increase computational robustness, and for metrology the quantized Hall effect directly defines the von Klitzing constant. Fundamentally, topological order is generated by singularities called topological defects in extended spaces, and is quantified in terms of Chern numbers, each of which measures different sorts of fields traversing surfaces enclosing these topological singularities. Here, inspired by high energy theories, we describe our synthesis and characterization of a singularity present in non-Abelian gauge theories - a Yang monopole - using atomic Bose-Einstein condensates in a five-dimensional space, and quantify the monopole in terms of Chern numbers measured on enclosing manifolds. While the well-known 1st Chern number vanished, the 2nd Chern number, measured for the first time in any physical settings, did not. By displacing the manifold, we then observed a phase transition from "topological" to "trivial" as the monopole left the manifold.