  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.
