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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 example,
topologically protected quantum control gives robust high-fidelity gate
operations and the bulk topology of quantum Hall system leads to the
quantization of the Hall conductivity. Topological order is quantified in terms
of singularities called topological defects that reside in an extended
parameter space. Here we engineered such a singularity argued in non- Abelian
gauge theories - a Yang monopole - using atomic Bose-Einstein condensates in a
parameter space. We quantified its field by measuring the Chern numbers on
enclosing manifolds. While the 1st Chern number vanished, the 2nd Chern number
didn.t. By displacing the manifold, we observed a transition from .topological.
to .trivial. as the monopole left the manifold. Our work illustrates the
synthesis of a noble topological defect in a quantum system.
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