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Quantum states can acquire a geometric phase called the Berry phase afteradiabatically traversing a closed loop, which depends on the path not the rateof motion. The Berry phase is analogous to the Aharonov-Bohm phase derived fromthe electromagnetic vector potential, and can be expressed in terms of anAbelian gauge potential called the Berry connection. Wilczek and Zee extendedthis concept to include non-Abelian phases -- characterized by the gaugeindependent Wilson loop -- resulting from non-Abelian gauge potentials. Usingan atomic Bose-Einstein condensate, we quantum-engineered a non-Abelian SU(2)gauge field, generated by a Yang monopole located at the origin of a5-dimensional parameter space. By slowly encircling the monopole, wecharacterized the Wilczek-Zee phase in terms of the Wilson loop, that dependedon the solid-angle subtended by the encircling path: a generalization ofStokes' theorem. This observation marks the observation of the Wilson loopresulting from a non-Abelian point source.

Wilson loop and Wilczek-Zee phase from a non-Abelian gauge field