Quantum states can acquire a geometric phase called the Berry phase after adiabatically traversing a closed loop, which depends on the path not the rate of motion. The Berry phase is analogous to the Aharonov–Bohm phase derived from the electromagnetic vector potential, and can be expressed in terms of an Abelian gauge potential called the Berry connection. Wilczek and Zee extended this concept to include non-Abelian phases—characterized by the gauge-independent Wilson loop—resulting from non-Abelian gauge potentials. Using an atomic Bose–Einstein condensate, we quantum-engineered a non-Abelian SU(2) gauge field, generated by a Yang monopole located at the origin of a 5-dimensional parameter space. By slowly encircling the monopole, we characterized the Wilczek–Zee phase in terms of the Wilson loop, that depended on the solid-angle subtended by the encircling path: a generalization of Stokes’ theorem. This observation marks the observation of the Wilson loop resulting from a non-Abelian point source.

量子态在绝热穿过闭环后可以获得称为 Berry 相的几何相，这取决于路径而不是运动速率。Berry 相类似于源自电磁矢量势的 Aharonov-Bohm 相，可以用称为 Berry 连接的阿贝尔规范势来表示。Wilczek 和 Zee 将这个概念扩展到包括非阿贝尔相（以与规范无关的威尔逊环为特征）由非阿贝尔规范势产生。使用原子玻色-爱因斯坦凝聚，我们对非阿贝尔 SU(2) 规范场进行了量子工程，该规范场由位于 5 维参数空间原点的杨单极子产生。通过缓慢环绕单极子，我们根据威尔逊环对 Wilczek-Zee 相进行了表征，这取决于环绕路径所对的立体角：斯托克斯定理的推广。该观察结果标志着对非阿贝尔点源产生的威尔逊环的观察结果。