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Emergence of fundamental forces from gauge symmetry is among our mostprofound insights about the physical universe. In nature, such symmetriesremain hidden in the space of internal degrees of freedom of subatomicparticles. Here we propose a way to realize and study gauge structures in realspace, manifest in external degrees of freedom of quantum states. We present amodel based on a ring-shaped lattice potential, which allows for both Abelianand non-Abelian constructs. Non trivial Wilson loops are shown possible viaphysical motion of the system. The underlying physics is based on the closeanalogy of geometric phase with gauge potentials that has been utilized tocreate synthetic gauge fields with internal states of ultracold atoms. Byscaling up to an array with spatially varying parameters, a discrete gaugefield can be realized in position space, and its dynamics mapped overmacroscopic size and time scales.

Synthetic Gauge Structures in Real Space in a Ring lattice