Synthetic Gauge Structures in Real Space in a Ring lattice

TL;DR

This paper proposes a method to realize and study synthetic gauge structures in real space using a ring-shaped lattice potential, enabling exploration of Abelian and non-Abelian gauge phenomena in quantum systems.

Contribution

It introduces a model for creating and analyzing synthetic gauge fields in real space through a ring lattice, extending the concept of gauge symmetry from internal to external degrees of freedom.

Findings

Possible realization of non-trivial Wilson loops via physical motion.

Synthetic gauge fields can be scaled up in an array with spatially varying parameters.

The approach maps gauge field dynamics over macroscopic size and time scales.

Abstract

Emergence of fundamental forces from gauge symmetry is among our most profound insights about the physical universe. In nature, such symmetries remain hidden in the space of internal degrees of freedom of subatomic particles. Here we propose a way to realize and study gauge structures in real space, manifest in external degrees of freedom of quantum states. We present a model based on a ring-shaped lattice potential, which allows for both Abelian and non-Abelian constructs. Non trivial Wilson loops are shown possible via physical motion of the system. The underlying physics is based on the close analogy of geometric phase with gauge potentials that has been utilized to create synthetic gauge fields with internal states of ultracold atoms. By scaling up to an array with spatially varying parameters, a discrete gauge field can be realized in position space, and its dynamics mapped over macroscopic size and time scales.