Measurement and Significance of Wilson Loops in Synthetic Gauges Fields

TL;DR

This paper introduces a method to measure Wilson loops in synthetic gauge fields using ultracold atoms, enabling identification of non-Abelian gauge structures without lattice confinement and allowing continuous variation between U(1) and U(2) groups.

Contribution

It presents a novel technique to determine Wilson loop matrices from atomic state amplitudes, facilitating the study of non-Abelian gauge fields in ultracold atom systems.

Findings

Method to determine Wilson loops without lattice confinement

Ability to realize both Abelian and non-Abelian gauge structures

Continuous tuning between U(1) and U(2) gauge groups

Abstract

We study Wilson loops as a necessary tool for unambiguous identification of non-Abelian synthetic gauge fields, with attention to certain crucial but often overlooked features, such as the requirement of at least three distinct loops. We devise a method to determine the complete Wilson loop matrix from the time evolved amplitudes of the internal atomic states of laser-coupled ultracold atoms that does not require lattice confinement. The analysis is done in the context of a new cyclic model that can realize both Abelian and non-Abelian structures within a single configuration with continuous variation possible between U(1) and U(2) gauge groups by varying the detuning of the laser fields.