# Synthesis and Observation of Non-Abelian Gauge Fields in Real Space

## TL;DR

This paper reports the experimental creation of non-Abelian gauge fields in real space using classical waves, demonstrating the non-Abelian Aharonov--Bohm effect and opening new avenues for topological physics.

## Contribution

It introduces a method to synthesize tunable non-Abelian gauge fields in real space and observes their non-commutative effects using classical wave interference.

## Key findings

- Successful synthesis of non-Abelian gauge fields in real space
- Observation of non-Abelian Aharonov--Bohm effect with classical waves
- Demonstration of non-commutativity via Sagnac interference

## Abstract

Gauge fields, real or synthetic, are crucial for understanding and manipulation of physical systems. The associated geometric phases can be measured, for example, from the Aharonov--Bohm interference. So far, real-space realizations of gauge fields have been limited to Abelian (commutative) ones. Here we report an experimental synthesis of non-Abelian gauge fields in real space and the observation of the non-Abelian Aharonov--Bohm effect with classical waves and classical fluxes. Based on optical mode degeneracy, we break time-reversal symmetry in different manners---via temporal modulation and the Faraday effect---to synthesize tunable non-Abelian gauge fields. The Sagnac interference of two final states, obtained by reversely-ordered path integrals, demonstrates the non-commutativity of the gauge fields. Our work introduces real-space building blocks for non-Abelian gauge fields, relevant for classical and quantum exotic topological phenomena.