Non-Abelian physics in light and sound

TL;DR

This paper reviews recent advances in using light and sound to explore non-Abelian physics, highlighting diverse effects and potential applications across multiple physics disciplines.

Contribution

It provides a comprehensive overview of non-Abelian phenomena in photonics and acoustics, covering foundational concepts and recent experimental realizations.

Findings

Discussion of matrix-valued geometric phases

Coverage of non-Abelian topological charges and gauge fields

Examples of non-Abelian effects in photonics and acoustics

Abstract

There has been a recent surge of interest in using light and sound as platforms for studying non-Abelian physics. Through a kaleidoscope of physical effects, light and sound provide diverse ways to manipulate their degrees of freedom to constitute the Hilbert space for demonstrating non-Abelian phenomena. The review aims to provide a timely and comprehensive account of this emerging topic. Starting from the foundation of matrix-valued geometric phases, we cover non-Abelian topological charges, non-Abelian gauge fields, non-Abelian braiding, non-Hermitian non-Abelian phenomena, and their realizations with photonics and acoustics. This topic is fast evolving at the intersection of atomic, molecular, optical physics, condensed matter physics, and mathematical physics, with fascinating prospects ahead.