Non-Abelian physics in light and sound

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.