Non-Abelian braiding of light

TL;DR

This paper demonstrates that non-Abelian Berry phases can be realized with classical light in topological photonic waveguides, enabling braiding effects that are wave phenomena derived from Maxwell's equations.

Contribution

It introduces a method to observe non-Abelian braiding of light in topological photonic systems, bridging concepts from electronic topological matter to classical optics.

Findings

Non-Abelian phases can be induced in classical light within topological waveguides.

Braiding of guided modes leads to measurable non-Abelian phase accumulation.

Effects persist at large photon numbers, confirming their wave nature from Maxwell's equations.

Abstract

Many topological phenomena first proposed and observed in the context of electrons in solids have recently found counterparts in photonic and acoustic systems. In this work, we demonstrate that non-Abelian Berry phases can arise when coherent states of light are injected into "topological guided modes" in specially-fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order in which the guided beams are wound around one another. Notably, these effects survive the limit of large photon occupation, and can thus also be understood as wave phenomena arising directly from Maxwell's equations, without resorting to the quantization of light. We propose an optical interference experiment as a direct probe of this non-Abelian braiding of light.