Photonic Non-Abelian Braid Monopole

Abstract: Monopoles and braids are exotic but elusive aspects of fundamental theories of light and matter. In lattice systems, monopoles of band-structure degeneracies are subject to well-established no-go (doubling) theorems that appear to universally apply in closed Hermitian systems and open non-Hermitian systems alike. However, the non-Abelian braid topology of non-Hermitian multi-band systems provides a remarkable loophole to these constraints. Here we make use of this loophole, and experimentally implement, for the first time, a monopole degeneracy in a non-Hermitian three-band system in the form of a single third-order exceptional point. We explicitly demonstrate the intricate braiding topology and the non-Abelian fusion rules underlying the monopole degeneracy. The experiment is carried out using a new design of single-photon interferometry, enabling eigenstate and spectral resolutions for non-Hermitian multi-band systems with widely tunable parameters. Thus, the union of state-of-the-art experiments, fundamental theory, and everyday concepts such as braids paves the way toward the highly exotic non-Abelian topology unique to non-Hermitian settings.