Observation of Braid-Protected Unpaired Exceptional Points

TL;DR

This paper demonstrates the experimental realization of an unpaired third-order exceptional point with non-Abelian braid topology in a non-Hermitian three-band system, revealing complex topological properties.

Contribution

It introduces a novel experimental approach to observe unpaired EP3 with non-Abelian braiding, expanding understanding of non-Hermitian topological phenomena.

Findings

Successfully implemented unpaired EP3 in a three-band system

Demonstrated non-Abelian braiding and fusion rules

Used a new single-photon interferometry design

Abstract

Spectral degeneracies (dubbed nodal points in momentum space) play fundamental roles in understanding exotic properties of light and matter. In lattice systems, unpaired band-structure degeneracies are subject to well-established no-go (doubling) theorems that universally apply to both closed Hermitian systems and open non-Hermitian systems. However, the non-Abelian braid topology of non-Hermitian multi-band systems provides a loophole to these constraints. Here we successfully leverage this loophole in a non-Hermitian three-band system, implementing an unpaired third-order exceptional point (EP3), which manifests as a non-Abelian monopole. We explicitly demonstrate the intricate braiding topology and non-Abelian, path-dependent, fusion rules underlying the unpaired EP3. The experiment uses a new design of single-photon interferometry, enabling eigenstate and spectral resolutions for multi-band systems with widely tunable parameters. Thus, the union of state-of-the-art experiments, fundamental theory, and everyday concepts such as braids pave the way toward the highly exotic non-Abelian topology unique to non-Hermitian settings.