Non-Hermitian Nested Hopf-Links and Conjoint Open-Arcs in Synthetic Non-Abelian Gauge Photonic Lattices

TL;DR

This paper explores the complex topological phenomena in non-Hermitian non-Abelian photonic lattices, revealing novel braid patterns, phase transitions, and localized skin effects driven by competing non-Hermitian effects and gauge phases.

Contribution

It introduces the formation of nested Hopf-links and conjoint open-arcs in non-Hermitian non-Abelian systems, demonstrating their topological phase transitions and unique localization behaviors.

Findings

Observation of braid patterns and Hopf-links in spectra

Identification of non-Hermitian topological phase transition at EP

Discovery of purely dipole skin effect without extended modes

Abstract

Non-Hermitian physics enriches the topological attributes of non-Abelian systems. Non-Abelian systems characterized by noncommutative braid patterns are associated with intriguing physical features and applications. Non-Abelian braiding of the non-Hermitian bands and anomalous skin mode localization may emerge due to a host of competing physical effects. The quest for the generality of their physical origin and the associated new phenomena, therefore, constitutes a pertinent question to consider. Here, we consider a synthetic gauge photonic lattice with competing sources of non-Hermiticity, i.e. NN and NNN hopping mismatches, non-Abelian SU(2) phases, and gain/loss processes. Formation of the distinctive braid patterns and nested Hopf-links is observed, which is followed by a non-Hermitian topological phase transition at EP and the opening of an imaginary gap beyond. The PBC and OBC eigenspectra and concomitant localization dynamics of the OBC eigenstates show rich physical features that are unattainable in their less complex counterparts. This includes the formation of the conjoint open-arcs in the OBC spectra which give rise to a completely localized purely dipole skin effect without any extended modes. This work sheds light on some of the key aspects of the synthetic non-Abelian gauge photonic systems in the presence of multiple competing non-Hermitian degrees of freedom that may stimulate further research in this direction.