Multi-Channel Non-Abelian Edge Pumping via Multi-Degeneracy Encircling
Abstract
Non-Abelian operations enable sequence-dependent control of light, yet experimental realizations in wave systems have remained confined to local bulk or same-boundary modes and have often required fragile gap-closing degeneracies. Conventional Thouless pumps, meanwhile, support only two-channel edge transfer across a single gap. Here we demonstrate multi-channel non-Abelian edge pumping on a silicon photonic chip by adiabatically encircling multiple band degeneracies in a multi-gap lattice. In a minimal three-band band-triangle, two opposite-charge Weyl points and one zero-charge degeneracy are linked by global band connectivity, yielding both opposite-boundary and same-boundary edge channels. Sequencing these channels produces non-Abelian braiding of three topologically protected edge modes that reside on distinct physical boundaries. The process remains fully gapped and is protected by topological winding rather than by maintained spectral degeneracies. The same band-triangle principle extends systematically to an arbitrary number of channels, establishing a scalable route to collective, sequence-controlled routing of topological states in integrated photonic circuits.
Related
- Torsion, valley holonomy, and Berry phases of quasiparticles encircling dislocations and defect complexes in graphene
- Genuine Multi-Entropy in Abelian Chern--Simons Theory: Exact Key-Ring Collapse and Its Breakdown for Generic Link States
- Symmetry and Vibrational Control of Multi-Channel HHG in Methane
- Probing Collective and Individual Kondo Screening: Multi-Stage, Multi-Channel Kondo Effects in a C3-Symmetric Four-Impurity Model
- Milestone in predicting core plasma turbulence: successful multi-channel validation of the gyrokinetic code GENE
BibTeX
@misc{mo2026multichannel,
title = {{Multi-Channel Non-Abelian Edge Pumping via Multi-Degeneracy Encircling}},
author = {Qingyang Mo and Jiacheng Sun and Zhongfu Li and Jiajun Li and Wange Song and Tao Li and Shuang Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07594},
eprint = {2611.07594},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07594},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Multi-Channel Non-Abelian Edge Pumping via Multi-Degeneracy Encircling
AU - Qingyang Mo
AU - Jiacheng Sun
AU - Zhongfu Li
AU - Jiajun Li
AU - Wange Song
AU - Tao Li
AU - Shuang Zhang
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07594
UR - https://arxiv.org/abs/2611.07594
AB - Non-Abelian operations enable sequence-dependent control of light, yet experimental realizations in wave systems have remained confined to local bulk or same-boundary modes and have often required fragile gap-closing degeneracies. Conventional Thouless pumps, meanwhile, support only two-channel edge transfer across a single gap. Here we demonstrate multi-channel non-Abelian edge pumping on a silicon photonic chip by adiabatically encircling multiple band degeneracies in a multi-gap lattice. In a minimal three-band band-triangle, two opposite-charge Weyl points and one zero-charge degeneracy are linked by global band connectivity, yielding both opposite-boundary and same-boundary edge channels. Sequencing these channels produces non-Abelian braiding of three topologically protected edge modes that reside on distinct physical boundaries. The process remains fully gapped and is protected by topological winding rather than by maintained spectral degeneracies. The same band-triangle principle extends systematically to an arbitrary number of channels, establishing a scalable route to collective, sequence-controlled routing of topological states in integrated photonic circuits.
ER -