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.