Programmable Lattices for Non-Abelian Topological Photonics and Braiding

Non-Abelian physics, originating from noncommutative sequences of operations, unveils novel topological degrees of freedom. In photonics, significant efforts have been devoted to developing reconfigurable non-Abelian platforms, serving both as classical testbeds for non-Abelian quantum phenomena and as programmable systems that harness topological complexities. Here, we establish topological spinor lattices for non-Abelian programmable photonics. We design a building block for reconfigurable unitary coupling between pseudospin resonances, achieving a universal set of rotation gates through the coupling loop. The lattice assembly of the building blocks enables the emulation of the extended quantum Hall family. We reveal the emergence of a non-Abelian interface even when the bulks are Abelian, which allows the topologically trivial engineering of topologically protected edge states. We also define the braid group for pseudospin observables, demonstrating non-Abelian braiding and the Yang-Baxter relations. Our results pave the way for realizing a reconfigurable emulator for Abelian and non-Abelian topological phenomena.