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  • Open Access

Programmable Lattices for Non-Abelian Topological Photonics and Braiding

Gyunghun Kim1, Jensen Li2, Xianji Piao3,*, Namkyoo Park4,†, and Sunkyu Yu1,‡

  • 1Intelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea
  • 2Centre for Metamaterial Research and Innovation, Department of Physics and Astronomy, University of Exeter, Exeter, United Kingdom
  • 3Wave Engineering Laboratory, School of Electrical and Computer Engineering, University of Seoul, Seoul 02504, Korea
  • 4Photonic Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea

  • *Contact author: piao@uos.ac.kr
  • †Contact author: nkpark@snu.ac.kr
  • ‡Contact author: sunkyu.yu@snu.ac.kr
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Phys. Rev. Lett. 136, 043804 – Published 30 January, 2026

DOI: https://doi.org/10.1103/rgfy-n6zd

Abstract

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.

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Phys. Rev. Lett. 136, 043804– Published 30 January, 2026
  • Received 10 February 2025
  • Revised 15 October 2025
  • Accepted 8 January 2026
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