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Non-Abelian braiding on photonic chips


Non-Abelian braiding has attracted substantial attention because of its pivotal role in describing the exchange behaviour of anyons—candidates for realizing quantum logics. The input and outcome of non-Abelian braiding are connected by a unitary matrix that can also physically emerge as a geometric-phase matrix in classical systems. Hence it is predicted that non-Abelian braiding should have analogues in photonics, although a feasible platform and the experimental realization remain out of reach. Here we propose and experimentally realize an on-chip photonic system that achieves the non-Abelian braiding of up to five photonic modes. The braiding is realized by controlling the multi-mode geometric-phase matrix in judiciously designed photonic waveguide arrays. The quintessential effect of braiding—sequence-dependent swapping of photon dwell sites—is observed in both classical-light and single-photon experiments. Our photonic chips are a versatile and expandable platform for studying non-Abelian physics, and we expect the results to motivate next-generation non-Abelian photonic devices.

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Fig. 1: Two-mode braiding in photonic waveguides.
Fig. 2: Measurement of the geometric phase in two-mode braiding.
Fig. 3: Non-Abelian braiding of three modes.
Fig. 4: Multi-mode braiding.

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Data availability

The data that support the findings of this work are available from the corresponding authors upon reasonable request.

Code availability

The codes used for performing the theoretical analysis and numerical simulations are available from X.-L.Z. upon reasonable request.


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This work was supported by the National Natural Science Foundation of China (11922416, 11974140, 61825502, 61827826 and 61960206003), China Postdoctoral Science Foundation (2019T120234) and the Hong Kong Research Grants Council (12302420, 12300419, 22302718 and C6013-18G). X.-L.Z. and G.M. thank C. T. Chan and R.-Y. Zhang for fruitful discussions.

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Authors and Affiliations



X.-L.Z. and G.M. conceived of the idea. X.-L.Z., Z.-G.C. and G.M. performed the theoretical analysis. X.-L.Z. performed numerical simulations and designed the experiment. F.Y. carried out the experimental measurements under the supervision of Z.-N.T. and Q.-D.C. The manuscript was written by X.-L.Z. and G.M. with inputs from all the authors. The project was supervised by G.M. and H.-B.S.

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Correspondence to Xu-Lin Zhang, Zhen-Nan Tian, Hong-Bo Sun or Guancong Ma.

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Nature Photonics thanks the anonymous reviewers for their contribution to the peer review of this work.

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Supplementary Notes 1–3, Figs. 1–12 and Table 1.

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Zhang, XL., Yu, F., Chen, ZG. et al. Non-Abelian braiding on photonic chips. Nat. Photon. 16, 390–395 (2022).

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