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Non-Abelian Thouless pumping in photonic waveguides

Nature Physics volume 18, pages 1080–1085 (2022)Cite this article

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Abstract

Thouless pumping enables topological transport and the direct measurement of topological invariants. So far, realizations of Thouless pumping rely on the adiabatic evolution of a physical system following a non-degenerate band, but it has been predicted that pumping can become non-Abelian in nature when degenerate bands exist. The resulting non-Abelian gauge fields and associated non-commutative operations would be promising for applications related to unitary matrices, such as photonic quantum logic. Here we propose the experimental realization of non-Abelian Thouless pumping in an on-chip photonic platform. By modulating the coupling coefficients within photonic waveguides with degenerate flat bands, we observe non-Abelian Thouless pumping in a three-step pumping device where the outcomes depend on the sequence of the pumping operations. We anticipate our versatile platform to reveal more complex non-Abelian topological physics and realize on-chip non-Abelian photonic devices in the future.

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Fig. 1: Lieb lattice consisting of photonic waveguides with modulated coupling coefficients.
Fig. 2: Mode switching and geometric phases in Thouless pumping.
Fig. 3: Non-Abelian nature of Thouless pumping.
Fig. 4: Non-Abelian Thouless pumping with multiple pumping operations.

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Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study 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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Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) under grant nos. 61590930, 11974140, 61805098, 61825502 and 61827826, as well as China Postdoctoral Science Foundation grant no. 2019M651200. X.-L.Z. thanks G. Ma for fruitful discussions.

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  1. These authors contributed equally: Yi-Ke Sun, Xu-Lin Zhang, Feng Yu.

Authors and Affiliations

  1. State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun, China

    Yi-Ke Sun, Xu-Lin Zhang, Feng Yu, Zhen-Nan Tian, Qi-Dai Chen & Hong-Bo Sun

  2. State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, Beijing, China

    Hong-Bo Sun

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Contributions

X.-L.Z. conceived the idea, performed the theoretical analysis and designed the experiment. Y.-K.S. and 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. with input from all the authors. The project was supervised by H.-B.S.

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

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Nature Physics thanks Liang Feng and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Notes 1–4, Figs. 1–16, Table 1 and refs. 1–6.

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Sun, YK., Zhang, XL., Yu, F. et al. Non-Abelian Thouless pumping in photonic waveguides. Nat. Phys. 18, 1080–1085 (2022). https://doi.org/10.1038/s41567-022-01669-x

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