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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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.
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 (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.
The authors declare no competing interests.
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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
Nature Physics (2022)