Two-dimensional non-Abelian Thouless pump.

Non-Abelian Thouless pumps are periodically driven systems designed by the non-Abelian holonomy principle, in which quantized transport of degenerate eigenstates emerges, exhibiting noncommutative features such that the outcome depends on the pumping sequence. The study of non-Abelian Thouless pump is currently restricted to 1D systems, while extending it to higher-dimensional systems will not only provide effective means to probe non-Abelian physics in high-dimensional topological systems, but also expand the dimension and type of associated non-Abelian geometric phase matrix for potential applications. Here, we propose the design and experimental realization of 2D non-Abelian Thouless pumps on a photonic chip with 2D photonic waveguide arrays, where degenerate photonic modes are topologically pumped simultaneously along two real-space directions. We reveal the associated non-Abelian group and experimentally demonstrate the non-Abelian feature by measuring the pumping sequence dependent output. The proposed 2D non-Abelian Thouless pump shows promising applications for robust optical interconnections and optical computing.