Thouless pump provides robust ways to realize quantized transport of waves and particles, and it casts the static 2D quantum Hall effect onto 1D dynamic systems where one of the momentum dimensions is replaced by the evolution time or path parameter. In the past few decades, various types of Abelian Thouless pump have been achieved theoretically and experimentally. However, the study of non-Abelian Thouless pump is scarce, which tells us that the order of two evolution loops with the same base point cannot be changed, and there has been no experimental observation of non-Abelian Thouless pump. Here we report the observation of a non-Abelian Thouless pump in coupled acoustic waveguide array. The non-Abelian property originates from the noncommutative combination of two different ${\mathbb{Z}}_3$ pump cycles that traverse across multiple band degeneracies in the parameter space in a three-band system. Moreover, we can pump a specific initial state to any state on any lattice site by applying these two ${\mathbb{Z}}_3$ pump cycles multiple times in a well-designed sequence. Our study paves the way for exploring and utilizing non-Abelian dynamical effects in classical wave systems and may offer different recipes for quantum walking, quantum optics, and quantum computation.

中文翻译：

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非阿贝尔 Thouless 泵的观察

Thouless 泵为实现波和粒子的量化传输提供了可靠的方法，并将静态二维量子霍尔效应投射到一维动态系统上，其中动量维度之一被演化时间或路径参数取代。在过去的几十年里，各种类型的 Abelian Thouless 泵在理论上和实验上都得到了实现。然而，非阿贝尔Thouless泵的研究却很少，这告诉我们两个基点相同的进化循环的顺序是不能改变的，也没有对非阿贝尔Thouless泵的实验观察。在这里，我们报告了在耦合声波导阵列中对非阿贝尔 Thouless 泵的观察。非阿贝尔性质源于两个不同的非交换组合${\mathbb{Z}}_3$在三波段系统的参数空间中跨越多个波段简并的泵循环。此外，我们可以通过应用这两个来将特定的初始状态泵送到任何格点上的任何状态${\mathbb{Z}}_3$泵以精心设计的顺序循环多次。我们的研究为探索和利用经典波系统中的非阿贝尔动力学效应铺平了道路，并可能为量子行走、量子光学和量子计算提供不同的方法。