You Oubo, Liang Shanjun, Xie Biye, Gao Wenlong, Ye Weimin, Zhu Jie, Zhang Shuang
Department of Physics, University of Hong Kong, Hong Kong, China.
Division of Science, Engineering and Health Studies, College of Professional and Continuing Education, Hong Kong Polytechnic University, Hong Kong, China.
Phys Rev Lett. 2022 Jun 17;128(24):244302. doi: 10.1103/PhysRevLett.128.244302.
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 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 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.
Thouless泵提供了实现波和粒子量子化输运的可靠方法，它将静态二维量子霍尔效应映射到一维动态系统中，其中一个动量维度被演化时间或路径参数所取代。在过去几十年里，各种类型的阿贝尔Thouless泵已在理论和实验上得以实现。然而，非阿贝尔Thouless泵的研究却很稀少，这意味着具有相同基点的两个演化回路的顺序不能改变，并且尚未有非阿贝尔Thouless泵的实验观测报道。在此，我们报告了在耦合声波导阵列中对非阿贝尔Thouless泵的观测。非阿贝尔特性源于两个不同的ℤ₃泵浦循环的非对易组合，这两个循环在一个三能带系统的参数空间中穿越多个能带简并点。此外，通过按精心设计的顺序多次应用这两个ℤ₃泵浦循环，我们可以将特定的初始态泵浦到任意晶格位置上的任意态。我们的研究为在经典波系统中探索和利用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。
