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The nature of complex eigenenergy enables unique band topology to the non-Hermitian (NH) lattice systems. Recently, there has been a fast growing interest in the elusive winding and braiding topologies of the NH single and double bands, respectively. Here, we explore the even more intricate NH multi-band topology and present the first experimental characterization of the three-band braid relations by acoustic systems. Based on a concise tight-binding model, we design a ternary cavity-tube structure equipped with a highly controllable unidirectional coupler, through which the acoustic NH Bloch bands are experimentally reproduced in a synthetic dimension. We identify the NH three-band braid relations from both the perspectives of eigenvalues and eigenstates, including a noncommutative braid relation and a swappable braid relation. Our results could promote the understanding of NH Bloch band topology and pave the way toward designing new devices for manipulating acoustic states., Comment: 5 figures

Topological features embedded in ancient braiding and knotting arts endow significant impacts on our daily life and even cutting-edge science. Recently, fast growing efforts are invested to the braiding topology of complex Bloch bands in non-Hermitian systems. This new classification of band topology goes far beyond those established in Hermitian counterparts. Here, we present the first acoustic realization of the topological non-Hermitian Bloch braids, based on a two-band model easily accessible for realizing any desired knot structure. The non-Hermitian bands are synthesized by a simple binary cavity-tube system, where the long-range, complex-valued, and momentum-resolved couplings are accomplished by a well-controlled unidirectional coupler. In addition to directly visualizing various two-band braiding patterns, we unambiguously observe the highly-elusive topological phase transitions between them. Not only do our results provide a direct demonstration for the non-Hermitian band topology, but also the experimental techniques open new avenues for designing unconventional acoustic metamaterials., Comment: Accepted by PRL