Experimental characterization of three-band braid relations in non-Hermitian acoustic lattices

The nature of complex eigenenergy enables unique band topology in non-Hermitian (NH) lattices. Recently, there has been 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 multiband topology and present an experimental characterization of the three-band braid relations by acoustic systems. Based on a concise tight-binding lattice model, we design a ternary cavity-tube structure equipped with a highly controllable unidirectional coupler, through which acoustic NH Bloch bands are experimentally reproduced in a synthetic space. We identify the NH braid relations from the global evolution of the eigenvalues and acoustic states, including a noncommutative braid relation σ_{1}σ_{2}≠σ_{2}σ_{1} and a swappable braid relation σ_{1}σ_{2}σ_{1}=σ_{2}σ_{1}σ_{2}. Our results could promote the understanding of NH Bloch band topology and pave the way toward designing practical devices for manipulating acoustic states.