Classical non-Abelian braiding of acoustic modes

Non-Abelian braiding is regarded as an essential process for realizing quantum logic. Its realizations in quantum systems often rely on the dynamic winding of anyons, which can be challenging to obtain. Implementing braiding in a classical system could, therefore, assist the experimental study of non-Abelian physics. Here we present the realization of the non-Abelian braiding of multiple degenerate acoustic waveguide modes. The dynamics of non-Abelian braiding can be captured by the non-Abelian Berry–Wilczek–Zee phase that connects the holonomic adiabatic evolutions of multiple degenerate states. The cyclic evolution of degenerate states induces a non-Abelian geometric phase, manifesting as the exchange of states. The non-Abelian characteristics are revealed by switching the order of two distinct braiding processes involving three modes. Our work demonstrates wave manipulations based on non-Abelian braiding and logic operations.