Observation of Non-Abelian Thouless Pump

TL;DR

This paper reports the experimental observation of a non-abelian Thouless pump in an acoustic waveguide array, demonstrating non-commutative topological effects arising from multi-band interactions and complex eigenstate evolution.

Contribution

It introduces the first experimental realization of a non-abelian Thouless pump, revealing non-commutative topological phenomena in a classical acoustic system.

Findings

Observation of non-abelian topological pumping in acoustic waveguides

Demonstration of path-dependent final states due to non-commutativity

Identification of eigenstate evolution across band degeneracies

Abstract

Thouless pump is a one-dimensional dynamic topological effect that stems from the same topological mechanism as the renowned two-dimensional Chern insulators, with one momentum dimension replaced by a time variant evolution parameter. The underlying physics is abelian, concerning topologies of individual bands. By introducing multi-band non-abelian topology into pumping, much richer physics is expected that goes beyond the abelian counterpart. Here we report the observation of a non-abelian Thouless pump in an acoustic waveguide array with judiciously engineered coupling configurations. The observed non-abelian effect originates from time-evolution of eigen-states in Z_3 pump cycles that traverse across several band degeneracies in the parameter space in a three-band system. Interestingly, the pump of the eigenstates exhibits non-commutativity, i.e. the final state depends critically on the order of the pumping paths. Our study paves ways for exploring and utilizing non-abelian dynamical effects in classical systems.