Topological Wannier cycles induced by sub-unit-cell artificial gauge flux in a sonic crystal

Gauge fields are at the heart of the fundamental science of our universe and various materials. For instance, Laughlin's gedanken experiment of gauge flux insertion played a major role in understanding the quantum Hall effects. Gauge flux insertion into a single unit-cell, though crucial for detecting exotic quantum phases and for the ultimate control of quantum dynamics and classical waves, however, has not yet been achieved in laboratory. Here, we report on the experimental realization of gauge flux insertion into a single plaquette in a lattice system with the gauge phase ranging from 0 to 2pi which is realized through a novel approach based on three consecutive procedures: the dimension extension, creating an engineered dislocation and the dimensional reduction. Furthermore, we discover that the single-plaquette gauge flux insertion leads to a new phenomenon termed as the topological Wannier cycles, i.e., the cyclic spectral flows across multiple band gaps which are manifested as the topological boundary states (TBSs) on the plaquette. Such topological Wannier cycles emerge only if the Wannier centers are enclosed by the flux-carrying plaquette. Exploiting acoustic metamaterials and versatile pump-probe measurements, we observe the topological Wannier cycles by detecting the TBSs in various ways and confirm the single-plaquette gauge flux insertion by measuring the gauge phase accumulation on the plaquette. Our work unveils an unprecedented regime for lattice gauge systems and a fundamental topological response which could empower future studies on artificial gauge fields and topological materials.