  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.
