  Bloch oscillations (BOs) are a fundamental phenomenon by which a wave packet
undergoes a periodic motion in a lattice when subjected to an external force.
Observed in a wide range of synthetic lattice systems, BOs are intrinsically
related to the geometric and topological properties of the underlying band
structure. This has established BOs as a prominent tool for the detection of
Berry phase effects, including those described by non-Abelian gauge fields. In
this work, we unveil a unique topological effect that manifests in the BOs of
higher-order topological insulators through the interplay of non-Abelian Berry
curvature and quantized Wilson loops. It is characterized by an oscillating
Hall drift that is synchronized with a topologically-protected inter-band
beating and a multiplied Bloch period. We elucidate that the origin of this
synchronization mechanism relies on the periodic quantum dynamics of Wannier
centers. Our work paves the way to the experimental detection of non-Abelian
topological properties in synthetic matter through the measurement of Berry
phases and center-of-mass displacements.
