  Thouless pumping, not only achieving quantized transport but also immune to
moderate disorder, has attracted growing attention in both experiments and
theories. Here, we explore how particle-particle interactions affect
topological transport in a periodically-modulated and tilted optical lattice.
Not limited to wannier states, our scheme ensures a dispersionless quantized
transport even for initial Gaussian-like wave packets of interacting bosons
which do not uniformly occupy a given band. This is because the tilting
potential leads to Bloch oscillations uniformly sampling the Berry curvatures
over the entire Brillouin zone. The interplay among on-site potential
difference, tunneling rate and interactions contributes to the topological
transport of bound and scattering states and the topologically resonant
tunnelings. Our study deepens the understanding of correlation effects on
topological states, and provides a feasible way for detecting topological
properties in interacting systems.
