  Experiments with bosonic atoms in optical superlattices allow for the
interesting possibility to study the adiabatic quantized pumping of bosonic
atoms in the presence of interactions. We investigate this exotic phenomenon
for bound bosonic pairs in the paradigmatic Su-Schrieffer-Heeger model where
the ground state exhibits topological phase transitions due to dimerized
hoppings. At unit filling we show that there exist crossovers and phase
transitions to bond-order phases of paired bosons known as pair-bond-order
phase as a function of attractive interactions. The pair bond order phase is
found to exhibit effective topological properties such as the presence of
polarized paired edge states. This is further analyzed by studying the
emergence and breakdown of the Thouless charge pumping of this bound bosonic
pairs by a parametric extension to the famous Rice-Mele model. Finally we
discuss how the pumping of paired bosons or different regimes of breakdown of
charge pumping can be probed by state-of-the art experiments with repulsively
bound bosons.
