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 properties due to dimerized hoppings. We show that at unit filling there exist crossovers and phase transitions to bond-order phases of paired bosons known as the pair-bond-order phase for 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 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, for example, with repulsively bound bosons.

We analyse the ground-state properties of three-body constrained bosons in a one dimensional optical lattice with staggered hoppings analogous to the double well optical lattice. By considering attractive and repulsive on-site interactions between the bosons, we obtain the phase diagram which exhibits various quantum phases. Due to the double-well geometry and three-body constraint several gapped phases such as the Mott insulators and dimer/bond-order phases emerge at commensurate densities in the repulsive interaction regime. Attractive interaction leads to the pair formation which leads to the pair bond order phase at unit filling which resembles the valence-bond solid phase of composite bosonic pairs. At incommensurate densities we see the signatures of the gapless pair superfluid phase.

We investigate a system of two-and three-body constrained dipolar bosons in a pair of onedimensional optical lattices coupled to each other by the non-local dipole-dipole interactions. Assuming attractive dipole-dipole interactions, we obtain the ground state phase diagram of the system by employing the cluster mean-field theory. The competition between the repulsive on-site and attractive nearest-neighbor interactions between the chains yields three kinds of superfluids; namely the trimer superfluid, pair superfluid and the usual single particle superfluid along with the insulating Mott phase at the commensurate density. Besides, we also realize simultaneous existence of Mott insulator and superfluid phases for the two-and three-body constrained bosons, respectively. We also analyze the stability of these quantum phases in the presence of a harmonic trap potential.

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