Quantum dynamics of one and two bosonic atoms in a combined tight-binding periodic and weak parabolic potential

Strongly interacting bosonic particles in a tight-binding periodic potential superimposed by a weak parabolic trap is a paradigm for many cold atom experiments. Here, after revisiting the single particle problem, we study interaction-bound dimers of bosonic atoms in the combined lattice and parabolic potential. We consider both repulsively- and attractively-bound dimers and find pronounced differences in their behaviour. We identify conditions under which attractive and repulsive dimers exhibit analogous dynamics. Our studies reveal that coherent transport and periodic oscillations of appropriately prepared one- and two-atom wavepackets can be achieved, which may facilitate information transfer in optical lattice based quantum computation schemes.