  We report a comprehensive study of the ground-state properties of one and two
bosonic impurities immersed in small one-dimensional optical lattices loaded
with a few interacting bosons. We model the system with a two-component
Bose-Hubbard model and solve the problem numerically by means of the exact
diagonalization (ED) method. We report binding energies of one and two
impurities across the superfluid (SF) to Mott-insulator (MI) transition and
confirm the formation of two-body bound states of impurities induced by
repulsive interactions. In particular, we found that an insulator bath induces
tightly bound di-impurity dimers, whereas a superfluid bath induces shallower
bound states.
