  We investigate the ground state properties of a non-locally coupled bosonic
system in a bilayer optical superlattice by considering bosons in one layer to
be of softcore in nature and separately allowing two and three body hardcore
constraints on the other layer. We find that the presence of different
constraints on bosons in one layer influences the overall phase diagram
exhibiting various Mott insulator phases at incommensurate densities due to the
presence of the superlattice potential apart from the usual Mott insulators at
commensurate densities. Moreover, the presence of two or three-body constraints
significantly modifies the Mott insulator-Superfluid phase transition points as
a function of the superlattice potential. Due to the various competing
interactions, constraints and superlattice potential the phase diagrams exhibit
significantly different features. We obtain the complete phase diagrams by
using the cluster-mean-field theory approach. We further extend this work to a
coupled two-leg ladder superlattice where we obtain similar physics using the
density matrix renormalization group method .
