The Mott insulator-superfluid transition for ultracold bosonic atoms in an optical lattice has been extensively studied in the framework of the Bose-Hubbard model with two-body on-site interactions.In this paper, we analyze the additional effect of the three-body on-site interactions on this phase transition in an optical lattice and the transitions between the various phases that arise in an optical superlattice. Using the mean-field theory and the density matrix renormalization group method, we find the phase diagrams depicting the relationships between various physical quantities in an optical lattice and superlattice. We also propose a possible experimental signature to observe the on-site three-body interactions.

We obtain the complete quantum phase diagram of bosons on a two-leg ladder in the presence of attractive onsite and repulsive interchain nearest neighbor interactions by imposing the onsite three body constraint. We find three distinct phases, namely, the atomic superfluid(ASF), dimer superfluid (DSF) and the dimer rung insulator (DRI). In the absence of the interchain nearest neighbor repulsion, the system exhibits a transition from the ASF to the DSF phase with increasing onsite attraction. However, the presence of the interchain nearest neighbor repulsion stabilizes a gapped DRI phase, which is flanked by the DSF phase. We also obtain the phase diagram of the system for different values of the interchain nearest neighbor interaction. By evaluating different order parameters, we obtain the complete phase diagram and the properties of the phase transitions using the self consistent cluster mean field theory.

In this paper we analyze the various phases exhibited by a system of ultracold bosons in a periodic optical superlattice using the mean field decoupling approximation. We investigate for a wide range of commensurate and incommensurate densities. We find the gapless superfluid phase, the gapped Mott insulator phase, and gapped insulator phases with distinct density wave orders.