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The Mott insulator-superfluid transition for ultracold bosonic atoms in anoptical lattice has been extensively studied in the framework of theBose-Hubbard model with two-body on-site interactions. In this paper, weanalyze the additional effect of the three-body on-site interactions on thisphase transition in optical lattice and the transitions between the variousphases that arise in an optical superlattice. Using the mean-field theory andthe density matrix renormalization group method, we find the phase diagramsdepicting the relationships between various physical quantities in an opticallattice and superlattice. We also suggest possible experimental signatures toobserve the three-body interactions.

Three body on-site interactions in ultracold bosonic atoms in optical lattices and superlattices