The competition between tunneling and interactions in bosonic lattice models generates a whole variety of different quantum phases. While, in the presence of a single species interacting via on-site interaction, the phase diagram presents only superfluid or Mott insulating phases, for long-range interactions or multiple species, exotic phases such as supersolid (SS) or pair-superfluid (PSF) appear. In this work, we show for the first time that the co-existence of effective multiple species and long-range interactions leads to the formation of a novel pair-supersolid (PSS) phase, namely a supersolid of composites. We propose a possible implementation with dipolar bosons in a bilayer two-dimensional optical lattice.
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