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Novel quantum phases of two-component bosons with pair hopping in synthetic dimension

We study two-component (or pseudospin-1/2) bosons with pair hopping interactions in synthetic dimension, for which a feasible experimental scheme on a square optical lattice is also presented. Previous studies have shown that two-component bosons with on-site interspecies interaction can only generate nontrivial interspecies paired superfluid (super-counter-fluidity or pair-superfluid) state. In contrast, apart from interspecies paired superfluid, we reveal two new phases by considering this additional pair hopping interaction. These novel phases are intraspecies paired superfluid (molecular superfluid) and an exotic non-integer Mott insulator which shows a non-integer atom number at each site for each species, but an integer for total atom number.