  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.
