  We examine particle entanglement, characterized by pseudo-spin squeezing, of
spin-1 bosonic atoms with coupled ground states in a one-dimensional optical
lattice. Both the superfluid and Mott-insulator phases are investigated
separately for ferromagnetic and antiferromagnetic interactions. Mode
entanglement is also discussed in the Mott insulating phase. The role of a
small but nonzero angle between the polarization vectors of counter-propagating
lasers forming the optical lattice on quantum correlations is investigated as
well.
