Quantum entanglement of spin-1 bosons with coupled ground states in optical lattices

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.