Entanglement in Spin Waves with Binary Dipolar Atoms in a 2D Optical Lattice

We study the area-dependent entropy and two-site entanglement in the spin waves with binary interacting dipolar Bose-Einstein condensates in a 2D optical lattice. The two species condensates at each site behave like an ensemble of spin-half particles with the interaction to its nearest neighbors and next nearest neighbors. We show that the ground state of a Bose-Einstein condensate lattice with nearest-neighbor and next-nearest-neighbor interactions exhibits spin wave and can be mapped into a harmonic lattice. The critical behavior of the area-dependent entropy and two-site entanglement is examined in the vicinity of a quantum phase transition.