We analyze the entanglement properties of the Bogoliubov vacuum, which is obtained as a second-order approximation to the ground state of an interacting Bose-Einstein condensate. We work in one- and two-dimensional lattices and study the entanglement between two groups of sites as a function of the geometry of the configuration and the strength of the interactions. As our measure of entanglement we use the logarithmic negativity, supplemented by an algorithmic check for bound entanglement where appropiate. The short-range entanglement is found to grow approximately linearly with the group sizes and to be favoured by strong interactions. Conversely, long-range entanglement is favoured by relatively weak interactions. No examples of bound entanglement are found.
Physical Review a (atomic, Molecular and Optical Physics), 2005, Vol 71