Spatial fragmentation of a Bose-Einstein condensate in a double-well potential

We present a theoretical study of the ground state of a Bose-Einstein condensate with repulsive interparticle interactions in a double-well potential, using a restricted variational principle. Within such an approach, there is a transition from a single condensate to a fragmented condensate as the strength of the central barrier of the potential is increased. We determine the nature of this transition through an approximate analytic solution as well as a numerical solution of our model, in the regime where the interparticle interactions can be treated perturbatively. The degree of fragmentation of the condensate is characterized by the degrees of first- and second-order spatial coherence across the barrier.