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arXiv:quant-ph/9802053 · Fortschritte der Physik

Some Remarks on the Fragmentation of Bose Condensates

Robert W. Spekkens, John E. Sipe

Published Nov 1, 1998• 2 citations
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Abstract

We show how fragmentation of a Bose-Einstein condensate can occur given repulsive inter-particle interactions and a non-uniform external potential.
DOI
10.1002/(sici)1521-3978(199811)46:6/8<873::aid-prop873>3.0.co;2-q

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Bose--Einstein condensation for particles with repulsive short-range pair interactions in a Poisson random external potential in Rd\mathbb R^dRd
We study Bose gases in ddd dimensions, d≥2d \ge 2d≥2, with short-range repulsive pair interactions, at positive temperature, in the canonical ensemble and in the thermodynamic limit. We assume the presence of hard Poissonian obstacles and focus on the non-percolation regime. For sufficiently strong interparticle interactions, we show that almost surely there cannot be Bose--Einstein condensation into a sufficiently localized, normalized one-particle state. The results apply to the eigenstates of the underlying one-particle Hamiltonian.
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.