Bose-Einstein condensates with attractive 1r interaction The case of self-trapping.pdf

a r X i v : 0 7 0 9 .2 8 6 6 v 1 [ q u a n t - p h ] 1 8 S e p 2 0 0 7 Bose-Einstein condensates with attractive 1/r interaction: The case of self-trapping I. Papadopoulos, P. Wagner, G. Wunner,? and J. Main 1. Institut fu?r Theoretische Physik, Universita?t Stuttgart, D-70550 Stuttgart, Germany (Dated: February 1, 2008) Amplifying on a proposal by O’Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive 1/r interaction, we point out that the instance of self-trapping of the condensate, without external trap potential, is physically best understood by introducing appro- priate ”atomic” units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters N2a/au and γ/N 2, where N is the particle number, a the scattering length, au the ”Bohr” radius and γ the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, for energies, sizes and peak densities, and compare with previous variational results. As a novel feature we point out the existence of a second solution of the extended Gross-Pitaevskii equation for negative scattering lengths, with and without trapping potential, which is born together with the ground state in a tangent bifurcation. This indicates the existence of an unstable collectively excited state of the condensate for negative scattering lengths. PACS numbers: 03.75.Hh, 34.20.Cf, 34.80.Qb, 04.40.-b I. INTRODUCTION Bose-Einstein condensation of dipolar gases has at- tracted much attention in recent years [1, 2, 3, 4, 5] because it offers the opportunity to create degenerate quantum gases with adjustable long- and short-range in- teractions, which gives rise to a wealth of novel phe- nomena [6, 7, 8, 9]. In particular, the achievement of Bose-Einstein condensation in a gas of chromium atoms [10], with a large dipole moment, has opened the way to promising experiments on dipolar quantum gases [11]