Bose-Einstein condensates with attractive 1/r interaction: The case of self-trapping

Journal Article · Thu Nov 15 00:00:00 EST 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.76.053604· OSTI ID:21028045

Papadopoulos, I; Wagner, P; Wunner, G; Main, J ^[1]

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1. Institut fuer Theoretische Physik, Universitaet Stuttgart, D-70550 Stuttgart (Germany)

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 an external trap potential, is physically best understood by introducing appropriate 'atomic' units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters N{sup 2}a/a{sub u} and {gamma}/N{sup 2}, where N is the particle number, a the scattering length, a{sub u} the 'Bohr' radius, and {gamma} the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, and for energies, sizes, and peak densities, and compare with previous variational results. 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.

• OSTI ID: 21028045
• Journal Information: Physical Review. A, Vol. 76, Issue 5; Other Information: DOI: 10.1103/PhysRevA.76.053604; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ATOMS
BIFURCATION
BOSE-EINSTEIN CONDENSATION
COMPARATIVE EVALUATIONS
CONDENSATES
DENSITY
EQUATIONS
EXCITED STATES
GROUND STATES
INTERACTIONS
MATHEMATICAL SOLUTIONS
PARTICLES
POTENTIALS
SCALING
SCATTERING LENGTHS
TRAPPING
TRAPS
VARIATIONAL METHODS
WAVE FUNCTIONS