Europhysics Letters (EPL)

Gross-Pitaevski equation and resonances in Bose-Einstein condensates

João da Providência, Asaad R. Sakhel, F. Bary Malik, H. R. Glyde

Published Feb 10, 2005• 0 citations

Abstract

The investigation provides a criterion for the occurrence of resonances for the scattering by potentials. The Gross-Pitaevski equation, used in describing physical properties in Bose-Einstein condensates, is not compatible with the occurrence of the observed resonances. On the other hand, Geltman-Bambini and Krauss-Stevens potentials could fulfill this criterion.

DOI: 10.1209/epl/i2004-10445-5

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Europhysics Letters (EPL)

Gross-Pitaevski equation and resonances in Bose-Einstein condensates

João da Providência, Asaad R. Sakhel, F. Bary Malik, H. R. Glyde

Published Feb 10, 2005• 0 citations

Publisher

Abstract

DOI: 10.1209/epl/i2004-10445-5

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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}^{2}a∕{a}_{u}

and $\ensuremath{\gamma}∕{N}^{2}$, where

N

is the particle number,

a

the scattering length,

{a}_{u}

the ``Bohr'' radius, and $\ensuremath{\gamma}$ 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.

\approx 10^{20}

, there exists a critical ground state occupation number above which the BEC is unstable, provided that its constituents interact with a $1/r^3 $ gravity at short scales.

\approx 10^{20}

, there exists a critical ground state occupation number above which the BEC is unstable, provided that its constituents interact with a $1/r^3 $ gravity at short scales.