Acta Physica Sinica

BOSE-EINSTEIN CONDERSATION OF NEUTRAL ATOMS WITH ATTRACTIVE INTERACTION IN A HAR MONIC TRAP

YAN KE-ZHU, TAN WEI-HAN, 上海大学物理系，上海 201800

Published Jan 1, 2000• 7 citations

Abstract

In this paper we present the numerical solutions of neutral atoms with attractive interaction in a harmonic trap. The calculated result shows the bistability curve of the number of condensate atoms versus the energy eigenvalues. The maximum number of atoms in and attractive Bose-Einstein condensate deduced hereby is in agreement with the experimental on the whole.

DOI: 10.7498/aps.49.1909

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Acta Physica Sinica

BOSE-EINSTEIN CONDERSATION OF NEUTRAL ATOMS WITH ATTRACTIVE INTERACTION IN A HAR MONIC TRAP

YAN KE-ZHU, TAN WEI-HAN, 上海大学物理系，上海 201800

Published Jan 1, 2000• 7 citations

Publisher

Abstract

DOI: 10.7498/aps.49.1909

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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.

{N}_{c}{=0.55(l}_{0}/|a|).

Our results also show that, by exchanging the frequencies ${\ensuremath{\omega}}_{z}$ and ${\ensuremath{\omega}}_{\ensuremath{\rho}},$ the geometry with ${\ensuremath{\omega}}_{\ensuremath{\rho}}<{\ensuremath{\omega}}_{z}$ favors the condensation of larger number of particles. We also simulate the time evolution of the condensate when changing the ground state from

a=0

a<0

using a 200 ms ramp. A conjecture on higher-order nonlinear effects is also added in our analysis with an experimental proposal to determine its signal and strength.