Journal de Physique I

Stability of Atomic Bose-Einstein Condensate with Negative Scattering Length

Weiping Zhang, Barry C. Sanders, A. Mann

Published Nov 1, 1996• 2 citations

Abstract

We discuss the stability of a small-scale Bose-Einstein condensate with negative scattering length. The stable state is found by obtaining the appropriate basis using self-consistent field theory for an attractive one-dimensional potential.

DOI: 10.1051/jp1:1996154

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Journal de Physique I

Stability of Atomic Bose-Einstein Condensate with Negative Scattering Length

Weiping Zhang, Barry C. Sanders, A. Mann

Published Nov 1, 1996• 2 citations

Publisher

Abstract

DOI: 10.1051/jp1:1996154

Related papers

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

I. Papadopoulos, P. Wagner, G. Wunner +1 more

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.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.

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Maciej Lewenstein, Li You

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Physical Review AFeb 1, 199623 citations

BOSE-EINSTEIN CONDENSATION OF ATOMS WITH ATTRACTIVE INTERACTION

Nail Akhmediev, Mrinmay Das, Alexei Vagov

We suggest that crucial effect on Bose-Einstein condensation in systems with attractive potential is three-body interaction. We investigate stationary solutions of the Gross-Pitaevskii equation with negative scattering length and a higher-order stabilising term in presence of an external parabolic potential. Stability properties of the condensate are similar to those for thermodynamic systems in statistical physics which have first order phase transitions. We have shown that there are three possible type of stationary solutions corresponding to stable, metastable and unstable phases. Results are discussed in relation to recently observed 7 Li condensate.We suggest that crucial effect on Bose-Einstein condensation in systems with attractive potential is three-body interaction. We investigate stationary solutions of the Gross-Pitaevskii equation with negative scattering length and a higher-order stabilising term in presence of an external parabolic potential. Stability properties of the condensate are similar to those for thermodynamic systems in statistical physics which have first order phase transitions. We have shown that there are three possible type of stationary solutions corresponding to stable, metastable and unstable phases. Results are discussed in relation to recently observed 7 Li condensate.

International Journal of Modern Physics BMar 10, 199961 citations

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.

We explore how to control the dynamical instability of a quasi-one dimensional (1D) stationary state Bose-Einstein condensate (BEC) consisting of fixed

N

atoms with arbitrary time-independent external potential and atomic scattering length. The dependence of the perturbed solutions on the velocity field, external potential, condensed atom number, and the initial perturbations is demonstrated analytically, that shows the stability, instability and undetermined stability of the system. Some sufficient conditions on the stability and controlling criteria to the instability are established. We take a BEC held in an optical lattice potential as an example establishing the stability regions on parameter space and illustrating the scheme for controlling instability. The results contain the known stability assertions for the lattice potential case and agree with the recent experimental findings qualitatively.

We study the stability of a Bose-Einstein condensate of harmonically trapped atoms with negative scattering length, specifically

{}^{7}\mathrm{Li}.

Our method is to solve the time-dependent nonlinear Schr\"odinger equation numerically. For an isolated condensate, with no gain or loss, we find that the system is stable (apart from quantum tunneling) if the particle number N is less than a critical number

{N}_{c}.

For

N>{N}_{c},

the system collapses to high-density clumps in a region near the center of the trap. The time for the onset of collapse is on the order of one trap period. Within numerical uncertainty, the results are consistent with the formation of a ``black hole'' of infinite density fluctuations, as predicted by Ueda and Huang [Phys. Rev. A (to be published)]. We numerically obtain ${N}_{c}\ensuremath{\approx}1251.$ We then include gain-loss mechanisms, i.e., the gain of atoms from a surrounding ``thermal cloud,'' and the loss due to two- and three-body collisions. The number N now oscillates in a steady state, with a period of about 145 trap periods. We obtain ${N}_{c}\ensuremath{\approx}1260$ as the maximum value in the oscillations.