Physical Review Letters

Bose-Einstein Condensation in Trapped Atomic Gases

Yu. Kagan, Georgy V. Shlyapnikov, Jook T. M. Walraven

Published Apr 8, 1996• 171 citations

Abstract

We discuss Bose-Einstein condensation in a trapped atomic gas and analyze how the sign of the scattering length a and the ratio \ensuremath{\eta} of the interaction between particles to the level spacing in the trap influence the behavior of the condensate wave function ${\ensuremath{\psi}}_{0}$. We find that for $a<0$ and $\ensuremath{\eta}\ensuremath{\ll}1$ it is possible to form a metastable Bose condensate, with a long characteristic lifetime with respect to contraction and transitions of particles to excited trap states. For $\ensuremath{\eta}\ensuremath{\gg}1$ a negative scattering length prevents the formation of the condensate. If $a>0$, then an increase of density is accompanied by the evolution of ${\ensuremath{\psi}}_{0}$ to a comparatively wide quasihomogeneous distribution.

DOI: 10.1103/physrevlett.76.2670

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Physical Review Letters

Bose-Einstein Condensation in Trapped Atomic Gases

Yu. Kagan, Georgy V. Shlyapnikov, Jook T. M. Walraven

Published Apr 8, 1996• 171 citations

Publisher

Abstract

{\ensuremath{\psi}}_{0}

. We find that for

a<0

and

\ensuremath{\eta}\ensuremath{\ll}1

it is possible to form a metastable Bose condensate, with a long characteristic lifetime with respect to contraction and transitions of particles to excited trap states. For

\ensuremath{\eta}\ensuremath{\gg}1

a negative scattering length prevents the formation of the condensate. If

a>0

, then an increase of density is accompanied by the evolution of

{\ensuremath{\psi}}_{0}

to a comparatively wide quasihomogeneous distribution.

DOI: 10.1103/physrevlett.76.2670

Related papers

Bose-Einstein condensation in an atomic gas with attractive interactions

Hualin Shi, Wei‐Mou Zheng

Physical Review AApr 1, 199731 citations

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Maciej Lewenstein, Li You

We study properties of the ground state of a bosonic gas of atoms in a tight trap. The atoms interact via model molecular potentials that may have either positive or negative scattering lengths. We discuss the possibility of Bose-Einstein condensation in such a system. We show that when the size of the trap becomes comparable to the correlation length of the condensate, stable Bose-Einstein condensation might occur independent of the sign of the scattering length. \textcopyright{} 1996 The American Physical Society.We study properties of the ground state of a bosonic gas of atoms in a tight trap. The atoms interact via model molecular potentials that may have either positive or negative scattering lengths. We discuss the possibility of Bose-Einstein condensation in such a system. We show that when the size of the trap becomes comparable to the correlation length of the condensate, stable Bose-Einstein condensation might occur independent of the sign of the scattering length. \textcopyright{} 1996 The American Physical Society.

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The properties and stability of a trapped Bose-Einstein condensate are strongly influenced by attractive interactions between the particles. We describe the spatial distribution, stability, and collisional loss rates for a weakly interacting gas in the mean-field limit. We show how the condensate contracts and becomes unstable as the number of condensate atoms increases. We further show how the number of atoms is limited by the collisional loss rates associated with the contraction of the condensate; this loss is in addition to the particle ejection decay indentified by Kagan et al. \textcopyright{} 1996 The American Physical Society.The properties and stability of a trapped Bose-Einstein condensate are strongly influenced by attractive interactions between the particles. We describe the spatial distribution, stability, and collisional loss rates for a weakly interacting gas in the mean-field limit. We show how the condensate contracts and becomes unstable as the number of condensate atoms increases. We further show how the number of atoms is limited by the collisional loss rates associated with the contraction of the condensate; this loss is in addition to the particle ejection decay indentified by Kagan et al. \textcopyright{} 1996 The American Physical Society.

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arXiv:cond-mat/0204529Apr 24, 20023 citations

{\ensuremath{\psi}}_{0}

. We find that for

a<0

and

\ensuremath{\eta}\ensuremath{\ll}1

it is possible to form a metastable Bose condensate, with a long characteristic lifetime with respect to contraction and transitions of particles to excited trap states. For

\ensuremath{\eta}\ensuremath{\gg}1

a negative scattering length prevents the formation of the condensate. If

a>0

, then an increase of density is accompanied by the evolution of

{\ensuremath{\psi}}_{0}

to a comparatively wide quasihomogeneous distribution.

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.