Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0110597 · Journal of Physics B Atomic Molecular and Optical Physics

The role of the initial state in the collapse of a Bose condensed gas

Thorsten Köhler

Published Aug 2, 2001• 2 citations
arXivHTMLPDF

Abstract

The stability of a Bose condensed gas with a negative scattering length is studied with regard to the role played by the initial state. A trapped ideal gas ground state is shown to be unstable when the Gross Pitaevskii equation still predicts the existence of a stable state. A possible relation to a recent experimental study of the critical conditions for stability or collapse of a Bose Einstein condensate (Roberts et al 2001 Phys. Rev. Lett. 86 4211) is discussed.

DOI
10.1088/0953-4075/34/16/106

Related papers

Stability of trapped Bose-Einstein condensates

F. Kh. Abdullaev, A. Gammal, Lauro Tomio +1 more

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.

arXiv:cond-mat/0102018•Physical Review A•Mar 12, 2001•201 citations

Collapse of the metastable state in an attractive Bose-Einstein condensate

Jae Gil Kim, Yoon-Hyuck Sean Choi, Eok Kyun Lee

The characteristic features of the collapse of the ground state in trapped one-component attractive Bose-Einstein condensates are studied by applying the catastrophe theory. From numerically obtained stable and unstable solutions of the Gross-Pitaevskii equation, we derive the catastrophe function defining the stability of the stationary points on the Gross-Pitaevskii energy functional. The bifurcation diagram and the universal scaling laws stemming from the catastrophe function show quantitative agreement with the numerical results.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jul 12, 2002•4 citations

Stability criterion for attractive Bose-Einstein condensates

Luc Bergé, Tristram J. Alexander, Yuri S. Kivshar

A general stability criterion is derived for the ground states of the Gross-Pitaevskii equation, which describes attractive Bose-Einstein condensates confined in a magnetic trap. These ground states are shown to avoid the collapse in finite time and are proven to be stable in two and three spatial dimensions.

arXiv:cond-mat/9907408•Physical Review A•Jul 18, 2000•50 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.

International Journal of Modern Physics B•Mar 10, 1999•61 citations

Singularity formation in the Gross-Pitaevskii equation and collapse in Bose-Einstein condensates

Andrei V. Rybin, Ilya P Vadeiko, G. G. Varzugin +1 more

We study the mechanisms of collapse of the condensate wave function in the Gross-Pitaevskii theory with attractive interparticle interaction. We reformulate the Gross-Pitaevskii equation as Newton's equations for a flux of particles, and introduce the collapsing fraction of particles. We assume that this collapsing fraction is expelled from the condensate due to dissipation. Using this hypothesis we analyze the dependence of the collapse behavior on the initial conditions. We find that, for a properly chosen negative scattering length, the remnant fraction of atoms becomes larger when the initial aspect ratio of the condensate is increased.

Physical Review A•Feb 12, 2004•3 citations

Ground state of a weakly interacting Bose gas of atoms in a tight trap

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.

Physical Review A•Feb 1, 1996•23 citations
The stability of a Bose condensed gas with a negative scattering length is studied with regard to the role played by the initial state. A trapped ideal gas ground state is shown to be unstable when the Gross Pitaevskii equation still predicts the existence of a stable state. A possible relation to a recent experimental study of the critical conditions for stability or collapse of a Bose Einstein condensate (Roberts et al 2001 Phys. Rev. Lett. 86 4211) is discussed.
In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.
The characteristic features of the collapse of the ground state in trapped one-component attractive Bose-Einstein condensates are studied by applying the catastrophe theory. From numerically obtained stable and unstable solutions of the Gross-Pitaevskii equation, we derive the catastrophe function defining the stability of the stationary points on the Gross-Pitaevskii energy functional. The bifurcation diagram and the universal scaling laws stemming from the catastrophe function show quantitative agreement with the numerical results.
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 study the mechanisms of collapse of the condensate wave function in the Gross-Pitaevskii theory with attractive interparticle interaction. We reformulate the Gross-Pitaevskii equation as Newton's equations for a flux of particles, and introduce the collapsing fraction of particles. We assume that this collapsing fraction is expelled from the condensate due to dissipation. Using this hypothesis we analyze the dependence of the collapse behavior on the initial conditions. We find that, for a properly chosen negative scattering length, the remnant fraction of atoms becomes larger when the initial aspect ratio of the condensate is increased.
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.