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

Journal of the Physical Society of Japan

Instability of the Bose-Einstein Condensate under Magnetic Trap

Takeya Tsurumi, Miki Wadati

Published Nov 29, 2013• 20 citations
OpenAlex

Abstract

We consider the Bose-Einstein condensate with attractive interparticle interactions (more precisely, negative s-wave scattering lengths) under a magnetic trap. By using a model equation, axially symmetric nonlinear Schrodinger equation with harmonic potential terms, we investigate the time-evolution of the wavefunction. We predict that the collapse of the condensate takes place when the number of atoms exceeds the critical value.

Related papers

Instability of a Bose-Einstein condensate with an attractive interaction

Antonios Eleftheriou, Kerson Huang

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.

arXiv:cond-mat/9908229•Physical Review A•Mar 2, 2000•55 citations

Singularity Formation and Self-Similar Solution in the Magnetically Trapped Bose-Einstein Condensate

Takeya Tsurumi, Miki Wadati

We investigate the singularity of the magnetically trapped Bose-Einstein condensate with attractive interatomic interactions. By using a model equation, three-dimensional attractive nonlinear Schrödinger equation with anisotropic harmonic potential terms, we show the scaling laws for the system near the singularity. We also discuss the self-similar behavior of the wavefunction in detail.

Journal of the Physical Society of Japan•Apr 15, 1998•11 citations

Collapse and Bose-Einstein Condensation in a Trapped Bose Gas with Negative Scattering Length

Yu. Kagan, A. E. Muryshev, Georgy V. Shlyapnikov

Evolution and collapse of a trapped Bose condensate with negative scattering length are predetermined by 3-body recombination of Bose-condensed atoms and by feeding of the condensate from the nonequilibrium thermal cloud. The collapse, starting once the number of condensate atoms reaches the critical value, ceases and turns to expansion when the density becomes so high that the recombination losses dominate over attractive interparticle interaction. As a result, we obtain a sequence of collapses, each of them followed by dynamic oscillations of the condensate. In every collapse the 3-body recombination burns only a part of the Bose-condensed atoms.

arXiv:cond-mat/9801168•Physical Review Letters•Aug 1, 1998•298 citations

Stability of solutions of the nonlinear Schrödinger equation for trapped Bose-condensed atoms with negative scattering lengths

Kimitaka Watanabe, T. Mukai, Takaaki Mukai

We analyze the time evolution of solutions of nonlinear Schr\"odinger equations that describe a condensate composed of atoms with negative scattering lengths in a harmonic potential trap. It is theoretically demonstrated that if an initial condensate has negative energies due to negative scattering lengths, then the solutions diverge in a finite time that is determined by the condensate's energy, its initial phase, and the trap parameter.

Physical Review A•May 1, 1997•9 citations

Collapses of Wavefunctions in Multi-Dimensional Nonlinear Schrödinger Equations under Harmonic Potential

Takeya Tsurumi, Miki Wadati

We extend the Zakharov's theory for collapses of Langmuir waves into the system under harmonic potential. As a possible application, we consider the collapse of the Bose-Einstein condensate with attractive interparticle interactions under magnetic trap.

Journal of the Physical Society of Japan•Oct 15, 1997•62 citations

Collapse of attractive Bose-Einstein condensed vortex states in a cylindrical trap

Sadhan K. Adhikari

The quantized vortex states of a weakly interacting Bose-Einstein condensate of atoms with attractive interatomic interaction in an axially symmetric harmonic oscillator trap are investigated using the numerical solution of the time-dependent Gross-Pitaevskii equation obtained by the semi-implicit Crank-Nicholson method. The collapse of the condensate is studied in the presence of deformed traps with the larger frequency along either the radial or the axial direction. The critical number of atoms for collapse is calculated as a function of the vortex quantum number L. The critical number increases with increasing angular momentum L of the vortex state but tends to saturate for large L.

arXiv:cond-mat/0107298•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Dec 18, 2001•68 citations
We consider the Bose-Einstein condensate with attractive interparticle interactions (more precisely, negative s-wave scattering lengths) under a magnetic trap. By using a model equation, axially symmetric nonlinear Schrodinger equation with harmonic potential terms, we investigate the time-evolution of the wavefunction. We predict that the collapse of the condensate takes place when the number of atoms exceeds the critical value.
We study the stability of a Bose-Einstein condensate of harmonically trapped atoms with negative scattering length, specifically 7Li.{}^{7}\mathrm{Li}.7Li. 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 Nc.{N}_{c}.Nc​. For N>Nc,N>{N}_{c},N>Nc​, 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.
Evolution and collapse of a trapped Bose condensate with negative scattering length are predetermined by 3-body recombination of Bose-condensed atoms and by feeding of the condensate from the nonequilibrium thermal cloud. The collapse, starting once the number of condensate atoms reaches the critical value, ceases and turns to expansion when the density becomes so high that the recombination losses dominate over attractive interparticle interaction. As a result, we obtain a sequence of collapses, each of them followed by dynamic oscillations of the condensate. In every collapse the 3-body recombination burns only a part of the Bose-condensed atoms.
The quantized vortex states of a weakly interacting Bose-Einstein condensate of atoms with attractive interatomic interaction in an axially symmetric harmonic oscillator trap are investigated using the numerical solution of the time-dependent Gross-Pitaevskii equation obtained by the semi-implicit Crank-Nicholson method. The collapse of the condensate is studied in the presence of deformed traps with the larger frequency along either the radial or the axial direction. The critical number of atoms for collapse is calculated as a function of the vortex quantum number L. The critical number increases with increasing angular momentum L of the vortex state but tends to saturate for large L.