arXiv:cond-mat/0104231 · Physical Review A

Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps

A. Gammal, T. Frederico, Lauro Tomio

Published Oct 10, 2001• 127 citations

Abstract

We calculated, within the Gross-Pitaevskii formalism, the critical number of atoms for Bose-Einstein condensates with two-body attractive interactions in cylindrical traps with different frequency ratios. In particular, by using the trap geometries considered by Roberts et al. [Phys. Rev. Lett. 86, 4211 (2001)], we show that the theoretical maximum critical numbers are given approximately by ${N}_{c}{=0.55(l}_{0}/|a|).$ 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 $a=0$ to $a<0$ 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.

DOI: 10.1103/physreva.64.055602

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arXiv:cond-mat/0104231 · Physical Review A

Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps

A. Gammal, T. Frederico, Lauro Tomio

Published Oct 10, 2001• 127 citations

arXiv HTML PDF

Abstract

{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.

DOI: 10.1103/physreva.64.055602

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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.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.

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{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.