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

A. Gammal; T. Frederico; Lauro Tomio

doi:10.1103/PhysRevA.64.055602

paper

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

arXiv:cond-mat/0104231 · doi:10.1103/PhysRevA.64.055602

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 the JILA group [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 $ω_{z}$ and $ω_{ρ}$ , the geometry with $ω_{ρ} < ω_{z}$ 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 200ms ramp. A conjecture on higher order nonlinear effects is also added in our analysis with an experimental proposal to determine its signal and strength.

(4 pages, 2 figures) To appear in Physical Review A

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

Abstract

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