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

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

2001-04-12

arxiv.org/abs/cond-mat/0104231v3

Phys. Rev. A 64, 055602 (2001).

Physics

Condensed Matter

Soft Condensed Matter

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

Scientific paper

10.1103/PhysRevA.64.055602

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 $\omega_z$ and $\omega_\rho$, the geometry with $\omega_\rho < \omega_z$ 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 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.

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