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 $N_c{=0.55(l}_0/|a|).\mathrm{}$ 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 $a=0\mathrm{}$ to $a<\mathrm{}0\mathrm{}$ 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.

• Received 12 April 2001

DOI:https://doi.org/10.1103/PhysRevA.64.055602