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

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 Nc50.55(l0 /uau). Our results also show that, by exchanging the frequencies vz and vr , the geometry with vr,vz favors the condensation of larger number of particles. We also simulate the time evolution of the condensate when changing the ground state from a50 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.