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 N-c=0.55(l(o)/\a\). Our results also show that. by exchanging the frequencies omega (z) and omega (p), the geometry with omega (p)<<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.