A. Gammal et al., Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps - art. no. 055602, PHYS REV A, 6405(5), 2001, pp. 5602
We calculated, within the Gross-Pitaevskii formalism, the critical number o
f atoms for Bose-Einstein condensates with two-body attractive interactions
in cylindrical traps with different frequency ratios. In particular. by us
ing the trap geometries considered by Roberts et al. [Phys. Rev. Lett. 86,
4211 (2001)], we show that the theoretical maximum critical numbers are giv
en approximately by N-c=0.55(l(o)/\a\). Our results also show that. by exch
anging 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 stat
e from a = 0 to a < 0 using a 200 ms ramp. A conjecture on higher-order non
linear effects is also added in our analysis with an experimental proposal
to determine its signal and strength.