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

A. Gammal·T. Frederico·Lauro Tomio
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Abstract

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 $ω_z$ and $ω_ρ$, the geometry with $ω_ρ< ω_z$ 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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A. Gammal, T. Frederico, Lauro Tomio. 2001-08-15. Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps. https://doi.org/10.1103/physreva.64.055602

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