Instability of a BoseEinstein condensate with an attractive interaction
Abstract
We study the stability of a BoseEinstein condensate of harmonically trapped atoms with negative scattering length, specifically ^{7}Li. Our method is to solve the timedependent nonlinear Schrödinger equation numerically. For an isolated condensate, with no gain or loss, we find that the system is stable (apart from quantum tunneling) if the particle number N is less than a critical number N_{c}. For N>N_{c}, the system collapses to highdensity clumps in a region near the center of the trap. The time for the onset of collapse is on the order of one trap period. Within numerical uncertainty, the results are consistent with the formation of a ``black hole'' of infinite density fluctuations, as predicted by Ueda and Huang [Phys. Rev. A (to be published)]. We numerically obtain N_{c}~1251. We then include gainloss mechanisms, i.e., the gain of atoms from a surrounding ``thermal cloud,'' and the loss due to two and threebody collisions. The number N now oscillates in a steady state, with a period of about 145 trap periods. We obtain N_{c}~1260 as the maximum value in the oscillations.
 Publication:

Physical Review A
 Pub Date:
 April 2000
 DOI:
 10.1103/PhysRevA.61.043601
 arXiv:
 arXiv:condmat/9908229
 Bibcode:
 2000PhRvA..61d3601E
 Keywords:

 03.75.Fi;
 42.65.Jx;
 32.80.Pj;
 Beam trapping selffocusing and defocusing;
 selfphase modulation;
 Optical cooling of atoms;
 trapping;
 Condensed Matter
 EPrint:
 Email correspondence to huang@mitlns.mit.edu