Bose-Einsein condensate with attractive interaction
Many experimental groups have achieved Bose-Einstein condensation in cold trapped atoms, at temperatures so low that the atoms would have solidified in free space. They remain in a gaseous state in the trap because of the quantum zero-point motion, which reduces the effectiveness of the attractive part of the interatomic potential.
For atoms with a postive scattering length, such as Rb and Na, the condensate is stable. For the case of negative scattering length, as in Li, the attractive potential has a stronger effect, and the condensate is metastable, with a lifetime of the order of minutes. What becomes of the condensate?
We study the stability by solving the time-dependent nonlinear Schrodinger equation numerically, for Li atoms trapped in a harmonic potential. 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 Nc. For N > Nc, the system collapses to high-density clumps in a region near the center of the trap. The time for the onset of collapse is on the order of 1 trap period. Within numerical uncertainty, the results are consistent with the formation of a ``black hole'' of infinite density fluctuations, as predicted earlier by Ueda and Huang. We obtain numerically Nc = 1251. We then include gain-loss mechanisms, i.e., the gain of atoms from a surrounding ``thermal cloud'', and the loss due to two- and three-body collisions. The number N now oscillates in a steady state, with a period of about 145 trap periods. We obtain Nc = 1260 as the maximum value in the oscillations.
A. Elefthrious and K. Huang, cond-mat/9908229 16 Aug 1999.
M. Ueda and K. Huang, Phys. Rev. A (in prress); cond-mat/9807359 27 Jul 1998.