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Instability of a Bose-Einstein Condensate with Attractive Interaction.pdf

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Instability of a Bose-Einstein Condensate with Attractive Interaction

a r X i v : c o n d - m a t / 9 9 0 8 2 2 9 v 1 1 6 A u g 1 9 9 9 Instability of a Bose-Einstein Condensate with Attractive Interaction Antonios Eleftheriou and Kerson Huang Department of Physics and Center for Theoretical Physics Massachusetts Institute of Technology Cambridge, MA 02139, USA (February 1, 2008) 03.75.Fi, 42.65.Jx, 32.80.Pj MIT-CTP #2886 We study the stability of a Bose-Einstein condensate of harmonically trapped atoms with negative scattering length, specifically 7Li. Our method is to solve the time-dependent nonlinear Schro?dinger 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 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 by Ueda and Huang [16]. 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. I. INTRODUCTION AND SUMMARY Bose-Einstein condensation has been observed in magnetically trapped dilute vapors of the alkali elements 87Rb [1], 23Na [2], 7Li [4], and 1H [3]. At the nanodegree temperatures of these experiments, the systems would have frozen solid long ago were they in free space. In the confining trap, however, zero-point motion keeps the atoms apart, and the systems remain gaseous. The case of 7Li is special, however, in that the interatomic interaction is predominantly attractive, as indicated by a negative scattering length. Thus, the condensate in 7Li s