Mean-field limit of bose-einstein condensates with attractive interactions in

William Hoston

Charles A. Sackett, Randall G. Hulet

The nature of Bose-Einstein condensation (BEC) in atomic vapours depends critically on the mean-field interaction of the atoms. When this interaction is attractive, the number of atoms in the condensate is limited. The interplay of this limit and the natural growth of the condensate during BEC leads to complicated dynamical behaviour. We develop a model for this behaviour based on the nonlinear Schrödinger equation and the quantum Boltzmann equation. The condensate occupation number is predicted to oscillate rapidly as the condensate alternately fills and collapses, and the oscillations are seen to persist for many cycles before the gas comes to equilibrium. Experimental evidence for these oscillations in the case of 7 Li is presented, along with details of the experimental apparatus and methods.

R. J. Dodd, Mark Edwards, Carl J. Williams +4 more

The properties and stability of a trapped Bose-Einstein condensate are strongly influenced by attractive interactions between the particles. We describe the spatial distribution, stability, and collisional loss rates for a weakly interacting gas in the mean-field limit. We show how the condensate contracts and becomes unstable as the number of condensate atoms increases. We further show how the number of atoms is limited by the collisional loss rates associated with the contraction of the condensate; this loss is in addition to the particle ejection decay indentified by Kagan et al. \textcopyright{} 1996 The American Physical Society.

Takafumi Kita

郭玉劲, 陆璐

Starting with the many-body Schrdinger Hamiltonian in R~2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gross-Pitaevskii energy functional in the meanfield regime, as the particle number N→∞ and however the scattering length κ→0. By fixing N|κ|, this leads to the mean-field approximation of Bose-Einstein condensates with attractive interactions in R~2.