A uniform 3D BEC with attractive interactions is unstable because the gas tends to infinitely increase its density in order to decrease its interaction energy. This limitation is remarkably removed by an external trapping potential which stabilizes the system by introducing zero-point kinetic energy [1, 2]. For an attractive BEC in a trap there is thus a critical number of atoms N c below which the condensate is stable. Increasing number of atoms in the BEC leads to the collapse of the gas just as in the uniform case. First experiments with attractively interacting trapped Bose gases were carried out with lithium atoms in their doubly polarized state (in which the nuclear and electronic spin components have the largest possible values along the direction of the magnetic field) [3]. Later the experiments with 85Rb (using tunable interactions) explored quantitatively the dependence of the critical number of atoms N c on the strength of interatomic interactions [4]. The dynamics of growth and collapse of BECs with attractive interactions has been directly investigated in two notable experiments with 7Li [5] and 85Rb [6].
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Khaykovich, L. (2008). Bright Solitons: Summary of Experimental Techniques. In: Kevrekidis, P.G., Frantzeskakis, D.J., Carretero-González, R. (eds) Emergent Nonlinear Phenomena in Bose-Einstein Condensates. Atomic, Optical, and Plasma Physics, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73591-5_3
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