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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 Nc 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 Rb (using tunable interactions) explored quantitatively the dependence of the critical number of atoms Nc 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 Li [5] and Rb [6]. Remarkably, the 3D collapse can be readily avoided if a BEC is confined along two directions. Along the free direction, the condensate dispersion owing to its kinetic energy is balanced by the attractive interatomic interactions, resulting in the formation of bright solitons. These solitons were demonstrated in two independent experiments with Li atoms [7, 8]. The similar approaches used in both experiments, demonstrate the spectacular flexibility of recently developed experimental techniques for manipulating ultracold dilute atomic gases. In this chapter we shall discuss these techniques starting with tunable interatomic interactions achieved by means of Feshbach resonances. We then describe the optical trapping of atomic BECs and the |
