Collapse of Bose-Einstein condensates with dipole-dipole interactions

Bose-Einstein condensation of dilute trapped atomic gases @1,2# essentially depends on the interparticle interactions. In most experiments so far the dominated interactions have been short-range van der Waals forces which are characterized by the s-wave scattering length a. Spatially homogeneous condensates with positive scattering length ~repulsive interaction! are stable while condensates with negative scattering length ~attractive interaction! are always unstable to local collapses @3# because the quantum pressure is absent in homogeneous condensates. The presence of trapping field allows one to achieve a metastable Bose-Einstein condensate ~BEC! @2# for a,0 if the number of particles is small enough to ensure the existence of local minima of the energy functional @3#. Recent progress in creating of ultracold molecular clouds @4,5# opens a new prospective for achieving BEC in a dilute gas of polar molecules and stimulates a growing interest in the study of BEC with dipole-dipole interactions @6–12#. Dipole-dipole forces are long range and essentially anisotropic. The net contribution of dipole-dipole interactions can be either repulsive ~positive dipole-dipole interaction energy! or attractive ~negative dipole-dipole interaction energy! depending on the form of condensate cloud, its orientation relative to dipole polarization axes and trap geometry. Thus stability and collapse of BEC strongly depend on clouds anisotropy which opens a whole bunch of new phenomena to be observed and makes the task of achieving and controlling the BEC especially challenging. Dipole-dipole interactions can dominate provided polar molecules are oriented by strong enough electric field. Similar effects can be achieved for ground-state atoms with electric dipole moments induced by a strong electric field @6,9#. Another possible physical realization is atoms with laser induced electric dipole moments @8#. Dipole-dipole interactions can be also essential in BEC of atomic gas with large magnetic dipole moments @7,11#. Magnetic interactions are usually dominated by van der Waals forces but effects of magnetic interactions can be essentially amplified by reducing scattering length a via a Feshbach resonance @13,10#. Analysis of this paper can be applied for both cases of electric and magnetic dipole-dipole interactions.