Atomic Bose-Einstein condensation with three-body interactions and collective excitations

Abstract

The stability of a Bose-Einstein condensed state of trapped ultra-cold atoms\nis investigated under the assumption of an attractive two-body and a repulsive\nthree-body interaction. The Ginzburg-Pitaevskii-Gross (GPG) nonlinear\nSchr\\"odinger equation is extended to include an effective potential dependent\non the square of the density and solved numerically for the s-wave. The lowest\nfrequency of the collective mode is determined and its dependences on the\nnumber of atoms and on the strength of the three-body force are studied. We\nshow that the addition of three-body dynamics can allow the number of condensed\natoms to increase considerably, even when the strength of the three-body force\nis very small compared with the strength of the two-body force. We also observe\na first-order liquid-gas phase transition for the condensed state up to a\ncritical strength of the effective three-body force.\n