Hamid Al-Jibbouri, Ivana Vidanovic, Antun Balaz, Axel Pelster
We investigate geometric resonances in Bose-Einstein condensates by solving the underlying time-dependent Gross-Pitaevskii (GP) equation for systems with two-and three-body interactions in an axially-symmetric harmonic trap. To this end, we use a recently developed analytical method [Phys. Rev. A 84, 013618 (2011)], based on a perturbative expansion and a Poincar\'e-Lindstedt analysis of a Gaussian variational approach, as well as a detailed numerical study of a set of ordinary differential equations for variational parameters. By changing the anisotropy of the confining potential, we numerically observe and analytically describe strong nonlinear effects: shifts in the frequencies and mode coupling of collective modes, as well as resonances. Furthermore, we discuss in detail the stability of a Bose-Einstein condensate in the presence of an attractive two-body interaction and a repulsive three-body interaction. We show that a small repulsive three-body interaction is able to extend the stability region of the condensate as it increases the critical number of atoms in the trap.
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http://arxiv.org/abs/1208.0991
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