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arXiv:cond-mat/0212193 · Journal of Physics B Atomic Molecular and Optical Physics

Dynamics of a Bose–Einstein condensate in an anharmonic trap

Herwig Ott, J Fort gh, Claus Zimmermann

Published Jun 19, 2003• 17 citations
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Abstract

We present a theoretical model for describing the dynamics of Bose–Einstein condensates in anharmonic trapping potentials. To first approximation the centre-of-mass motion is separated from the internal condensate dynamics and the problem is reduced to the well known scaling solutions for the Thomas–Fermi radii. We discuss the validity of this approach and analyse the model for an anharmonic waveguide geometry which was recently realized in an experiment (Ott et al 2002 Preprint cond-mat/0212220).

DOI
10.1088/0953-4075/36/13/311

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We present a theoretical model for describing the dynamics of Bose–Einstein condensates in anharmonic trapping potentials. To first approximation the centre-of-mass motion is separated from the internal condensate dynamics and the problem is reduced to the well known scaling solutions for the Thomas–Fermi radii. We discuss the validity of this approach and analyse the model for an anharmonic waveguide geometry which was recently realized in an experiment (Ott et al 2002 Preprint cond-mat/0212220).
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In this paper, we present a theoretical study of a Bose-Einstein condensate of interacting bosons in a quartic trap in one, two, and three dimensions. Using Thomas-Fermi approximation, suitably complemented by numerical solutions of the Gross-Pitaevskii equation, we study the ground sate condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate, and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement.
The collective excitations of a one-dimensional dipolar Bose—Einstein condensate trapped in an anharmonic potential are investigated theoretically. Using the variational approach, we obtain the coupled equations of motion for the center-of-mass coordinate of the condensate and its width. In particular, analytical expressions for the low-lying excitation modes are given. The results show that dipole-dipole interactions reduce the frequency shift induced by quartic distortion. The interplay between dipole-dipole interactions and anharmonic distortion for the collapse and revival of the collective excitations originating from the nonlinear coupling between the two modes are also discussed.
The dynamics of weakly interacting three-dimensional Bose-Einstein condensates (BECs), trapped in external axially symmetric plus anharmonic distortion potential are studied. Within a variational approach and time-dependent Gross-Pitaevskii equation, the coupled condensate width equations are derived. By modulating anharmonic distortion of the trapping potential, nonlinear features are studied numerically and illustrated analytically, such as mode coupling of oscillation modes, and resonances. Furthermore, the stability of attractive interaction BEC in both repulsive and attractive anharmonic distortion is examined. We demonstrate that a small repulsive and attractive anharmonic distortion is effective in reducing (extending) the condensate stability region since it decreases (increases) the critical number of atoms in the trapping potential.