Stability of a Bose-Einstein condensate in an anharmonic trap

Abstract

We study the stability of Bose-Einstein condensate (BEC) with repulsive and attractive interatomic interactions in a harmonic plus quartic trap $[V(r)=\frac{1}{2}m{\ensuremath{\omega}}^{2}{r}^{2}+\ensuremath{\lambda}{r}^{4}]$. We find that BEC with repulsive interaction becomes more stable for $\ensuremath{\lambda}>0$. For $\ensuremath{\lambda}<0$, we observe a different metastability of the condensate even when the scattering length is positive. For BEC with attractive interaction, we observe dramatic change in the stability factor $\frac{{A}_{\text{cr}}|{a}_{\text{sc}}|}{{a}_{\text{ho}}}$ due to the anharmonicity. The frequencies of the collective excitations are also modified by the atomic interaction and by the anharmonicity.