Attractive Bose-Einstein condensates in three dimensions under rotation: Revisiting the problem of stability of the ground state in harmonic traps

We study harmonically trapped ultracold Bose gases with attractive interparticle interactions under external rotation in three spatial dimensions and determine the critical value of the attraction strength where the gas collapses as a function of the rotation frequency. To this end, we examine the stationary ground state in the corotating frame with a many-body approach as well as within the Gross-Pitaevskii theory of systems in traps with different anisotropies. In contrast to recently reported results [N. A. Jamaludin, N. G. Parker, and A. M. Martin, Phys. Rev. A 77, 051603(R) (2008)], we find that the collapse is not postponed in the presence of rotation. Unlike repulsive gases, the properties of the attractive system remain practically unchanged under rotation in isotropic and slightly anisotropic traps.

Figure 1

Many-body calculations for the critical parameter ${\lambda }_c$ as a function of the frequency of the external rotation $\Omega$, for the cases of isotropic [$\varepsilon =0$, $\zeta =1$; lower (red) line] and slightly anisotropic [$\varepsilon =0.1$, $\zeta =1$; upper (blue) line] confining traps. The critical interaction ${\lambda }_c$ remains practically unaffected (note the scale!) for the whole region of $\Omega \in [0,{\Omega }_r=\sqrt{1-\varepsilon }\hspace{0.5em}$). The number of particles is $N=12$. See text for more details. All quantities are dimensionless.