Matter waves with orbital angular momentum: Collapse suppression and bistability

We explore the influence of the orbital angular momentum on the dynamics of vortex-free elliptic clouds of Bose-Einstein condensates with attractive interatomic interactions. We show that the number of atoms corresponding to the collapse threshold can be radically increased for such rotating nonlinear matter waves trapped in a radially symmetric harmonic potential. Moreover, rotating anisotropic traps can simultaneously support two differently aligned elliptical matter wave states stabilized against the collapse.