Dynamics of a collapsing and exploding Bose-Einstein condensed vortex state

Using the time-dependent mean-field Gross-Pitaevskii equation we study the dynamics of small repulsive Bose-Einstein condensed vortex states of [Formula Presented] atoms in a cylindrical trap with low angular momentum [Formula Presented] per atom [Formula Presented] when the atomic interaction is suddenly turned attractive by manipulating the external magnetic field near a Feshbach resonance. Consequently, the condensate collapses and ejects atoms via explosion and a remnant condensate with a smaller number of atoms emerges that survives for a long time. Details of this collapse and explosion are compared critically with a similar experiment performed with zero angular momentum [Formula Presented] by Donley et al. [Nature (London) 412, 295 (2001)]. A suggestion for a future experiment with the vortex state is made. 5555 2002 The American Physical Society.