Splitting of a doubly quantized vortex through intertwining in Bose-Einstein condensates

The stability of doubly quantized vortices in dilute Bose-Einstein condensates of Na is examined at zero temperature. The eigenmode spectrum of the Bogoliubov equations for a harmonically trapped cigar-shaped condensate is computed and it is found that the doubly quantized vortex is spectrally unstable towards division into two singly quantized vortices. By numerically solving the full three-dimensional time-dependent GrossPitaevskii equation, it is found that the two singly quantized vortices intertwine before decaying. This work provides an interpretation of recent experiments @A. E. Leanhardt et al., Phys. Rev. Lett. 89, 190403 ~2002!#.