Vortex rings in toroidal Bose-Einstein condensates

We study vortex ring solutions of the Gross-Pitaevskii equation for Bose-Einstein condensates confined in toroidal traps. Analogously to the Feynman-Onsager ansatz for a single vortex line, we assume a condensate wavefunction that describes a quantized vortex ring. This leads to a modified Gross-Pitaevskii equation that incorporates vortex ring solutions. By numerically solving this equation, we have obtained the density profiles and the vortex core structure. We have also calculated the nucleation energy of a vortex ring, and have analyzed its dependence on the ring position. Finally, a qualitative description of the vortex ring dynamics is presented.