Three-dimensional Matter-wave Vortices in Optical Lattices

We reveal that a repulsive Bose-Einstein condensate confined in a three-dimensional (3D) optical lattice supports vortex states which are spatially localized in all three dimensions and possess highly nontrivial particle flow. We demonstrate that the lattice stabilizes extended vortex lines that are normally unstable to transverse modulations, and show that stable vortices localized inside the 3D lattice may be easily generated via a nonadiabatic loading process