Three-dimensional matter-wave vortices in optical lattices

We study the localization of vortices in a three-dimensional band-gap. We report that not only planar, two-dimensional matter-wave gap vortices persist in the presence of the third dimension, but also the three-dimensional lattice may support novel types of quite unusual vortex-like structures which survive perturbations of both phase and atomic density. One remarkable result of the lattice geometry is that we may study coherent interactions of planar vortices, and even find stationary structures of an arbitrarily long stack of vortices. We find that the lattice stabilizes the vortex line, and leads to robust evolution of the perturbed state. The three-dimensional geometry also allows the existence of exotic vortex states which have no two-dimensional equivalent