Supersonic optical tunnels for Bose-Einstein condensates

We propose a method for the stabilization of a stack of parallel vortex rings in a Bose-Einstein condensate. The method makes use of a 'hollow' laser beam containing an optical vortex. Using realistic experimental parameters we demonstrate numerically that our method can stabilize up to nine vortex rings. Furthermore we point out that the condensate flow through the tunnel formed by the core of the optical vortex can be made supersonic by inserting a laser-generated hump potential. We show that long-living immobile condensate solitons generated in the tunnel exhibit sonic horizons. Finally, we discuss prospects of using these solitons for analogue gravity experiments.