  We study the establishment of vortex entanglement in remote and weakly
interacting Bose Einstein condensates. We consider a two-mode photonic resource
entangled in its orbital angular momentum (OAM) degree of freedom and, by
exploiting the process of light-to-BEC OAM transfer, demonstrate that such
entanglement can be efficiently passed to the matter-like systems. Our proposal
thus represents a building block for novel low-dissipation and long-memory
communication channels based on OAM. We discuss issues of practical
realizability, stressing the feasibility of our scheme and present an operative
technique for the indirect inference of the set vortex entanglement.
