  We study the coherence properties of optical vortices stored in atomic
ensembles. In the presence of thermal diffusion, the topological nature of
stored optical vortices is found not to guarantee slow decoherence. Instead the
stored vortex state has decoherence surprisingly larger than the stored
Gaussian mode. Generally, the less phase gradient, the more robust for stored
coherence against diffusion. Furthermore, calculation of coherence factor shows
that the center of stored vortex becomes completely incoherent once diffusion
begins and, when reading laser is applied, the optical intensity at the center
of the vortex becomes nonzero. Its implication for quantum information is
discussed. Comparison of classical diffusion and quantum diffusion is also
presented.
