  We experimentally investigate the optical storage of perfect optical vortex
(POV) and spatially multimode perfect optical vortex (MPOV) beams via
electromagnetically induced transparency (EIT) in a hot vapor cell. In
particular, we study the role that phase gradients and phase singularities play
in reducing the blurring of the retrieved images due to atomic diffusion. Three
kinds of manifestations are enumerated to demonstrate such effect. Firstly, the
suppression of the ring width broadening is more prominent for POVs with larger
orbital angular momentum (OAM). Secondly, the retrieved double-ring MPOV beams'
profiles present regular dark singularity distributions that are related to
their vortex charge difference. Thirdly, the storage fidelities of the
triple-ring MPOVs are substantially improved by designing line phase
singularities between multi-ring MPOVs with the same OAM number but $\pi$
offset phases between adjacent rings. Our experimental demonstration of MPOV
storage opens new opportunities for increasing data capacity in quantum
memories by spatial multiplexing, as well as the generation and manipulation of
complex optical vortex arrays.
