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.
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