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Building an efficient quantum memory in high-dimensional Hilbert spaces isone of the fundamental requirements for establishing high-dimensional quantumrepeaters, where it offers many advantages over two-dimensional quantumsystems, such as a larger information capacity and enhanced noise resilience.To date, there have been no reports about how to achieve an efficienthigh-dimensional quantum memory. Here, we experimentally realize a quantummemory that is operational in Hilbert spaces of up to 25 dimensions with astorage efficiency of close to 60%. The proposed approach exploits thespatial-mode-independent interaction between atoms and photons which areencoded in transverse size-invariant orbital angular momentum modes. Inparticular, our memory features uniform storage efficiency and low cross-talkdisturbance for 25 individual spatial modes of photons, thus allowing storingarbitrary qudit states programmed from 25 eigenstates within thehigh-dimensional Hilbert spaces, and eventually contributing to the storage ofa 25-dimensional qudit state. These results would have great prospects for theimplementation of long-distance high-dimensional quantum networks and quantuminformation processing.

Highly efficient storage of 25-dimensional photonic qudit in a cold-atom-based quantum memory