Not yet reviewed by Pith; the record is open.

Quantum memories are indispensible for establishing a long-distance quantum network. High-dimensional quantum memories enable a higher channel capacity compared to a quantum memory working in a two-dimensional space, and have a lower requirement for storage lifetime in the field of quantum coomunication. The photonic transverse spatial modes such as Laguerra-Gaussian modes orbital angular momentum (OAM) are ideal candidates for encoding high-dimensional information, because it can form an infinite-dimensional Hilbert space. Although the faithful storage of an OAM qubit or qutrit has been realized in pioneering works, the longest storage lifetime for the former is only in the order of a few microseconds, and hundreds of nano-seconds for the latter. Here we implement a quantum memory for OAM qubits and qutrits using a cold atomic ensemble, the experimental results clearly show that our memory can still beat the classical limit after a storage time of $400\mu s$,which is two orders of magnitude higher than the previous work. The retrieval efficiency at this time equals to $44\%$ of the value when the storage time is set to be $10\mu s$. Our work is very promising for establishing a high dimensional quantum network.