  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.
