Atomic thermal motion effect on efficiency of a high-speed quantum memory

We discuss the influence of atomic thermal motion on the efficiency of multimode quantum memory in two configurations: over the free expand of atoms cooled beforehand in a magneto-optical trap, and over complete mixing of atoms in a closed cell at room temperature. We consider the high-speed quantum memory, and assume that writing and retrieval are short enough, and the displacements of atoms during these stages are negligibly small. At the same time we take in account thermal motion during the storage time, which, as well known, must be much longer than durations of all the other memory processes for successful application of memory cell in communication and computation. We will analyze this influence in terms of eigenmodes of the full memory cycle and show that distortion of the eigenmodes, caused by thermal motion, leads to the efficiency reduction. We will demonstrate, that in the multimode memory this interconnection has complicated character. Graphical abstract