Why the two-pulse photon echo is not a good quantum memory protocol

We consider in this paper a two-pulse photon echo sequence in the prospect of quantum light storage. We analyze the conditions where quantum storage could be realistically performed. We simply and analytically calculate the efficiency in that limit, and clarify the role of the exactly pi-rephasing pulse in the sequence. Our physical interpretation of the process is well supported by its experimental implementation in a Tm3+:yttrium aluminum garnet crystal thanks to an accurate control of the rephasing pulse area. We finally address independently the fundamental limitations of the quantum fidelity. Our work allows us to point out on one side the real drawbacks of this scheme for quantum storage and on the other side its specificities which can be a source of inspiration to conceive more promising procedures with rare-earth ion doped crystals.