Quantum memory of single $\gamma $-ray photon by Doppler Frequency Comb

We propose to store and retrieve a single $\gamma $-ray photon by a series of resonant M\"{o}ssbauer targets each moves with different velocities. Such velocity spectrum forms a frequency comb due to Doppler effect, which we name as Doppler frequency comb (DFC). The performance of this $\gamma $-ray photon quantum memory scheme is similar to the usual atomic frequency comb (AFC) which is used for optical quantum storage. However, instead of burning comb structure in a broad inhomogeneous broadening profile, which is not available in M\"{o}ssbauer solids, DFC utilizes very narrow resonant line-width to achieve quantum memory of energetic single $\gamma $-ray photon. Depending on the motion direction of the M\"{o}ssbauer targets, a series of input $\gamma $-ray signals can be retrieved in either the same or reversed order of the input signals.