  Time reversibility is absent from some recently proposed quantum memory
protocols such as Absorption Frequency Comb (AFC). Focusing on AFC memory, we
show that quantum efficiency and fidelity are reduced dramatically, as a
consequence of non-reversibility, when the spectral width of the incoming
signal approaches the memory bandwidth. Non-reversibility is revealed through
spectral dispersion, giving rise to phase mismatching. We propose a modified
AFC scheme that restores reversibility. This way, signals can be retrieved with
excellent efficiency over the entire memory bandwidth. This study could be
extended to other quantum memory rephasing schemes in inhomogeneously broadened
absorbing media.
