Analysis of Optical Deshelving in Photon Echo-based Quantum Memories

Storage time extension in photon echoes using optical deshelving via a robust spin state has been investigated for absorption-dependent optical leakage, where an incomplete population transfer, even by a \pi optical pulse obviates the phase recovery condition of the deshelving. We analyze an optical depth-dependent echo leakage mechanism in the storage time extended photon echoes for the usage of optical deshelving to photon echo-based quantum memories.