the photon loss of the channels and detectors. Therefore, the final experimental datas should be handled as the following two stages: the raw measured datas and the processed datas after subtracting the loss of the channels and detectors. The latter reflects the actual entanglement state at the moment just after applying the probe pulse. The $M$ values of entanglement state evolving with storage time are showed in Figure 2a, where the energy of the light pulses is 225 $pJ$. The data point below the boundary curve of fixed $M$ value indicates that there is an entanglement depth at least $N/M$. Our experimental datas show that the number of entanglement subgroups increases as the memory time elapsing, i.e. the decoherence effects caused by the thermal motions of atoms [@nPhys_msmemory; @Dou_FORD] will tremendously influence the structure of entanglement, which is consistent with the physical picture depicted in Figure 1d.

During the process of verifying the existence of entanglement, the collective enhancement effect contributes to the transducing of Stokes photon due to the phase coherence of $W$ state [@nature_DLCZ]. The variation of $p_{1}$ with the delay of the probe pulse is shown in Figure 3a. Due to the decoherence of phase mainly resulting 