evolution of entanglement depth in a dissipative environment.

Experimental implement and results. {#experimental-implement-and-results. .unnumbered}
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To herald multipartite entanglement W state, we adopt the SRS regime as proposed in the Duan-Lukin-Cirac-Zoller (DLCZ) protocol originally aiming at realizing applicable quantum repeaters  [@nature_DLCZ]. However, we have to conceive a far off-resonance scheme to avoid the huge fluorescence noise in room-temperature atomic ensemble  [@Dou_npj; @Dou_FORD; @Pang_hybrid], which does not exist in cold ensembles and diamonds [@Chou_cold; @science_diamond]. The energy levels of the $\Lambda $-type configuration are shown in Figure 1a. This process will generate the product state of correlated photon-atoms pairs, which can be expressed as [@science_diamond] $$\label{eq1}
\left | \psi _{s} \right \rangle= \left [ 1+\varepsilon_{s} S^{\dagger}a^{\dagger}\right ]\left | vac \right \rangle$$ where $\varepsilon_{s}$ is the excitation probability of Stokes photon, $\left |vac\right \rangle=\left |vac_{opt}\right \rangle\bigotimes \left |vac_{ato}\right \rangle$ is the initial product state of photon-atoms system, $S$ and $a$ are the annihilation operators of spin wave and Stokes photon, respectively. Here, we set the intensity of control light pulse so weak that the excitation probability $\varepsilon_{s}$ is much smaller than unity. Therefore, we can ignore the higher-order terms in the creating of $\left | \psi _{s} \right \rangle$ with extremly small 