schematic diagram of creation and verification of multipartite entanglement.** **a.** The energy levels of creating and verifying W state. Solid lines represent three-level $\Lambda$-type configuration of atoms, two ground states label $\left|g\right\rangle$ ($6S_{1/2}, F=3$) with electronic spin down and $\left|s\right\rangle$ ($6S_{1/2}, F=4$) with electronic spin up, which are hyperfine ground states of cesium atoms (splitting is $\Delta g = 9.2{\rm{GHz}}$) ; excited state labels $\left| {\rm{e}} \right\rangle $ ($6P_{3/2}, F^{'}=2,3,4,5$). The shaded area between energy levels represent broad virtual energy levels induced by the short pump and probe laser pulse (2ns). **b.** The experimental scheme of creating and certifying the multipartite entanglement. The Hanbury Brown-Twiss interferometer is used for analyzing the statistics of the correlated Stokes and anti-Stokes photons, which can further reveal the informations of entanglement depth. **c.** The representation of the dashed arrow means that every atom has equal probability to be spin up or down, which is the main feature of the W state. **d.** The decoherence effects may change the structure of the multipartite entanglement. We take the two excitations event as example to show the evolutions of entanglement depth. The distributed cesium atoms with different colors illustrate the entanglement distribution with several subgroups. The set 