pulse, which determines the excitation probability of the Stokes photon during the SRS process.

The $M$ values of multipartite entanglement created by different pulse energies, 115.5$pJ$, 225$pJ$, 330$pJ$ respectively, are shown in Figure 4a. The relation among entanglement depth and excitation probability, light pulse energy is also analyzed and shown in Figure 4b. The results show that the stronger light pulse energy has a higher $p_{1}$ probability because of the higher converting efficiency of $W$ state, but has a smaller $M$ value, which indicates that the structure of multipartite entanglement has not been deteriorated by noises. Actually, for conveniently and efficiently evaluating the scale of entanglement, the aforementioned definition of entanglement depth only delivers a lower bound of the actual entanglement scale [@NC_million-atoms], since the scale of genuine entanglement depth should be associated with the largest size of all subgroups. Thus, it is reasonable that the same lower bound of entanglement depth is observed with different excitation probabilities.

Discussion and Conclusion. {#discussion-and-conclusion. .unnumbered}
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In summary, we have experimentally demonstrated a multipartite entanglement of billions of motional atoms heralded by single photon. With the quantum memory built-in and broadband capacities, we have efficiently displayed the dynamical evolution of entanglement depth 