from the motions of warm atoms, the effects of collective enhancement become deteriorative, which results in the exponential decay of $p_{1}$. What is more, we measure the cross-correlation between the correlated photons and the autocorrelation of the retrieved anti-Stokes photon as shown in Figure 3b. The degrade of quantum correlation and single-photon characteristic implies the variation of the structure of multipartite entanglement according to the relation of $p_{2}$ and $g_{AS_{1}-AS_{2}|S}^{(2)}$ (see Methods), which are consistent with the deduced $M$ values in Figure 2. Our results well exhibit the transition from quantum to classical in multipartite entanglement of billions of motional atoms heralded by single photon.

From another perspective, we can demonstrate how the entanglement depth varies with the delay time. In order to determine the informations of entanglement depth, the number of total caesium atoms involved in the interaction is the key parameter that should be measured precisely. The atomic density and total atomic number can be obtained by fitting the measured transmission rates of light with different frequency according to the absorption model (see Methods). The results show that there are nearly at least 8.85 billion motional atoms sharing the one excitation constituting the W state. As is shown 