state into an anti-Stokes photon, as shown in Figure 1a and Figure 1b. In order to obtain the information of entanglement depth, we analyze the photon number statistics of the correlated Stokes and anti-Stokes photons via a Hanbury Brown-Twiss interferometer (see Methods). Due to the decoherence effects, as Figure 1d shows, the atomic ensemble with high-order excitations evolves to several subgroups, where each part shares only single excitation [@NC_million-atoms]. Suppose that the whole atomic ensemble is in a pure state, containing $M$ separable parts, which can be expressed in a product form $\left |\psi  \right \rangle=\left |\psi _{1}\right \rangle\otimes \left |\psi _{2}\right \rangle...\otimes \left |\psi _{M}  \right \rangle$, where $M$ indicates the number of separable subgroups, $\left |\psi _{i}\right \rangle(i=1,...,M)$ represents each separable group that may contain individual multipartite entanglement, while different subgroups are independent from the others (see Methods). Then, we can define entanglement depth as $D=N/M$, with $N$ is the number of total atoms participating in interaction [@NC_million-atoms].

In order to quantify the multipartite entanglement, we adopt the entanglement witnesses incorporated with photon number statistics of the correlated photons pair. Such witness is efficient especially when the vacuum component of the state is dominant [@NC_million-atoms]. For each given 