Therefore, the illuminated volume can be calculated as, $$\label{eq6}
V=\pi ln10\int_{-\frac{l}{2}}^{\frac{l}{2}}W_{w}^{2}(1+\frac{z^{2}}{z_{w}^{2}})dz$$ where $l=75.3\times10^{-3}m$ is the length of cesium cell, and beam waist $W_{w}=100\times10^{-6}m$, Rayleigh length $z_{w}=3.69\times10^{-2}m$. Finally, the total number of atoms $N$ involved into the creation of entanglement is $N=nV=8.85\times 10^{9}$.

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