properties of collective observables are completely determined by the single-particle expectation values. In particular, the noise in the transverse component of the total angular momentum is $\Delta J_z = \sqrt N \Delta F_z^{(1)}$, where $\Delta F_z^{(1)}$ is the uncertainty in the transverse spin component of a single atom, and squeezing has the same limit as for a single spin-$F$ particle. The final degree of squeezing depends only on the dimensionless time integrated interaction strength $K \equiv g_2 \int \phi(t) \, dt$, that is proportional to the total number of photons in the squeezer pulse. Fig. \[fig:internal-squeezing\] shows the degree of squeezing as function of this parameter.

![ Internal spin squeezing, equivalent to squeezing of a single $F=4$ spin. The squeezing parameters $\chi_0$, $\zeta_0$, and $\xi_0$ are shown as function of the integrated interaction strength, $K=g_2 \int \phi(t)\,dt$. The squeezing parameters are, in general, defined as follows: $\chi^2 = 2(\Delta J_z)^2 / (NF)$ is the uncertainty of the transverse spin component with respect to that in the original CSS [@PhysRevA.47.5138], $\zeta^2 = 2(\Delta J_z)^2 / \langle J_x \rangle$ is the uncertainty compared to that of a CSS with the same longitudinal mean spin [@Nature.409.63], $\xi^2 = 2NF (\Delta
   J_z)^2 / \langle 