the total angular momentum and the twisting operator.

When the reference state is the $x$-polarized coherent spin state and we take the standard spin projection eigenbasis ${|{\phi_\alpha}\rangle}={|{F,m_F^x=F-\alpha}\rangle}$, the oscillators associated with $\hat J_z$ and $\hat T$ are the first and second ones, respectively. The idea of using both these oscillators in a quantum memory and a proposal on how to experimentally access the latter by means of stimulated four-photon processes is presented in Ref. [@PhysRevLett.95.053602].

We remark here that any process that acts coherently on each atom (e.g., coupling to a classical field) changes the reference state itself but does not influence the atomic oscillators around the reference state. In this sense, internal spin squeezing as a coherent process does not squeeze any of the collective atomic oscillators. In particular, it does not squeeze the quadrature operator $\hat P_z$ that is assigned to the $z$ component of the angular momentum. It does reduce the noise in $\hat J_z$, but only because $\hat J_z \approx [2N (\Delta F_z^{(1)})_0^2]^{1/2} \hat P_z$ and the normalization factor in the brackets is reduced in the new reference state. In Sec. \[sec:spsq\], we will investigate spin squeezing in more details.

#### General case.

If ${|{a}\rangle}$ and 