Photonic principle squeezing and atomic spin squeezing

We study the photonic principle quadrature squeezing and atomic spin squeezing, and demonstrate that the latter reduces to the former in the limit of a large number of atoms for even and odd states. We exemplify this reduction by treating the even and odd spin coherent states, for which analytical solutions are readily obtained, and prove that even spin coherent states always exhibit spin squeezing, whereas odd spin coherent states do not, analogous to the squeezing characteristic of even and odd photonic coherent states. Finally, we examine the squeezing transfer between photons and atoms via the Dicke Hamiltonian, where a perfect transfer of squeezing is demonstrated in the limit of a large number of atoms