  We study relations between bosonic quadrature squeezing and atomic spin
squeezing, and find that the latter reduces to the former in the limit of a
large number of atoms for even and odd states. We demonstrate this reduction by
treating 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 bosonic 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.
