  We study the quantum phase transition of a N two-level atomic ensemble
interacting with an optical degenerate parametric process, which can be
described by the finite size Dicke Hamiltonian plus counter-rotating and
quadratic field terms. Analytical closed forms of the critical coupling value
and their corresponding separable ground states are derived in the weak and
strong coupling regimes. The existence of bipartite entanglement between the
two-level-system ensemble and photon field as well as between ensemble
components for moderate coupling is shown through numerical analysis. Given a
finite size, our results also indicate the co-existence of squeezed fields and
squeezed atomic ensembles.
