  Information about quantum phase transitions in conventional condensed matter
systems, must be sought by probing the matter system itself. By contrast, we
show that mixed matter-light systems offer a distinct advantage in that the
photon field carries clear signatures of the associated quantum critical
phenomena. Having derived an accurate, size-consistent Hamiltonian for the
photonic field in the well-known Dicke model, we predict striking behavior of
the optical squeezing and photon statistics near the phase transition. The
corresponding dynamics resemble those of a degenerate parametric amplifier. Our
findings boost the motivation for exploring exotic quantum phase transition
phenomena in atom-cavity, nanostructure-cavity, and
nanostructure-photonic-band-gap systems.
