  We investigate quantum phase transitions, quantum criticality, and Berry
phase for the ground state of an ensemble of non-interacting two-level atoms
embedded in a non-linear optical medium, coupled to a single-mode quantized
electromagnetic field. The optical medium is pumped externally through a
classical electric field, so that there is a degenerate parametric
amplification effect, which strongly modifies the field dynamics without
affecting the atomic sector. Through a semiclassical description the different
phases of this extended Dicke model are described. The quantum phase transition
is characterized with the expectation values of some observables of the system
as well as the Berry phase and its first derivative, where such quantities
serve as order parameters. It is remarkable that the model allows the control
of the quantum criticality through a suitable choice of the parameters of the
non-linear optical medium, which could make possible the use of a low intensity
laser to access the superradiant region experimentally.
