  We study the quantum statistical properties of the collective excitations of
an atomic ensemble inside a high-finesse cavity. In the large-detuning regime,
it is found that the virtual photon exchange can induce a long-range
interaction between atoms, which results in correlated excitations. In
particular, the atomic blockade phenomenon occurs when the induced long-range
interaction effectively suppresses the double atomic excitation, when the
average photon number takes certain values, which makes the two nearest energy
levels degenerate. We also show that quantum phase transitions occur in the
indirectly-interacting atomic ensemble when the average photon number reaches
several critical points. In this sense, the quantum statistical properties of
the collective excitations are very sensitive to the change of the average
photon number. Our model exhibits quantum phase transitions similar to the ones
in the Lipkin-Meshkov-Glick model. Our proposal could be implemented in a
variety of systems including cavity quantum electrodynamics (QED),
Bose-Einstein condensates, and circuit QED.
