  Measurements of the birefringence of a single atom strongly coupled to a
high-finesse optical resonator are reported, with nonlinear phase shifts
observed for intracavity photon number much less than one. A proposal to
utilize the measured conditional phase shifts for implementing quantum logic
via a quantum-phase gate (QPG) is considered. Within the context of a simple
model for the field transformation, the parameters of the "truth table" for the
QPG are determined.
