  We present the theory of interaction between a polar vibration in a
semiconductor and an electromagnetic mode of a surrounding cavity. Tuning the
cavity frequency near the transverse optical phonon frequency couples the
phonon-induced polarization field within the dielectric and the electromagnetic
field in the cavity. Depending on engineering parameters, we predict that this
cavity quantum electrodynamic interaction may reach the strong coupling regime.
The resonances of the system are in the terahertz spectral region, and while
spectroscopic measurements are a possible route for the detection of such a
system, we emphasize the possibility of measuring the Rabi oscillation directly
in the time domain with femtosecond optical pulses.
