Theory of Rabi interaction between an infrared-active phonon and cavity-resonant modes

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.