Evolution of Quantum States in an Electro-Optic Phase Modulator

We present a quantum mechanical model to evaluate the time evolution of quantum states of light in an electro-optic phase modulator (EOPM). The phase modulator is analogous to a multilevel atomic system with equally spaced energy levels, each of which corresponds to the sidebands of the phase modulated optical field. Using perturbation theory, we solve the equations governing the interaction of the optical field with a modulating field both with and without phase velocity mismatch. A unitary operator that evolves any given quantum state allows us to evaluate the response of EOPM for single photon, coherent and squeezed states. We apply these results to the analysis of frequency coded quantum key distribution scheme.