Polarization phase gate and three-photon GHZ state using coherently enhanced Kerr nonlinearity

We study the nonlinear optical response of a five-level atomic system in the regimes of electromagnetically induced transparency and coherent Raman gain, corresponding to two different schemes of light-atom interaction. Our analytical and numerical results show that greatly enhanced Kerr nonlinearity and efficient cross phase modulation may be achieved between a weak probe field and a weak signal field. The cross phase modulation via Kerr nonlinearity is then exploited toward the realization of a polarization quantum phase gate and the generation of a three-photon GHZ state.