Phase gate for a photonic quantum network

We give a fully quantum description of a simple model for a quantum phase g ate which could be used for quantum communication in future optical quantum networks. The carriers of information are modelled as two-photon wavepacke ts which interact with an atom inside a two port cavity in a polarization-d ependent manner. Owing to this interaction the different polarization state s of the wavepackets suffer phase shifts which are intensity dependent. Thi s process is well known as the Kerr effect.