Controlled-NOT gate for manipulating photonic polarization states in a two-mode optical cavity

We investigate the coherent interaction between two cavity modes with left or right circular polarizations and a traveling atom in the four-level Y configuration. With large single-photon detunings for both cavity modes and in the presence of a strong classical field, all one-photon and two-photon transitions may be well eliminated so that a close-loop four-photon transition starting from the only populated ground state becomes absolutely dominant. This physical scenario is then exploited to devise an efficient controlled-NOT gate for manipulating polarization states of two intracavity photons. In the Lamb-Dicke limit and in the strong coupling regime, the expected controlled-NOT operation is found to have a rather high gate fidelity and a moderate photon loss.