Cavity QED quantum phase gates for a single longitudinal mode of the intracavity field

In this work, a single three-level atom driven by a single longitudinal mode of a high-Q cavity is used to implement two-qubit quantum phase gates (QPG) for the intracavity field. The two qubits are associated with the zero- and one-photon Fock states of each of the two opposite circular polarization states of the field. The three-level atom mediates the conditional phase gate provided the two circular polarization states and the atom interact in a V-type configuration and the two-photon resonance condition is satisfied.