Cavity QED quantum phase gates for a single longitudinal mode of the   intracavity field
  A single three-level atom driven by a longitudinal mode of a high-Q cavity is used to implement two-qubit quantum phase gates for the intracavity field. The two qubits are associated to the zero-and one-photon Fock states of each of the two opposite circular polarization states of the field. The three-level atom yields the conditional phase gate provided the two polarization states and the atom interact in a $V$-type configuration and the two photon resonance condition is fulfilled. Microwave and optical implementations are discussed with gate fidelities being evaluated against several decoherence mechanisms such as atomic velocity fluctuations or the presence of a weak magnetic field. The use of coherent states for both polarization states is investigated to assess the entanglement capability of the proposed quantum gates. 
R. Garc\'ia--Maraver, R. Corbal\'an, K. Eckert, S. Rebi\'c, M. Artoni,   and J. Mompart