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We show that the simultaneous interaction of two single-photon fields with asingle atom in the V configuration can in principle produce a conditional phasegate of arbitrarily high fidelity, for an appropriate choice of the interactiontime, as long as the fields con be described by a single temporal mode (as inan optical cavity); this requires a ``gated'' interaction, where, e.g.,dynamical coupling techniques could be used to get the fields in and out of thecavity, and a large detuning induced by a strong external field could be usedto turn the atom-field interaction on and off at the right times. With theseassumptions, our analysis shows that the largest gate fidelities are obtainedfor a cavity containing a single atom, and that adding more atoms in effect``dilutes'' the system's nonlinearity. We also study how spontaneous emissionlosses into non-cavity modes degrade the fidelity, and consider as well acouple of alternate atomic level schemes, namely two- and five-level systems.

Conditional phase gate between two photons through control of the interaction time with a single atom in a cavity