Conditional phase gate using an optomechanical resonator

We explore the possibility of using an optomechanical resonator to induce a conditional phase gate for single photons. The problem provides an illustration of the application to optomechanical systems of a recently developed input-output formalism for single- (or few-) photon states of the radiation field. At the two-photon level, we find significant departures from expectations based on a semiclassical treatment. We also find a tradeoff between the maximum achievable conditional phase and the fidelity of the final state, consistent with other multimode studies of conditional phases based on optical nonlinearities.