We investigate the origin of imperfections in the fidelity of a two-photon controlled-phase gate based on two-level-emitter nonlinearities. We focus on a passive system that operates without external modulations to enhance its performance. We demonstrate that the fidelity of the gate is limited by opposing requirements on the input pulse width for one- and two-photon-scattering events. For one-photon scattering, the spectral pulse width must be narrow compared with the emitter linewidth, while two-photon-scattering processes require the pulse width and emitter linewidth to be comparable. We find that these opposing requirements limit the maximum fidelity of the two-photon controlled-phase gate to $84\%$ for photons with Gaussian spectral profiles.

• Received 14 December 2016

DOI:https://doi.org/10.1103/PhysRevA.95.062304