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We investigate atom-photon entangling gates based on cavity quantumelectrodynamics (QED) for a finite photon-pulse duration, where not only thephoton loss but also the temporal mode-mismatch of the photon pulse becomes asevere source of error. We analytically derive relations between cavityparameters, including transmittance, length, and effective cross-sectional areaof the cavity, that minimize both the photon loss probability and the errorrate due to temporal mode-mismatch by taking it into account as state-dependentpulse delay. We also investigate the effects of pulse distortion usingnumerical simulations for the case of short pulse duration.

Optimal cavity design for minimizing errors in cavity-QED-based atom-photon entangling gates with finite temporal duration