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

TL;DR

This paper analyzes how to optimize cavity parameters in cavity-QED systems to minimize errors caused by photon loss and temporal mode-mismatch during atom-photon entangling gates with finite photon pulse durations, providing fundamental design guidelines.

Contribution

It derives analytical relations for cavity parameters that minimize both photon loss and mode-mismatch errors, introducing the concept of an optimal cavity length for atom-photon gates.

Findings

Identifies cavity parameters that minimize error rates.

Proposes an optimal cavity length for improved gate fidelity.

Validates analysis with numerical simulations of short pulses.

Abstract

We investigate atom-photon entangling gates based on cavity quantum electrodynamics (QED) for a finite photon-pulse duration, where not only the photon loss but also the temporal mode-mismatch of the photon pulse becomes a severe source of error. We analytically derive relations between cavity parameters, including transmittance, length, and effective cross-sectional area of the cavity, that minimize both the photon loss probability and the error rate due to temporal mode-mismatch by taking it into account as state-dependent pulse delay. We also investigate the effects of pulse distortion using numerical simulations for the case of short pulse duration. We believe that these analyses are the first to suggest that a cavity has an optimal length for the atom-photon gate, providing a fundamental guideline for implementing quantum information processing.