Two photon conditional phase gate based on Rydberg slow light polaritons

TL;DR

This paper analyzes the fidelity of a deterministic two-photon quantum phase gate using Rydberg-EIT polaritons, accounting for various loss and dispersion effects, and provides experimental guidelines for high-fidelity implementation.

Contribution

It offers an analytical framework for the phase shift and fidelity of Rydberg-based photon gates, including effects of losses, dispersion, and transverse size, highlighting the advantages of Rydberg-EIT.

Findings

Flatness of the effective interaction suppresses finite size corrections.

Losses and scattering significantly impact gate fidelity.

Experimental parameters for high-fidelity gates are identified.

Abstract

We analyze the fidelity of a deterministic quantum phase gate for two photons counterpropagating as polaritons through a cloud of Rydberg atoms under the condition of electromagnetically induced transparency (EIT). We provide analytical results for the phase shift of the quantum gate, and provide an estimation for all processes leading to a reduction to the gate fidelity. Especially, the influence of losses form the intermediate level, dispersion of the photon wave packet, scattering into additional polariton channels, finite lifetime of the Rydberg state, as well as effects of transverse size of the wave packets are accounted for. We show that the flatness of the effective interaction, caused by the blockade phenomena, suppresses the corrections due to the finite transversal size. This is a strength of Rydberg-EIT setup compared to other approaches. Finally, we provide the experimental requirements for the realization of a high fidelity quantum phase gate using Rydberg polaritons.