Provable Optimality of the Square-Tooth Atomic Frequency Comb Quantum Memory

TL;DR

This paper provides a rigorous proof that the square-tooth shape in atomic frequency comb quantum memories yields the highest retrieval efficiency, even considering realistic experimental constraints, thus guiding optimal AFC design.

Contribution

It presents the first analytical proof of the universal optimality of the square-tooth AFC shape for maximizing retrieval efficiency under finite optical depth.

Findings

Square-tooth AFC shape is proven optimal for retrieval efficiency.

The optimality holds even with background absorption and finite linewidth.

Square-tooth AFC outperforms Lorentzian and Gaussian shapes in efficiency.

Abstract

Atomic frequency comb (AFC) quantum memories are a promising technology for quantum repeater networks because they enable multi-mode, long-time, and high-fidelity storage of photons with on-demand retrieval. The optimization of the retrieval efficiency of an AFC memory is important because it strongly impacts the entanglement distribution rate in quantum networks. Despite initial theoretical analyses and recent experimental demonstrations, a rigorous proof of the universally optimal configuration for the highest AFC retrieval efficiency has not been presented. In this paper we present a simple analytical proof which shows that the optimized square tooth offers the highest retrieval efficiency among all tooth shapes, under the physical constraint of finite optical depth of an atomic ensemble. The optimality still holds when the non-zero background absorption and the finite optical linewidth of atoms are considered. We further compare square, Lorentzian and Gaussian tooth shapes to reinforce the practical advantage of the square-tooth AFC in retrieval efficiency. Our proof lays rigorous foundation for the recipe of creating optimal AFC under realistic experimental conditions.