Optimization of photon storage fidelity in ordered atomic arrays

TL;DR

This paper develops a formalism to optimize photon storage fidelity in ordered atomic arrays, demonstrating that small arrays can achieve efficiencies comparable to large disordered ensembles by leveraging interference effects.

Contribution

It introduces a general method to find maximum storage efficiency in discrete atomic arrays, surpassing traditional continuous medium models.

Findings

Storage error scales as (log N)^2 / N^2 in atomic arrays.

A 4x4 atom array can match the efficiency of a disordered ensemble with optical depth ~600.

Ordered arrays enable high-fidelity photon storage with fewer atoms.

Abstract

A major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage error, when the ensemble is describable by a continuous medium governed by the Maxwell-Bloch equations. The validity of this model can break down, however, in systems such as dense, ordered atomic arrays, where strong interference in emission can give rise to phenomena such as subradiance and "selective" radiance. Here, we develop a general formalism that finds the maximum storage efficiency for a collection of atoms with discrete, known positions, and a given spatial mode in which an optical field is sent. As an example, we apply this technique to study a finite two-dimensional square array of atoms. We show that such a system enables a storage error that scales with atom number $N_\mathrm{a}$ like $\sim (\log N_\mathrm{a})^2/N_\mathrm{a}^2$, and that, remarkably, an array of just $4 \times 4$ atoms in principle allows for an efficiency comparable to a disordered ensemble with optical depth of around 600.