Three-dimensional theory of quantum memories based on Lambda-type atomic ensembles

TL;DR

This paper develops a comprehensive three-dimensional model for quantum memories using Lambda-type atomic ensembles, analyzing how physical parameters like Fresnel number and optical depth influence storage efficiency and mode optimization.

Contribution

It introduces a 3D theoretical framework for quantum memories that accounts for finite spatial extent and identifies key parameters affecting performance.

Findings

Backward memory is more efficient at large Fresnel numbers.

High optical depths enable efficient storage even at small Fresnel numbers.

Optimal modes and spin-waves are characterized for different parameters.

Abstract

We develop a three-dimensional theory for quantum memories based on light storage in ensembles of Lambda-type atoms, where two long-lived atomic ground states are employed. We consider light storage in an ensemble of finite spatial extent and we show that within the paraxial approximation the Fresnel number of the atomic ensemble and the optical depth are the only important physical parameters determining the quality of the quantum memory. We analyze the influence of these parameters on the storage of light followed by either forward or backward read-out from the quantum memory. We show that for small Fresnel numbers, the forward memory provides higher efficiencies, whereas for large Fresnel numbers, the backward memory is advantageous. The optimal light modes to store in the memory are presented together with the corresponding spin-waves and outcoming light modes. We show that for high optical depths such Lambda-type atomic ensembles allow for highly efficient backward and forward memories even for small Fresnel numbers $F\gtrsim 0.1$.