Entangled collective-spin states of atomic ensembles under non-uniform atom-light interaction

TL;DR

This paper investigates how non-uniform atom-light interactions affect the generation and verification of entanglement in atomic ensembles, providing a simplified effective model applicable to complex states.

Contribution

It introduces a model that describes non-uniformly coupled atomic spins as an effective uniform system, accounting for geometry and coupling variations, applicable to complex entangled states.

Findings

Effective atom-light coupling is reduced by a factor related to geometry.

The model remains valid for complex entangled states with arbitrary phase-space distributions.

An analytic formula for observable entanglement considering coupling differences is derived.

Abstract

We consider the optical generation and verification of entanglement in atomic ensembles under non-uniform interaction between the ensemble and an optical mode. We show that for a wide range of parameters a system of non-uniformly coupled atomic spins can be described as an ensemble of uniformly coupled spins with a reduced effective atom-light coupling and a reduced effective atom number, with a reduction factor of order unity given by the ensemble-mode geometry. This description is valid even for complex entangled states with arbitrary phase-space distribution functions as long as the detection does not resolve single spins. Furthermore, we derive an analytic formula for the observable entanglement in the case, of relevance in practice, where the ensemble-mode coupling differs between state generation and measurement.