# Comparison of three approaches to light scattering by dilute cold atomic ensembles

## TL;DR

This paper compares three models—coupled-dipole, random-walk, and shadow effect—for light scattering in dilute cold atomic ensembles, highlighting their accuracy and applicability in different regimes.

## Contribution

It provides a systematic comparison of three different theoretical approaches to light scattering in dilute cold atomic ensembles, clarifying their validity ranges.

## Key findings

- Random-walk model accurately predicts steady-state scattering in low-density samples.
- Shadow effect approximation is surprisingly accurate up to optical depths of about 15.
- Coupled-dipole model captures cooperative effects like superradiance.

## Abstract

Collective effects in atom-light interaction is of great importance for cold-atom-based quantum devices or fundamental studies on light transport in complex media. Here we discuss and compare three different approaches to light scattering by dilute cold atomic ensembles. The first approach is a coupled-dipole model, valid at low intensity, which includes cooperative effects, like superradiance, and other coherent properties. The second one is a random-walk model, which includes classical multiple scattering and neglects coherence effects. The third approach is a crude approximation only based on the attenuation of the excitation beam inside the medium, the so-called "shadow effect". We show that in the case of a low-density sample, the random walk approach is an excellent approximation for steady-state light scattering, and that the shadow effect surprisingly gives rather accurate results at least up to optical depths on the order of 15.