# Influence of atomic motion on the collective effects in dense and cold atomic ensembles

## TL;DR

This paper investigates how atomic motion affects collective phenomena in dense, cold atomic ensembles, revealing that even minimal Doppler shifts can qualitatively alter these effects by disrupting sub-radiant states.

## Contribution

It demonstrates that atomic motion can significantly modify collective effects in dense, cold atomic ensembles, even with small Doppler shifts, highlighting a new understanding of atomic interactions.

## Key findings

- Atomic motion suppresses sub-radiant collective states.
- Quantitative and qualitative changes in collective effects due to atomic motion.
- Effects observed even with Doppler shifts much smaller than the natural linewidth.

## Abstract

We show that atomic motion leads not only to noticeable quantitative, but in some cases also to qualitative modification of collective effects in dense and cold atomic ensembles even in the case when the characteristic Doppler shifts are tens of times smaller than the natural linewidth. The observed influence is explained as a result of the suppression of the impact of sub-radiant collective states caused by the displacement of the atoms.