Cooperative effects in one-dimensional random atomic gases: Absence of single atom limit

TL;DR

This paper investigates superradiance in one-dimensional atomic gases, revealing that photon localization persists regardless of atom number due to cooperative effects, contrasting with three-dimensional behavior.

Contribution

The study provides an analytic approach to photon escape rates in 1D atomic gases, showing the persistent localization effect caused by long-range cooperation, not disorder.

Findings

Photon escape rates are analytically derived for 1D atomic gases.

Photon localization always occurs in 1D, independent of atom number.

Localization stems from cooperative effects, not disorder.

Abstract

We study superradiance in a one-dimensional geometry, where N>>1 atoms are randomly distributed along a line. We present an analytic calculation of the photon escape rates based on the diagonalization of the N x N coupling matrix Uij = cos xij, where xij is the dimensionless random distance between any two atoms. We show that unlike a three-dimensional geometry, for a one- dimensional atomic gas the single-atom limit is never reached and the photon is always localized within the atomic ensemble. This localization originates from long-range cooperative effects and not from disorder as expected on the basis of the theory of Anderson localization.