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

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.

5 pages, 3 figures

References in corpus (2)

• Photon localization and Dicke superradiance in atomic gases
• Eigenvalue distributions of large Euclidean random matrices for waves in random media

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