Cooperative effects in one-dimensional random atomic gases: Absence of single-atom limit
1 Department of Physics, Technion-Israel Institute of Technology - 32000 Haifa, Israel
2 Department of Education in Technology and Science, Technion-Israel Institute of Technology 32000 Haifa, Israel
Received: 17 December 2012
Accepted: 12 February 2013
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 × 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.
PACS: 42.25.Dd – Wave propagation in random media / 42.50.Nn – Quantum optical phenomena in absorbing, amplifying, dispersive and conducting media; cooperative phenomena in quantum optical systems / 72.15.Rn – Localization effects (Anderson or weak localization)
© EPLA, 2013