Cooperative effects and disorder: A scaling analysis of the spectrum of the effective atomic Hamiltonian

Abstract

We study numerically the spectrum of the non-Hermitian effective Hamiltonian that describes the dipolar interaction of a gas of $N\gg 1$ atoms with the radiation field. We analyze the interplay between cooperative effects and disorder for both scalar and vectorial radiation fields. We show that for dense gases, the resonance width distribution follows, both in the scalar and vectorial cases, a power law $P(\Gamma )\sim {\Gamma }^{-4/3}$ that originates from cooperative effects between more than two atoms. This power law is different from the $P(\Gamma )\sim {\Gamma }^{-1}$ behavior, which has been considered as a signature of Anderson localization of light in random systems. We show that in dilute clouds, the center of the energy distribution is described by Wigner's semicircle law in the scalar and vectorial cases. For dense gases, this law is replaced in the vectorial case by the Laplace distribution. Finally, we show that in the scalar case the degree of resonance overlap increases as a power law of the system size for dilute gases, but decays exponentially with the system size for dense clouds.

11 pages, 12 figures

References in corpus (4)

• Photon localization and Dicke superradiance in atomic gases
• Eigenvalue distributions of large Euclidean random matrices for waves in random media
• Effect of superradiance on transport of diffusing photons in cold atomic gases
• Superradiance and multiple scattering of photons in atomic gases

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• Van der Waals dephasing for Dicke subradiance in cold atomic clouds
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• Robust Correlation-Induced Localization Under Time-Reversal Symmetry Breaking
• Breaking of reciprocity and the Pancharatnam-Berry phase for light scattered by a disordered cold atom cloud