Superradiance and multiple scattering of photons in atomic gases

We study the influence of cooperative effects such as superradiance and subradiance, on the scattering properties of dilute atomic gases. We show that cooperative effects lead to an effective potential between pairs of atoms that decays like $1/r$. In the case of superradiance, this potential is attractive for close enough atoms and can be interpreted as a coherent mesoscopic effect. We consider a model of multiple scattering of a photon among superradiant pairs and calculate the elastic mean free path and the group velocity. We study first the case of a scalar wave which allows to obtain and to understand basic features of cooperative effects and multiple scattering. We then turn to the general problem of a vector wave. In both cases, we obtain qualitatively similar results and derive, for the case of a scalar wave, analytic expressions of the elastic mean free path and of the group velocity for an arbitrary (near resonance) detuning.Comment: 12 pages, 7 figure

Intensity correlations and mesoscopic fluctuations of diffusing photons in cold atoms

We study the angular correlation function of speckle patterns that result from multiple scattering of photons by cold atomic clouds. We show that this correlation function becomes larger than the value given by Rayleigh law for classical scatterers. These large intensity fluctuations constitute a new mesoscopic interference effect specific to atom-photon interactions, that could not be observed in other systems such as weakly disordered metals. We provide a complete description of this behavior and expressions that allow for a quantitative comparison with experiments.Comment: 4 pages, 2 figure

Effect of superradiance on transport of diffusing photons in cold atomic gases

We show that in atomic gases cooperative effects like superradiance and subradiance lead to a potential between two atoms that decays like $1/r$. In the case of superradiance, this potential is attractive for close enough atoms and can be interpreted as a coherent mesoscopic effect. The contribution of superradiant pairs to multiple scattering properties of a dilute gas, such as photon elastic mean free path and group velocity, is significantly different from that of independent atoms. We discuss the conditions under which these effects may be observed and compare our results to recent experiments on photon transport in cold atomic gases.Comment: 4 pages and 1 figur

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

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.Comment: 5 pages, 3 figure

Self-dual Ginzburg-Landau vortices in a disk

We study the properties of the Ginzburg-Laundau model in the self-dual point for a two-dimensional finite system . By a numerical calculation we analyze the solutions of the Euler-Lagrange equations for a cylindrically symmetric ansatz. We also study the self-dual equations for this case. We find that the minimal energy configurations are not given by the Bogomol'nyi equations but by solutions to the Euler Lagrange ones. With a simple approximation scheme we reproduce the result of the numerical calculation.Comment: 8 pages, 4 figures, RevTex macro