Coherent light propagation through cold atomic clouds beyond the independent scattering approximation

Abstract

We calculate the relative permittivity of a cold atomic gas under weak probe illumination, up to second order in the density. Within the framework of a diagrammatic representation method, we identify all the second order diagrams that enter into the description of the relative permittivity for coherent light transmission. These diagrams originate from pairwise position correlation and recurrent scattering. Using coupled dipole equations, we numerically simulate the coherent transmission with scalar and vector waves, and find good agreement with the perturbative calculations. We applied this perturbative expansion approach to a classical gas at rest, but the method is extendable to thermal gas with finite atomic motion and to quantum gases where non-trivial pair correlations can be naturally included.

Bistable optical transmission through arrays of atoms in free space

“…In some cases, the theory can be solved even analytically, with sufficiently small atomic separations (ka) < (π/3) 1/2 needed for bistability of spatially uniform modes. The bistability threshold ka ∼ 1 applies even for the case of just two atoms and equals the separation at which the single-atom linewidth γ becomes less than the collective line shift, originating from recurrent scattering where the light is scattered more than once by the same atom [77][78][79][80][81][82].…”

Resonant forward-scattered field in the high-saturation regime: Elastic and inelastic contributions

“…While superradiance and subradiance effects [27,28] have been reported in dilute systems (see, e.g., [29][30][31]), we found that our experimental results can be well explained, keeping superradiance and subradiance effects out of the picture. Modifications of the light scattering properties due to dipole-dipole interactions [32][33][34][35][36][37][38][39] are also not expected to play a role here.…”

Transport of light through a dense ensemble of cold atoms in a static electric field

“…For high densities, the problem is difficult to solve even in the absence of external fields when * has been calculated only up to second order in ρ/k 3 0 [5,6]. Numerical methods employed in this work proved to be very useful to guide and test analytical theories in this research field [8].…”

“…In this Appendix, we present a solution of the anisotropic diffusion equation (5) with the boundary conditions (7) and (8) in a cylindrical sample depicted in the inset of Fig. 1.…”

“…Surprisingly enough, even such a simplified model turns out to be difficult to treat analytically once the number of atoms per wavelength cubed of the resonant light λ 0 becomes significant [4][5][6]. Numerical analysis of light scattering by resonant point scatterers has become a powerful tool to test analytic theories [7,8] and to explore fundamental phenomena [9,10] in multiple scattering.…”