Optical-depth scaling of light scattering from a dense and cold atomic Rb87 gas

Abstract

We report investigation of near-resonance light scattering from a cold and dense atomic gas of 87 Rb atoms. Measurements are made for probe frequencies tuned near the F = 2 → F ′ = 3 nearly closed hyperfine transition, with particular attention paid to the dependence of the scattered light intensity on detuning from resonance, the number of atoms in the sample, and atomic sample size. We find that, over a wide range of experimental variables, the optical depth of the atomic sample serves as an effective single scaling parameter which describes well all the experimental data.

Comparison of three approaches to light scattering by dilute cold atomic ensembles

“…Surprisingly, even if the scattered light is observed in one particular direction, this simple approach can provide quite accurate results up to moderate optical depth on the order of 15, with only a global free multiplicative factor for the intensity scale. This approach has already been used to explain recent experiments on the collective reduction of the radiation pressure force [15,24], on off-axis scattering by very elongated clouds [16], and might also explain the effect reported in Ref. [25].…”

“…If the initial beam profile also has a simple intensity distribution, one can integrate over the transverse directions to get the total transmission, and thus the total attenuation, which is also the total scattered light. For instance, supposing the incoming beam to be a plane wave and the atomic cloud to be a Gaussian sphere (rms size R in all directions, peak density ρ 0 , peak optical depth b = √ 2πρ 0 σ sc R), one obtains (see [16,24]) that the total scattering cross-section of the cloud is…”

“…For high optical depth, the cross-section increases only logarithmically, which appears as a collective saturation of the scattered light. This saturation comes from the fact that the atoms in the back of the cloud are less illuminated due to the extinction of the light caused by the destructive interference between the incident and the scattered fields ("shadow effect") [5,15,16,24]. This result tells nothing about the angular distribution of the scattered light, but it is an excellent approximation for the total scattered light.…”

“…The curves were averaged as in Fig. 1. consequence, in an experiment where several parameters can be varied (size, atom number, detuning), it is generally relevant to plot the experimental data as a function of the optical depth [16].…”

“…Several experiments have also been performed in a simpler situation, dealing with steady-state scattering from dilute and large clouds [13][14][15][16], and those experiments have been interpreted in various ways, depending on which theoretical model was used for comparison.…”