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arXiv:1908.05260 · Physical Review A

Photon scattering from a cold, Gaussian atom cloud

F. Robicheaux, R. T. Sutherland

Published Jan 8, 2020• 6 citations
arXivHTMLPDF

Abstract

We study the effect of a weakly driven atomic cloud's polarization distribution on its photon scattering line shape in the limit where the atoms can be treated as stationary and randomly distributed. We find three distinct polarization regimes. First, for dilute clouds, the polarization magnitude is relatively constant. Second, for denser clouds, polarization builds at the front of the cloud for near-resonant light. Third, when the cloud condenses to the point where its dimensions become comparable to the wavelength, light focuses towards the back of the cloud for red detuning. For these regimes, we show which ``mean-field'' frameworks accurately describe the differing photon-scattering line shapes. Finally, for even denser clouds, mean-field models become inaccurate and necessitate the full point dipole model that includes atom-atom correlations.

DOI
10.1103/physreva.101.013805

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We study the effect of a weakly driven atomic cloud's polarization distribution on its photon scattering line shape in the limit where the atoms can be treated as stationary and randomly distributed. We find three distinct polarization regimes. First, for dilute clouds, the polarization magnitude is relatively constant. Second, for denser clouds, polarization builds at the front of the cloud for near-resonant light. Third, when the cloud condenses to the point where its dimensions become comparable to the wavelength, light focuses towards the back of the cloud for red detuning. For these regimes, we show which ``mean-field'' frameworks accurately describe the differing photon-scattering line shapes. Finally, for even denser clouds, mean-field models become inaccurate and necessitate the full point dipole model that includes atom-atom correlations.
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Abstract We report a theoretical investigation of angular distribution of a single-photon superradiance from cold and dilute atomic clouds. In the present work we focus our attention on the dependence of superradiance on the size and shape of the cloud. We analyze the dynamics of the afterglow of atomic ensemble excited by pulse radiation. Two theoretical approaches are used. The first is the quantum microscopic approach based on a coupled-dipole model. The second approach is random walk approximation. We show that the results obtained in both approaches coincide with a good accuracy for incoherent fluorescence excited by short resonant pulses. We also show that the superradiance decay rate changes with size differently for radiation emitted into different directions.
The second-order correlation function for light emitted from a strongly and near-resonantly driven dilute cloud of atoms is discussed. Because of the strong driving, the fluorescence spectrum separates into distinct peaks, for which the spectral properties can be defined individually. It is shown that the second-order correlations for various combinations of photons from different spectral lines exhibit bunching together with super-Poissonian or sub-Poissonian photon statistics, tunable by the choice of the detector positions. Additionally, a Cauchy-Schwarz inequality is violated for photons emitted from particular spectral bands. The emitted light intensity is proportional to the square of the number of particles, and thus can potentially be intense. Three different averaging procedures to model ensemble disorder are compared.
It is shown that homogeneous line-broadening in a diffuse cold atom cloud is proportional to the resonant optical depth of the cloud. Furthermore, it is demonstrated how the strong directionality of the coherent interactions causes the cloud's spectra to depend strongly on its shape, even when the cloud is held at constant densities. These two numerical observations can be predicted analytically by extending the single-photon wave-function model. Lastly, elongating a cloud along the line of laser propagation causes the excitation probability distribution to deviate from the exponential decay predicted by the Beer--Lambert law to the extent where the atoms at the back of the cloud are more excited than the atoms at the front. These calculations are conducted at the low densities relevant to recent experiments.
Collective effects in the atom–light interaction are of great importance for cold-atom-based quantum devices or fundamental studies on light transport in complex media. Here we discuss and compare three different approaches to light scattering by dilute cold atomic ensembles. The first approach is a coupled-dipole model, valid at low intensity, which includes cooperative effects, such as superradiance, and other coherent properties. The second one is a random-walk model, which includes classical multiple scattering and neglects coherence effects. The third approach is a crude approximation based only on the attenuation of the excitation beam inside the medium, the so-called shadow effect. We show that in the case of a low-density sample, the random-walk approach is an excellent approximation for steady-state light scattering and that the shadow effect surprisingly gives rather accurate results at least up to optical depths on the order of 15.