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Coherent Scattering of Near-Resonant Light by a Dense Microscopic Cold Atomic Cloud

Abstract : We measure the coherent scattering of light by a cloud of laser-cooled atoms with a size comparable to the wavelength of light. By interfering a laser beam tuned near an atomic resonance with the field scattered by the atoms, we observe a resonance with a redshift, a broadening, and a saturation of the extinction for increasing atom numbers. We attribute these features to enhanced light-induced dipole-dipole interactions in a cold, dense atomic ensemble that result in a failure of standard predictions such as the " cooperative Lamb shift ". The description of the atomic cloud by a mean-field model based on the Lorentz-Lorenz formula that ignores scattering events where light is scattered recurrently by the same atom and by a microscopic discrete dipole model that incorporates these effects lead to progressively closer agreement with the observations, despite remaining differences. The understanding of light propagation in dense media relies traditionally on a continuous description of the sample characterized by macroscopic quantities such as susceptibility or refractive index [1,2]. Their derivation from a microscopic theory is in general challenging owing to the interactions between the light-induced dipoles that can be large when the light is tuned near an atomic resonance. In dilute media, their role can be analyzed using the perturbative approach of Friedberg, Hartmann, and Manassah (FHM) [3], which predicts in particular a " cooperative Lamb shift " measured recently in inhomo-geneously broadened media [4,5] and cold dilute atomic gases [6]. For an atom slab, the FHM approach was shown to correspond to the low-density limit of the local-field model introduced by Lorentz [7], which replaces the action of all the atoms of the medium on a particular one by an average effective field [1,2], thus ignoring correlations between the light-induced dipoles. This mean-field approach leads to the Lorentz-Lorenz formula, which allows calculating the index of refraction of many dense media with an excellent accuracy [1,8]. However, it was pointed out [7,9] that in the absence of inhomo-geneous broadening, such as in cold atomic ensembles, the mean-field response may not be valid due to recurrent scattering where the field radiated by one atom can be scattered back by another atom [10,11]. Recurrent scattering should become important when the incident light (wavelength λ ¼ 2π=k) is tuned near an atomic resonance, and the atomic density approaches k 3. This calls for an experiment operating in this regime, where a comparison between the standard mean-field theories of light scattering and a microscopic approach, including recurrent scattering, can be performed. Here, we perform this comparison. To do so, we need to access a quantity relevant to both the macroscopic and the microscopic approaches. The coherent electric field hE sc i scattered by the cloud fulfills this condition: it is obtained by averaging the scattered field E sc over many realizations of the spatial random distribution of atoms, and its evolution is governed by the macroscopic Maxwell's equations in the cloud considered as an homogeneous medium described by a susceptibility. In the case of cold atomic gases, the near-resonance coherent optical response has been explored experimentally using mostly dilute, optically thick ensembles [12–19]. Recently, we studied the light scattered by a microscopic dense cloud of cold atoms at 90° of a near-resonant excitation laser [20]. In that situation, we were sensitive to the incoherent component hjE sc − hE sc ij 2 i of the scattered light. We could therefore not compare our results with mean-field predictions for continuous media, which are only relevant for the coherent part. In this work, we study the coherent scattering by our microscopic cloud. The cloud contains up to a few hundreds laser-cooled rubidium-87 atoms and has a size smaller than the wavelength of the optical D 2 transition. We illuminate the sample with a tightly focused laser with a waist larger than the cloud size. We access the coherent scattering by measuring the extinction resulting from the interference of the laser field with the field scattered by the cloud. We observe a saturation of the extinction, a broadening of the line, and a small redshift when we vary the number of atoms from 10 to 180. We show that the measured shift and width do not agree with the FHM perturbative approach. The description of the atomic cloud by a mean-field model based on the Lorentz-Lorenz
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Stephan Jennewein, Mondher Besbes, N Schilder, S. d. Jenkins, Christophe Sauvan, et al.. Coherent Scattering of Near-Resonant Light by a Dense Microscopic Cold Atomic Cloud. Physical Review Letters, American Physical Society, 2016, 116 (23), pp.233601. ⟨10.1103/PhysRevLett.116.233601⟩. ⟨hal-01643262⟩

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