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. DOI: 10.1103/PhysRevLett.116.233601 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 inhomogeneously 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 inhomogeneous 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 o...
We study two-dimensional hexagonal photonic lattices of silicon Mie resonators with a topological optical band structure in the visible spectral range. We use 30 keV electrons focused to nanoscale spots to map the local optical density of states in topological photonic lattices with deeply subwavelength resolution. By slightly shrinking or expanding the unit cell, we form hexagonal superstructures and observe the opening of a bandgap and a splitting of the double-degenerate Dirac cones, which correspond to topologically trivial and non-trivial phases. Optical transmission spectroscopy shows evidence of topological edge states at the domain walls between topological and trivial lattices.
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