We study the emergence of collective scattering in the presence of dipole-dipole interactions when we illuminate a cold cloud of rubidium atoms with a near-resonant and weak intensity laser. The size of the atomic sample is comparable to the wavelength of light. When we gradually increase the number of atoms from 1 to ∼450, we observe a broadening of the line, a small redshift and, consistently with these, a strong suppression of the scattered light with respect to the noninteracting atom case. We compare our data to numerical simulations of the optical response, which include the internal level structure of the atoms. DOI: 10.1103/PhysRevLett.113.133602 PACS numbers: 42.50.Ct, 03.65.Nk, 32.80.Qk, 42.50.Nn When resonant emitters, such as atoms, molecules, quantum dots, or metamaterial circuits, with a transition at a wavelength λ, are confined inside a volume smaller than λ 3 , they are coupled via strong dipole-dipole interactions. In this situation, the response of the ensemble to near-resonant light is collective and originates from the excitation of collective eigenstates of the system, such as super-and subradiant modes [1][2][3]. Dipole-dipole interactions affect the response of the system and the collective scattering of near-resonant light differs from the case of an assembly of noninteracting emitters [4]. It has even been predicted to be suppressed for a dense gas of cold twolevel atoms [5].Following the recent measurement of the collective Lamb shift [6] in a Fe layer [7], in a hot thermal vapor [8], and in arrays of trapped ions [9], it was pointed out [10] that the collective response of interacting emitters is different between ensembles exhibiting inhomogeneous broadening, such as solid state systems or thermal vapors, and those free of it, such as cold-atom clouds. In particular, inhomogeneous broadening suppresses the correlations induced by the interactions between dipoles, leading to the textbook theory of the optical response of continuous media [10,11]. In the absence of broadening, however, this theory fails and should be revisited to include the lightinduced correlations [12][13][14][15][16][17][18][19]. Several recent experiments aiming at studying collective scattering with identical emitters used large and optically thick ensembles of cold atoms [20][21][22][23]. However, the case of a cold-atom ensemble with a size comparable to the optical wavelength has not been studied experimentally, nor has the transition between the well-understood case of scattering by an individual atom [24] to collective scattering. In particular, the suppression of light scattering when the number of atoms increases in a regime of collective scattering has never been directly observed.Here, we study-both experimentally and theoreticallythe emergence of collective effects in the optical response of a cold-atom sample due to dipole-dipole interactions, as we gradually increase the number of atoms. To do so, we send low-intensity near-resonant laser light onto a cloud containing from 1 to ∼450 cold 87 Rb ato...

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...