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. 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...

Exact electrodynamics versus standard optics for a slab of cold dense gas

“…The general result was that at higher atom numbers (∼180) ab initio simulations analogous to the ones we have described here came closer to the experimental results than the predictions from optics. However, "[t]he remaining difference with the microscopic model shows that a quantitative understanding of the light-induced interactions even in a relatively simple situation is still a challenge" [8].…”

“…The theoretical result (63) was recently tested experimentally, albeit in a hot gas with moving atoms [11], and found to work quite well, apart from a shift between the theory and the observations proportional to the density of the gas. In a cold and dense trapped cloud of atoms an analogous expression was shown to fail [8], but in a very dilute gas analogous expressions, derived from the standard optics, are expected to provide qualitative estimates for the shift even for cold atoms [9].…”

“…In physical terms, in standard EDPM the problems with Beer's law can be attributed to etalon effects, reflections of light from the faces of the dielectric slab. When we deal with samples that have relevant features of the size of a wavelength like the slab [11], or that are of a size comparable to a wavelength [7,8], the usual approximations of optics such as slowly varying envelope approximation and paraxial approximation tend to break down, not to mention ray optics. One then has to solve the full Maxwell equations, an onerous requirement even numerically [8,[63][64][65].…”

“…The growing throughput of computers available to researchers is making such a plan practical. These methods, whether called classicalelectrodynamics simulations or coupled-dipole simulations, are now a routine theoretical tool [2,4,7,8,[14][15][16][17][18][19][20][21][22][23][24][25][26]. Closely related numerical techniques based on the analysis of the eigenstates of the coupled system of the light and the atoms [15,[27][28][29][30][31][32] or density matrices and quantum trajectories [33][34][35] are also widely used today.…”

“…This subject is obviously very old, but cold atomic samples afford an opportunity for experiments in unprecedented regimes and in unprecedented detail. Correspondingly, new experiments are emerging rapidly [1][2][3][4][5][6][7][8][9][10]. The measurements of the optical response have been dominated by trapped inhomogeneous atomic ensembles, but also those with atoms confined in a slab geometry are emerging in increasing numbers in both thermal vapor cells using a hot gas [11] and in the ultracold regime [12].…”