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arXiv:1706.01235 · Physical Review A

Homogenization of an ensemble of interacting resonant scatterers

Nick J. Schilder, Christophe Sauvan, Yvan R. P. Sortais, Antoine Browaeys, Jean‐Jacques Greffet

Published Jul 13, 2017• 21 citations
arXivHTMLPDF

Abstract

We study theoretically the concept of homogenization in optics using an ensemble of randomly distributed resonant stationary atoms with density $\ensuremath{\rho}$. The ensemble is dense enough for the usual condition for homogenization, viz. $\ensuremath{\rho}{\ensuremath{\lambda}}^{3}\ensuremath{\gg}1$, to be reached. Introducing the coherent and incoherent scattered powers, we define two criteria to define the homogenization regime. We find that when the excitation field is tuned in a broad frequency range around the resonance, neither of the criteria for homogenization is fulfilled, meaning that the condition $\ensuremath{\rho}{\ensuremath{\lambda}}^{3}\ensuremath{\gg}1$ is not sufficient to characterize the homogenized regime around the atomic resonance. We interpret these results as a consequence of the light-induced dipole-dipole interactions between the atoms, which implies a description of scattering in terms of collective modes rather than as a sequence of individual scattering events. Finally, we show that, although homogenization can never be reached for a dense ensemble of randomly positioned laser-cooled atoms around resonance, it becomes possible if one introduces spatial correlations in the positions of the atoms or nonradiative losses, such as would be the case for organic molecules or quantum dots coupled to a phonon bath.

DOI
10.1103/physreva.96.013825

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We study theoretically the concept of homogenization in optics using an ensemble of randomly distributed resonant stationary atoms with density \ensuremathρ\ensuremath{\rho}\ensuremathρ. The ensemble is dense enough for the usual condition for homogenization, viz. \ensuremathρ\ensuremathλ3\ensuremath≫1\ensuremath{\rho}{\ensuremath{\lambda}}^{3}\ensuremath{\gg}1\ensuremathρ\ensuremathλ3\ensuremath≫1, to be reached. Introducing the coherent and incoherent scattered powers, we define two criteria to define the homogenization regime. We find that when the excitation field is tuned in a broad frequency range around the resonance, neither of the criteria for homogenization is fulfilled, meaning that the condition \ensuremathρ\ensuremathλ3\ensuremath≫1\ensuremath{\rho}{\ensuremath{\lambda}}^{3}\ensuremath{\gg}1\ensuremathρ\ensuremathλ3\ensuremath≫1 is not sufficient to characterize the homogenized regime around the atomic resonance. We interpret these results as a consequence of the light-induced dipole-dipole interactions between the atoms, which implies a description of scattering in terms of collective modes rather than as a sequence of individual scattering events. Finally, we show that, although homogenization can never be reached for a dense ensemble of randomly positioned laser-cooled atoms around resonance, it becomes possible if one introduces spatial correlations in the positions of the atoms or nonradiative losses, such as would be the case for organic molecules or quantum dots coupled to a phonon bath.
We study theoretically the scattering of light by an ensemble of N resonant atoms in a subwavelength volume. We consider the low intensity regime so that each atom responds linearly to the field. While N noninteracting atoms would scatter N^{2} more than a single atom, we find that N interacting atoms scatter less than a single atom near resonance. In addition, the scattered power presents strong fluctuations, either from one realization to another or when varying the excitation frequency. We analyze this counterintuitive behavior in terms of collective modes resulting from the light-induced dipole-dipole interactions. We find that for small samples and sufficiently large atom number, their properties are governed only by their volume.
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.
We analyze resonant light scattering by a cloud of cold atoms with randomly distributed positions in a regime where resonant dipole-dipole interactions between scatterers cannot be neglected. Using a microscopic approach we calculate numerically the collective eigenmodes of the cloud for many realizations. It is found that there always exists a small number of polaritonic modes. Using a macroscopic approach, we show that the atomic cloud is equivalent to a homogeneous particle with an effective permittivity and that there is a one-to-one correspondence between the microscopic polaritonic modes and the modes of the homogeneous particle.
The main objective of this research is to study a particular case of light-matter interaction: the scattering of light in dense atomic samples.The regime of high atomic densities is represented by samples where the distance between neighboring atoms is on the order of the wavelength associated with the atomic transition.In this regime, short-range atomic interactions cannot be neglected, and in these systems, we expect to observe significant modifications in collective effects such as subradiance or superradiance.Overall, the propagation of light through this type of system is not well-known to the scientific community, and the existing models work to describe very specific situations.To pave the way for achieving our overall goal, this work proposes an experimental setup to obtain a dense cloud of 88 Sr, which is the chemical species we work with in our laboratory.For this purpose, atoms previously trapped using a Magneto-Optical Trap are transferred to a Crossed Optical Dipole Trap.During the optimization and characterization of the optical trap, problems were encountered in producing an image with quantitative information of the atomic ensemble and in transferring a large number of atoms in a very small trapping volume.These problems were resolved with the implementation of a Phase Contrast Imaging system and the implementation of an Optical Molasses as an additional cooling step.Under these conditions, we obtained a cloud that can be suitable for conducting studies on collective effects, transitioning from the dilute to the dense regime.The initial experiments, once our atomic ensemble was prepared, involve measuring the coherent transmission of a low-intensity beam through the cloud.For this purpose, incident light near the resonance of a dipolar transition of the type J = 0 ↔ J = 1 of 88 Sr is used, interacting with a homogeneous region of the sample.Simulations of this type of process can be performed using the Coupled Dipole Model, which describes the overall response of light scattering by the sample considering dipole-dipole interactions mediated by light.With this work, we aim to advance the understanding of density effects by comparing the coherent optical response of the dense cloud with the theory based on the Coupled Dipole Model.
We analyze the scattering of light from dipolar emitters whose disordered positions exhibit correlations induced by static, long-range dipole-dipole interactions. The quantum-mechanical position correlations are calculated for zero-temperature bosonic atoms or molecules using variational and diffusion quantum Monte Carlo methods. For stationary atoms in dense ensembles in the limit of low light intensity, the simulations yield solutions for the optical responses to all orders of position correlation functions that involve electronic ground and excited states. We calculate how coherent and incoherent scattering, collective linewidths, line shifts, and eigenmodes, and disorder-induced excitation localization are influenced by the static interactions and the density. We find that dominantly repulsive static interactions in strongly confined oblate and prolate traps introduce short-range ordering among the dipoles, which curtails large fluctuations in the light-mediated resonant dipole-dipole interactions. This typically results in an increase in coherent reflection and optical depth, accompanied by reduced incoherent scattering. The presence of static dipolar interactions permits the highly selective excitation of subradiant eigenmodes in dense clouds. This effect becomes even more pronounced in a prolate trap, where the resonances narrow below the natural linewidth. When the static dipolar interactions affect the optical transition frequencies, the ensemble exhibits inhomogeneous broadening due to the nonuniformly experienced static dipolar interactions that suppress cooperative effects, but we argue that, e.g., for Dy atoms such inhomogeneous broadening is negligible. Published by the American Physical Society 2024
Cooperative scattering has been the subject of intense research in the last years. In this article, we discuss the concept of cooperative scattering from a broad perspective. We briefly review the various collective effects that occur when light interacts with an ensemble of atoms. We show that some effects that have been recently discussed in the context of ‘single-photon superradiance’, or cooperative scattering in the linear-optics regime, can also be explained by ‘standard optics’, i.e. using macroscopic quantities such as the susceptibility or the diffusion coefficient. We explain why some collective effects depend on the atomic density, and others on the optical depth. In particular, we show that, for a large and dilute atomic sample driven by a far-detuned laser, the decay of the fluorescence, which exhibits superradiant and subradiant dynamics, depends only on the on-resonance optical depth. We also discuss the link between concepts that are independently studied in the quantum-optics community and in the mesoscopic-physics community. We show that the coupled-dipole model predicts a departure from Ohm’s law for the diffuse light, that incoherent multiple scattering can induce a saturation of fluorescence and we also show the similarity between the weak-localization correction to the diffusion coefficient and the inaccuracy of Lorentz local field correction to the susceptibility.