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arXiv:1802.03563 · Physical Review A

Coherent scattering of near-resonant light by a dense, microscopic cloud of cold two-level atoms: Experiment versus theory

Stephan Jennewein, Ludovic Brossard, Yvan R. P. Sortais, Antoine Browaeys, Patrick Cheinet, Jacques Robert, P. Pillet

Published May 15, 2018• 79 citations
arXivHTMLPDF

Abstract

We measure the coherent scattering of low-intensity, near-resonant light by a cloud of laser-cooled two-level rubidium atoms with a size comparable to the wavelength of light. We isolate a two-level atomic structure by applying a 300-G magnetic field. We measure both the temporal and the steady-state coherent optical response of the cloud for various detunings of the laser and for atom numbers ranging from 5 to 100. We compare our results to a microscopic coupled-dipole model and to a multimode, paraxial Maxwell-Bloch model. In the low-intensity regime, both models are in excellent agreement, thus validating the Maxwell-Bloch model. Comparing to the data, the models are found in very good agreement for relatively low densities ($n/{k}^{3}\ensuremath{\lesssim}0.1$), while significant deviations start to occur at higher density. This disagreement indicates that light scattering in dense, cold atomic ensembles is still not quantitatively understood, even in pristine experimental conditions.

DOI
10.1103/physreva.97.053816

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We measure the coherent scattering of low-intensity, near-resonant light by a cloud of laser-cooled two-level rubidium atoms with a size comparable to the wavelength of light. We isolate a two-level atomic structure by applying a 300-G magnetic field. We measure both the temporal and the steady-state coherent optical response of the cloud for various detunings of the laser and for atom numbers ranging from 5 to 100. We compare our results to a microscopic coupled-dipole model and to a multimode, paraxial Maxwell-Bloch model. In the low-intensity regime, both models are in excellent agreement, thus validating the Maxwell-Bloch model. Comparing to the data, the models are found in very good agreement for relatively low densities (n/k3\ensuremath≲0.1n/{k}^{3}\ensuremath{\lesssim}0.1n/k3\ensuremath≲0.1), while significant deviations start to occur at higher density. This disagreement indicates that light scattering in dense, cold atomic ensembles is still not quantitatively understood, even in pristine experimental conditions.
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 study the emergence of a collective optical response of a cold and dense 87Rb^{87}\mathrm{Rb}87Rb atomic cloud to a near-resonant low-intensity light when the atom number is gradually increased. Experimental observations are compared with microscopic stochastic simulations of recurrent scattering processes between the atoms that incorporate the atomic multilevel structure and the optical measurement setup. We analyze the optical response of an inhomogeneously broadened gas and find that the experimental observations of the resonance line shifts and the total collected scattered light intensity in cold atom clouds substantially deviate from those of thermal atomic ensembles, indicating strong light-induced resonant dipole-dipole interactions between the atoms. At high densities, the simulations also predict a significantly slower decay of light-induced excitations in cold than in thermal atom clouds. The role of dipole-dipole interactions is discussed in terms of resonant coupling examples and the collective radiative excitation eigenmodes of the system.
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 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.
Starting from a microscopic theory for atomic scatterers, we describe the scattering of light by a single atom and study the coherent propagation of light in a cold atomic cloud in the presence of a magnetic field B\mathbf{B}B in the mesoscopic regime. Nonpertubative expressions in BBB are given for the magneto-optical effects and optical anisotropy. We then consider the multiple-scattering regime and address the fate of the coherent-backscattering (CBS) effect. We show that, for atoms with nonzero spin in their ground state, the CBS interference contrast can be increased compared to its value when B=0B=0B=0, a result at variance with classical samples. We validate our theoretical results by a quantitative comparison with experimental data.
When a quasiresonant laser beam illuminates an optically thick cloud of laser-cooled rubidium atoms, the average diffuse intensity reflected off the sample is enhanced in a narrow angular range around the direction of exact backscattering. This phenomenon is known as coherent backscattering (CBS). By detuning the laser from resonance, we are able to modify the light scattering mean-free path inside the sample and we record accordingly the variations of the CBS cone shape. We then compare the experimental data with theoretical calculations and Monte Carlo simulations including the effect of the light polarization and of the internal structure of the atoms. We confirm that the internal structure strongly affects the enhancement factor of the cone and we show that the unusual shape of the atomic medium---approximately a spherically-symmetric, Gaussian density profile---strongly affects the width and shape of the cone.