Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1302.3322 · Journal of Plasma Physics

Fluid description of the cooperative scattering of light by spherical atomic clouds

N. Piovella, Romain Bachelard, Ph. W. Courteille

Published Mar 14, 2013• 2 citations
arXivHTMLPDF

Abstract

Abstract When a cold atomic gas is illuminated by a quasi-resonant laser beam, light-induced dipole–dipole correlations make the scattering of light a cooperative process. Once a fluid description is adopted for the atoms, many scattering properties are captured by the definition of a complex refractive index. The solution of the scattering problem is here presented for spherical atomic clouds of arbitrary density profiles, such as parabolic densities characteristic of ultra-cold clouds. A new solution for clouds with infinite boundaries is derived, which is particularly useful for the Gaussian densities of thermal atomic clouds. The presence of Mie resonances, a signature of the cloud acting as a cavity for the light, is discussed. These resonances leave their fingerprint in various observables such as the scattered intensity or in the radiation pressure force, and can be observed by tuning the frequency of the incident laser field or the atom number.

DOI
10.1017/s0022377813000275

Related papers

Mie resonances in inhomogeneous atomic clouds

Romain Bachelard, Ph. W. Courteille, Robin Kaiser +1 more

Despite the quantum nature of the process, collective scattering by dense cold samples of two-level atoms can be interpreted classically describing the sample as a macroscopic object with a complex refractive index. We demonstrate that Mie resonances can be easily observable in the cooperative scattering by tuning the frequency of the incident laser field or the atomic number. The solution of the scattering problem is obtained for spherical atomic clouds who have the parabolic density characteristic of BECs, and the cooperative radiation pressure force calculated exhibits resonances in the cloud displacement for dense clouds. Reminescent to uniform clouds which show a complex structure of narrow peaks, these densities show resonances, yet under the form of quite regular and contrasted oscillations.

•Sep 6, 2011•0 citations

Resonances in Mie scattering by an inhomogeneous atomic cloud

Romain Bachelard, Ph. W. Courteille, Robin Kaiser +1 more

Despite the quantum nature of the process, collective scattering by dense cold samples of two-level atoms can be interpreted classically describing the sample as a macroscopic object with a complex refractive index. We demonstrate that resonances in Mie theory can be easily observable in the cooperative scattering by tuning the frequency of the incident laser field or the atomic number. The solution of the scattering problem is obtained for spherical atomic clouds who have the parabolic density characteristic of BECs, and the cooperative radiation pressure force calculated exhibits resonances in the cloud displacement for dense clouds. At odds from uniform clouds which show a complex structure including narrow peaks, these densities show resonances, yet only under the form of quite regular and contrasted oscillations.

arXiv:1109.1243•Europhysics Letters (EPL)•Jan 1, 2012•34 citations

Observation of cooperative Mie scattering from an ultracold atomic cloud

H. Bender, Christian Stehle, Sebastian Slama +4 more

Scattering of light at a distribution of scatterers is an intrinsically cooperative process, which means that the scattering rate and the angular distribution of the scattered light are essentially governed by bulk properties of the distribution, such as its size, shape, and density, although local disorder and density fluctuations may have an important impact on the cooperativity. Via measurements of the radiation pressure force exerted by a far-detuned laser beam on a very small and dense cloud of ultracold atoms, we are able to identify the respective roles of superradiant acceleration of the scattering rate and of Mie scattering in the cooperative process. They lead, respectively, to a suppression or an enhancement of the radiation pressure force. We observe a maximum in the radiation pressure force as a function of the phase shift induced in the incident laser beam by the cloud's refractive index. The maximum marks the borderline of the validity of the Rayleigh-Debye-Gans approximation from a regime, where Mie scattering is more complex. Our observations thus help to clarify the intricate relationship between Rayleigh scattering of light at a coarse-grained ensemble of individual scatterers and Mie scattering at the bulk density distribution.

arXiv:1004.5096•Physical Review A•Jul 26, 2010•39 citations

Cooperativity in light scattering by cold atoms

Tom Bienaimé, Romain Bachelard, N. Piovella +1 more

Abstract A cloud of cold N two‐level atoms driven by a resonant laser beam shows cooperative effects both in the scattered radiation field and in the radiation pressure force acting on the cloud center‐of‐mass. The induced dipoles synchronize and the scattered light presents superradiant and/or subradiant features. We present a quantum description of the process in terms of a master equation for the atomic density matrix in the scalar, Born‐Markov approximations, reduced to the single‐excitation limit. From a perturbative approach for weak incident field, we derive from the master equation the effective Hamiltonian, valid in the linear regime. We discuss the validity of the driven timed Dicke ansatz and of a partial wave expansion for different optical thicknesses and we give analytical expressions for the scattered intensity and the radiation pressure force on the center of mass. We also derive an expression for collective suppression of the atomic excitation and the scattered light by these correlated dipoles.

arXiv:1204.5598•Fortschritte der Physik•Jun 18, 2012•104 citations

Coherent Scattering of Near-Resonant Light by a Dense Microscopic Cold Atomic Cloud

Stephan Jennewein, Mondher Besbes, Nick J. Schilder +6 more

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.

arXiv:1510.08041•Physical Review Letters•Jun 8, 2016•131 citations

Collective resonance fluorescence in small and dense atom clouds: Comparison between theory and experiment

S. D. Jenkins, Janne Ruostekoski, Juha Javanainen +5 more

We study the emergence of a collective optical response of a cold and dense $^{87}\mathrm{Rb}$ 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.

arXiv:1606.02757•Physical Review A•Aug 24, 2016•86 citations
Abstract When a cold atomic gas is illuminated by a quasi-resonant laser beam, light-induced dipole–dipole correlations make the scattering of light a cooperative process. Once a fluid description is adopted for the atoms, many scattering properties are captured by the definition of a complex refractive index. The solution of the scattering problem is here presented for spherical atomic clouds of arbitrary density profiles, such as parabolic densities characteristic of ultra-cold clouds. A new solution for clouds with infinite boundaries is derived, which is particularly useful for the Gaussian densities of thermal atomic clouds. The presence of Mie resonances, a signature of the cloud acting as a cavity for the light, is discussed. These resonances leave their fingerprint in various observables such as the scattered intensity or in the radiation pressure force, and can be observed by tuning the frequency of the incident laser field or the atom number.
Despite the quantum nature of the process, collective scattering by dense cold samples of two-level atoms can be interpreted classically describing the sample as a macroscopic object with a complex refractive index. We demonstrate that Mie resonances can be easily observable in the cooperative scattering by tuning the frequency of the incident laser field or the atomic number. The solution of the scattering problem is obtained for spherical atomic clouds who have the parabolic density characteristic of BECs, and the cooperative radiation pressure force calculated exhibits resonances in the cloud displacement for dense clouds. Reminescent to uniform clouds which show a complex structure of narrow peaks, these densities show resonances, yet under the form of quite regular and contrasted oscillations.
Despite the quantum nature of the process, collective scattering by dense cold samples of two-level atoms can be interpreted classically describing the sample as a macroscopic object with a complex refractive index. We demonstrate that resonances in Mie theory can be easily observable in the cooperative scattering by tuning the frequency of the incident laser field or the atomic number. The solution of the scattering problem is obtained for spherical atomic clouds who have the parabolic density characteristic of BECs, and the cooperative radiation pressure force calculated exhibits resonances in the cloud displacement for dense clouds. At odds from uniform clouds which show a complex structure including narrow peaks, these densities show resonances, yet only under the form of quite regular and contrasted oscillations.
Scattering of light at a distribution of scatterers is an intrinsically cooperative process, which means that the scattering rate and the angular distribution of the scattered light are essentially governed by bulk properties of the distribution, such as its size, shape, and density, although local disorder and density fluctuations may have an important impact on the cooperativity. Via measurements of the radiation pressure force exerted by a far-detuned laser beam on a very small and dense cloud of ultracold atoms, we are able to identify the respective roles of superradiant acceleration of the scattering rate and of Mie scattering in the cooperative process. They lead, respectively, to a suppression or an enhancement of the radiation pressure force. We observe a maximum in the radiation pressure force as a function of the phase shift induced in the incident laser beam by the cloud's refractive index. The maximum marks the borderline of the validity of the Rayleigh-Debye-Gans approximation from a regime, where Mie scattering is more complex. Our observations thus help to clarify the intricate relationship between Rayleigh scattering of light at a coarse-grained ensemble of individual scatterers and Mie scattering at the bulk density distribution.
Abstract A cloud of cold N two‐level atoms driven by a resonant laser beam shows cooperative effects both in the scattered radiation field and in the radiation pressure force acting on the cloud center‐of‐mass. The induced dipoles synchronize and the scattered light presents superradiant and/or subradiant features. We present a quantum description of the process in terms of a master equation for the atomic density matrix in the scalar, Born‐Markov approximations, reduced to the single‐excitation limit. From a perturbative approach for weak incident field, we derive from the master equation the effective Hamiltonian, valid in the linear regime. We discuss the validity of the driven timed Dicke ansatz and of a partial wave expansion for different optical thicknesses and we give analytical expressions for the scattered intensity and the radiation pressure force on the center of mass. We also derive an expression for collective suppression of the atomic excitation and the scattered light by these correlated dipoles.
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.