Cooperativity in light scattering by cold atoms

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.

Observation of Single-Photon Superradiance and the Cooperative Lamb Shift in an Extended Sample of Cold Atoms

“…Our two most important results are (a) direct time domain measurements of superradiant emission from a spatially extended and low density cloud of cold 87 Rb atoms, and (b) the corresponding cooperative Lamb shift of the atomic resonance studied. These quantities are each found to scale approximately linearly with the number of atoms, characteristic of a cooperative process in such cold atom systems [30]. The results are also found to be in good qualitative agreement with a vector light scattering simulation of the processes [13,14], and to correspond closely with predictions of a scalar coupled dipole model [31,32].…”

Cooperatively enhanced dipole forces from artificial atoms in trapped nanodiamonds

“…Remarkably this is overcome to a great extent by cooperative effects. While the impact of cooperativity on different aspects of quantum optics has been extensively studied 9 , its impact on optical forces has been theoretically predicted 10,11 but experimental evidence remains limited to light scattering 12 and dissipative forces 13 . We show in our experiment that, due to cooperative effects, the dipole force is enhanced by more than one order of magnitude compared with the force that would be obtained considering independent artificial atoms.…”

Interplay between radiation pressure force and scattered light intensity in the cooperative scattering by cold atoms

“…This factor of two corresponds to the well-known 'extinction paradox' [25,26] for which the extinction cross-section is twice as large as the one predicted by geometrical optics due to the diffraction contribution. The residual deviations from the factor of 2 between the scattering and geometrical crosssections might be associated with a still moderate size of our sample [27], or to dipole blockade effects [28,29] around 2σ geo (σ geo = L x L y for our square geometry), which is damped for increasing sizes of the sphere [30,31]. When b 0 1 the scattering cross-section can be written as σ sca = (L x L y )b 0 = N σ 0 , where σ 0 = λ 2 /π is the resonant scattering cross-section for a single atom in the scalar wave description (it differs from the well-known cross-section for vectorial light σ 0 = 3λ 2 /(2π)).…”