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arXiv:1607.01157 · Physical Review A

Collective effects in the radiation pressure force

Romain Bachelard, N. Piovella, William Guerin, Robin Kaiser

Published Sep 20, 2016• 13 citations
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Abstract

We discuss the role of diffuse, Mie, and cooperative scattering on the radiation pressure force acting on the center of mass of a cloud of cold atoms. Even though a mean-field ansatz (the ``timed Dicke state''), previously derived from a cooperative scattering approach, has been shown to agree satisfactorily with experiments, diffuse scattering also describes very well most features of the radiation pressure force on large atomic clouds. We compare in detail an incoherent, random walk model for photons and a diffraction approach to the more complete description based on coherently coupled dipoles. We show that a cooperative scattering approach, although it provides a quite complete description of the scattering process, is not necessary to explain the previous experiments on the radiation pressure force.

DOI
10.1103/physreva.94.033836

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We discuss the role of diffuse, Mie, and cooperative scattering on the radiation pressure force acting on the center of mass of a cloud of cold atoms. Even though a mean-field ansatz (the ``timed Dicke state''), previously derived from a cooperative scattering approach, has been shown to agree satisfactorily with experiments, diffuse scattering also describes very well most features of the radiation pressure force on large atomic clouds. We compare in detail an incoherent, random walk model for photons and a diffraction approach to the more complete description based on coherently coupled dipoles. We show that a cooperative scattering approach, although it provides a quite complete description of the scattering process, is not necessary to explain the previous experiments on the radiation pressure force.
Atomic clouds prepared in ``timed Dicke'' states, i.e. states where the phase of the oscillating atomic dipole moments linearly varies along one direction of space, are efficient sources of superradiant light emission [Scully et al., Phys. Rev. Lett. 96, 010501 (2006)]. Here, we show that, in contrast to previous assertions, timed Dicke states are not the states automatically generated by incident laser light. In reality, the atoms act back on the driving field because of the finite refraction of the cloud. This leads to nonuniform phase shifts, which, at higher optical densities, dramatically alter the cooperative scattering properties, as we show by explicit calculation of macroscopic observables, such as the radiation pressure force.
In this paper, we study cooperative scattering of low intensity light by a cloud of N two-level systems. We include the incident laser field driving these two-level systems and compute the radiation pressure force on the center of mass of the cloud. This signature is of particular interest for experiments with laser cooled atoms. Including the complex coupling between dipoles in a scalar model for dilute clouds of two-level systems, we obtain expression for cooperative scattering forces taking into account the collective Lamb shift. We also derive the expression of the radiation pressure force on a large cloud of two-level systems from an heuristic approach and show that at lowest driving intensities this force is identical for a product and an entangled state.
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 investigate the modifications of the frequency-comb-induced radiation pressure force on cold 87^{87}87Rb atoms that are induced by the collective effects. Collective effects include both coherent and incoherent contributions and depend on the optical thickness of the atomic cloud. We observe reduction and broadening of the comb-induced force when the cloud's optical thickness increases, and compare the measured results with predictions of a coherent model based on the timed Dicke state approach and an incoherent scattering model based on the shadow effect explained by Beer-Lambert law. Both models describe the experimental results well, indicating that an incoherent scattering approach is sufficient to explain the observed modifications of the comb-induced force even for larger optical thicknesses. The results support the analogy between the frequency comb and continuous-wave laser-atom interaction and thus pave the way toward novel frequency comb applications in laser cooling, quantum communication, and light-atom interfaces based on structured and disordered atomic systems.
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.