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arXiv:physics/0504039 · Physical Review A

Multiple scattering of photons by atomic hyperfine multiplets

Cord Axel Müller, Christian Miniatura, David Wilkowski, Robin Kaiser, Dominique Delande

Published Nov 10, 2005• 13 citations
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Abstract

Mesoscopic interference effects in multiple scattering of photons depend crucially on the internal structure of the scatterers. In the present paper, we develop the analytical theory of multiple photon scattering by cold atoms with arbitrary internal hyperfine multiplets. For a specific application, we calculate the enhancement factor of elastic coherent backscattering as a function of detuning from an entire hyperfine multiplet of neighboring resonances that cannot be considered isolated. Our theory permits one to understand why atoms behave differently from classical Rayleigh point-dipole scatterers, and how the classical description is recovered for larger but still microscopic objects like molecules or clusters.

DOI
10.1103/physreva.72.053405

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Mesoscopic interference effects in multiple scattering of photons depend crucially on the internal structure of the scatterers. In the present paper, we develop the analytical theory of multiple photon scattering by cold atoms with arbitrary internal hyperfine multiplets. For a specific application, we calculate the enhancement factor of elastic coherent backscattering as a function of detuning from an entire hyperfine multiplet of neighboring resonances that cannot be considered isolated. Our theory permits one to understand why atoms behave differently from classical Rayleigh point-dipole scatterers, and how the classical description is recovered for larger but still microscopic objects like molecules or clusters.
An analytical microscopic theory for the resonant multiple scattering of light by cold atoms with arbitrary internal degeneracy is presented. It permits us to calculate the average amplitude and the average intensity for one-photon states of the full transverse electromagnetic field in a dilute medium of unpolarized atoms. Special emphasis is laid upon an analysis in terms of irreducible representations of the rotation group. It allows us to sum explicitly the ladder and maximally crossed diagrams, giving the average intensity in the Boltzmann approximation and the interference corrections responsible for weak localization and coherent backscattering. The exact decomposition into field modes shows that the atomic internal degeneracy contributes to th ed epolarization of the average intensity and suppresses the interference corrections. Static as well as dynamic quantities such as the transport velocity, diffusion constants and relaxation times for all field modes and all atomic transitions are derived.
Since the work of Anderson on localization, interference effects for the propagation of a wave in the presence of disorder have been extensively studied, as exemplified in coherent backscattering (CBS) of light. In the multiple scattering of light by a disordered sample of thermal atoms, interference effects are usually washed out by the fast atomic motion. This is no longer true for cold atoms where CBS has recently been observed. However, the internal structure of the atoms strongly influences the interference properties. In this paper, we consider light scattering by an atomic dipole transition with arbitrary degeneracy and study its impact on coherent backscattering. We show that the interference contrast is strongly reduced. Assuming a uniform statistical distribution over internal degrees of freedom, we compute analytically the single- and double-scattering contributions to the intensity in the weak-localization regime. The so-called ladder and crossed diagrams are generalized to the case of atoms and permit to calculate enhancement factors and backscattering intensity profiles for polarized light and any closed atomic dipole transition.
We present an analysis of the dephasing present in the multiple scattering of photons by atoms with a quantum internal structure. The corresponding phase coherence times τϕτ_ϕτϕ​ are obtained as a function of the Zeeman degeneracy of the atomic dipole transition and the polarization state of the photons. These results allow for an explanation of the recent experiments on coherent backscattering of photons from a gas of cold rubidium atoms where the height of the backscattering cone depends on the atomic internal degrees of freedom coupled to the polarization of the photons. Some consequences of these results are presented, and analogies with the case of electronic systems are highlighted.
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.
We study the influence of cooperative effects such as superradiance and subradiance on the scattering properties of dilute atomic gases. We show that cooperative effects lead to an effective potential between two atoms that decays as 1∕r1∕r1∕r. In the case of superradiance, this potential is attractive for close enough atoms and can be interpreted as a coherent mesoscopic effect. We consider a model of multiple scattering of a photon among superradiant pairs and calculate the elastic mean free path and the group velocity. We study first the case of a scalar wave which allows us to obtain and to understand basic features of cooperative effects and multiple scattering. We then turn to the general problem of a vector wave. In both cases, we obtain qualitatively similar results and derive, for the case of a scalar wave, analytic expressions for the elastic mean free path and for the group velocity for an arbitrary detuning (near resonance).
We study the angular correlation function of speckle patterns that result from multiple scattering of photons by cold atomic clouds. We show that this correlation function becomes larger than the value given by Rayleigh law for classical scatterers. These large intensity fluctuations constitute a new mesoscopic effect specific to atom-photon interactions, that could not be observed in other systems such as weakly disordered metals. We provide a complete description of this behavior and expressions that allow for a quantitative comparison with experiments.