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Journal of Physics A Mathematical and General

Multiple scattering of light by atoms with internal degeneracy

Cord Axel Müller, Christian Miniatura

Published Nov 13, 2002• 51 citations
Publisher

Abstract

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.

DOI
10.1088/0305-4470/35/47/314

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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.
The interference contrast observed in coherent backscattering by cold atoms is drastically reduced with respect to classical disordered media. We study the impact of the degeneracy of the resonant atomic dipole transition on multiple scattering of polarised photons. An analytical treatment allows to derive the diffusion coefficient and depolarisation times for the average light intensity, and dephasing times for the weak localisation corrections. The calculated CBS signals reproduce the experimental results.
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.
Recent experimental results show that the interference contrast observed in coherent backscattering (CBS) of light by cold atoms is drastically reduced with respect to classical disordered media. In the present theoretical contribution, we study the impact of the degeneracy of the atomic dipole transition on weak localization of light. The nonscalar components of the atomic scattering operator are characteristics of the internal structure, and strongly modify the interference properties of multiple light scattering. A systematic analysis in terms of irreducible tensors permits to calculate exact analytical expressions for the single and double scattering contributions to the CBS signal for arbitrarily degenerate atomic dipole transitions. Furthermore, we sum up the series of ladder and crossed diagrams that describe the average scattered light intensity and the weak localization corrections, respectively. We find that the degeneracy of the atomic transition has negligible impact on the average light amplitude, small impact on the average intensity, but decisive impact on the interference corrections. The internal degrees of freedom very effectively reduce the interference of weak localization and, therefore, the CBS signal for any degenerate atomic dipole transition.
Recent experimental results show that the interference contrast observed in coherent backscattering (CBS) of light by cold atoms is drastically reduced with respect to classical disordered media. In the present theoretical contribution, we study the impact of the degeneracy of the atomic dipole transition on weak localisation of light. The non-scalar components of the atomic scattering operator are characteristic of the internal structure, and strongly modify the interference properties of multiple light scattering. A systematic analysis in terms of irreducible tensors permits to calculate exact analytical expressions for the single and double scattering contributions to the CBS signal for arbitrarily degenerate atomic dipole transitions. Furthermore, we sum up the series of ladder and crossed diagrams that describe the average scattered light intensity and the weak localisation corrections, respectively. We find that the degeneracy of the atomic transition has negligeable impact on the average light amplitude, small impact on the average intensity, but decisive impact on the interference corrections. The internal degrees of freedom very effectively reduce the interference leading to weak localisation and, therefore, the CBS signal for any degenerate atomic dipole transition.
We outline the nonperturbative theory of multiple scattering of resonant, intense laser light off a dilute cloud of cold atoms. A combination of master equation and diagrammatic techniques allows a quantitative description of nonlinear diffusive transport as well as of coherent backscattering of the injected electromagnetic field, notwithstanding the exponential growth of Hilbert space with the number of atomic scatterers. As an exemplary application, we monitor the laser light's intensity profile within the medium, the spectrum of the backscattered light, and the coherent backscattering peak's height with increasing pump intensity. Our theory establishes a general, microscopic, scalable approach to nonlinear transport phenomena in complex quantum materials.