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:cond-mat/0206298

Phase coherence times in the multiple scattering of photons by cold atoms

Éric Akkermans, Christian Miniatura, Cord Axel Müller

Published Jun 16, 2002• 1 citation
arXivHTMLPDF

Abstract

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 $τ_ϕ$ 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.

DOI
10.48550/arxiv.cond-mat/0206298

Related papers

Weak localization of light by cold atoms: The impact of quantum internal structure

Cord Axel Müller, Thibaut Jonckheere, Christian Miniatura +1 more

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.

arXiv:quant-ph/0107030•Physical Review A•Oct 2, 2001•62 citations

Weak localisation of light by atoms with quantum internal structure

Cord Axel Müller, Christian Miniatura

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.

arXiv:quant-ph/0304048•Apr 6, 2003•0 citations

Multiple scattering of photons by atomic hyperfine multiplets

Cord Axel Müller, Christian Miniatura, David Wilkowski +2 more

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.

arXiv:physics/0504039•Physical Review A•Nov 10, 2005•13 citations

Multiple scattering of photons by a cold atomic gas

Éric Akkermans, Ohad Assaf

We show that photons propagating in a mesoscopic gas of atoms acquire a correlation stronger than the value predicted by Rayleigh law. This enhanced correlation results from cross-terms based on the effects of spatial disorder and atomic quantum internal degrees of freedom. The great sensitivity of these cross-terms upon dephasing, such as a Zeeman splitting induced by a magnetic field, opens the possibility of a new kind of high precision spectroscopy.

Journal of Modern Optics•Nov 10, 2007•0 citations

Multiple scattering of light by atoms with internal degeneracy

Cord Axel Müller, Christian Miniatura

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.

Journal of Physics A Mathematical and General•Nov 13, 2002•51 citations

Localisation faible de la lumière dans un gaz d'atomes froids : rétrodiffusion cohérente et structure quantique interne

Cord Axel Müller

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.

•Jan 1, 2001•1 citation
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.
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.
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.
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.