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

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Phase coherence in multiple scattering: weak and intense monochromatic light wave propagating in a cold strontium cloud

David Wilkowski, Yannick Bidel, T. Chanelière, Robin Kaiser, Bruce G. Klappauf, Christian Miniatura

Published Aug 1, 2005• 2 citations
Publisher

Abstract

For large bulk disordered media, light transport is generally successfully described by a diffusion process. This picture assumes that any interference is washed out under configuration average. However, it is now known that, under certain circumstances, some interference effects survive the disorder average and in turn lead to wave localizations effects. In this paper, we investigate coherence of a monochromatic laser light propagating in an optically thick sample of laser-cooled strontium atoms. For this purpose, we use the coherent backscattering effect as an interferometric tool. At low laser probe beam intensities, phase coherence is fully preserved and the interference contrast is maximal. At higher intensities, saturation effects start to set in and the interference contrast is reduced.

DOI
10.1117/12.621377

Related papers

Coherent Backscattering of Light by Cold Atoms

G. Labeyrie, F. De Tomasi, J.-C. Bernard +3 more

Light propagating in an optically thick sample experiences multiple scattering. It is now known that interferences alter this propagation, leading to an enhanced backscattering, a manifestation of weak localization of light in such diffuse samples. This phenomenon has been extensively studied with classical scatterers. In this Letter we report the first experimental evidence for coherent backscattering of light in a laser-cooled gas of rubidium atoms.

arXiv:physics/9911010•Physical Review Letters•Dec 20, 1999•268 citations

Saturation-induced coherence loss in coherent backscattering of light

T. Chanelière, David Wilkowski, Yannick Bidel +2 more

We use coherent backscattering of light by cold strontium atoms to study phase-breaking mechanisms in the multiple-scattering regime. As the probe light intensity is increased, the atomic optical transition starts to be saturated. Nonlinearities and inelastic scattering then occur. The latter induces a characteristic phase-breaking time that reduces the wave coherence. In our experiment, this leads to a strong reduction of the enhancement factor of the coherent backscattering cone. The results at different probe detuning are also presented.

arXiv:physics/0309095•Physical Review E•Sep 3, 2004•56 citations

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

Coherent Light Transport in a Cold Strontium Cloud

Yannick Bidel, Bruce G. Klappauf, J. C. Bernard +5 more

We study light coherent transport in the weak localization regime using magneto-optically cooled strontium atoms. The coherent backscattering cone is measured in the four polarization channels using light resonant with a J(g) = 0-->J(e) = 1 transition of the strontium atom. We find an enhancement factor close to 2 in the helicity preserving channel, in agreement with theoretical predictions. This observation confirms the effect of internal structure as the key mechanism for the contrast reduction observed with a rubidium cold cloud [G. Labeyrie et al., Phys. Rev. Lett. 83, 5266 (1999)]. Experimental results are in good agreement with Monte Carlo simulations taking into account geometry effects.

arXiv:physics/0202016•Physical Review Letters•May 7, 2002•102 citations

Coherent backscattering of light by an inhomogeneous cloud of cold atoms

G. Labeyrie, Dominique Delande, Cord Axel Müller +2 more

When a quasiresonant laser beam illuminates an optically thick cloud of laser-cooled rubidium atoms, the average diffuse intensity reflected off the sample is enhanced in a narrow angular range around the direction of exact backscattering. This phenomenon is known as coherent backscattering (CBS). By detuning the laser from resonance, we are able to modify the light scattering mean-free path inside the sample and we record accordingly the variations of the CBS cone shape. We then compare the experimental data with theoretical calculations and Monte Carlo simulations including the effect of the light polarization and of the internal structure of the atoms. We confirm that the internal structure strongly affects the enhancement factor of the cone and we show that the unusual shape of the atomic medium---approximately a spherically-symmetric, Gaussian density profile---strongly affects the width and shape of the cone.

Physical Review A•Mar 27, 2003•47 citations

Coherent transport in presence of disorder and nonlinearity

Thomas Wellens

This thesis presents the author's work on multiple scattering of intense laser light by cold atoms in chapter 2 and nonlinear coherent backscattering in chapter 3. The basic concepts and most important results should be understandable from reading these chapters on their own, whereas we refer to the subsequent collection of articles (P1-P11) for more detailed treatments. In chapter 2.1, we review scattering of light by a single two-level atom, with special emphasis on the fact that the atoms are nonlinear and inelastic scatterers, which will be relevant for multiple scattering. In chapter 2.2, we treat double scattering by two distant atoms, before we generalize this technique to a dilute disordered sample of many atoms in chapter 2.3. Both 2.2 and 2.3 apply in the perturbative regime of low laser intensity, where, by analyzing scattering of two photons, we clarify the different roles of nonlinearity and inelasticity concerning the coherent backscattering interference. Chapter 2.4 discusses the master equation as a complementary approach, applicable at arbitrarily high laser intensity, but only for a small number of atoms. In addition, we present an equivalent new approach, which explicitly takes advantage of the large distance between the atoms, and thereby combines the advantages of the master equation and the scattering approach. As discussed in chapter 2.5, this new approach opens the way to a non-perturbative theory for multiple scattering of intense laser light by dilute atomic clouds. Chapter 3 presents our diagrammatic theory for nonlinear coherent backscattering of classical (or single-particle quantum) waves. In chapter 3.1, we explain the most important assumptions of the theory: weak disorder and small nonlinearity, in particular existence of a stable, stationary solution of the nonlinear wave equation. In chapter 3.2, we explain why - contrary to seemingly convincing intuitive reasoning - the nonlinearity indeed changes the height of the coherent backscattering interference peak. In order to describe this effect quantitatively, a diagrammatic theory is sketched in chapters 3.3 and 3.4, where the nonlinear Born series and the nonlinear ladder and crossed diagrams are introduced. Chapter 3.5 presents the transport equations which result from the complete summation of ladder and crossed diagrams - non-perturbatively in the strength of the nonlinearity. We discuss the conditions under which the nonlinearity reduces or enhances the coherent backscattering interference, as compared to the linear case. In order to confirm the validity of the diagrammatic analysis, we compare these results with numerical simulations in chapter 3.6. We conclude with a short account of our work on speckle instabilities for nonlinear point scatterers in chapter 3.7. Finally, chapter 4 describes some future perspectives of our work, in particular the application of the diagrammatic theory to describe the impact of nonlinearity on weak localization and Anderson localization, and possible extensions to the quantum many-particle regime.

•Jan 1, 2009•0 citations
For large bulk disordered media, light transport is generally successfully described by a diffusion process. This picture assumes that any interference is washed out under configuration average. However, it is now known that, under certain circumstances, some interference effects survive the disorder average and in turn lead to wave localizations effects. In this paper, we investigate coherence of a monochromatic laser light propagating in an optically thick sample of laser-cooled strontium atoms. For this purpose, we use the coherent backscattering effect as an interferometric tool. At low laser probe beam intensities, phase coherence is fully preserved and the interference contrast is maximal. At higher intensities, saturation effects start to set in and the interference contrast is reduced.
We use coherent backscattering of light by cold strontium atoms to study phase-breaking mechanisms in the multiple-scattering regime. As the probe light intensity is increased, the atomic optical transition starts to be saturated. Nonlinearities and inelastic scattering then occur. The latter induces a characteristic phase-breaking time that reduces the wave coherence. In our experiment, this leads to a strong reduction of the enhancement factor of the coherent backscattering cone. The results at different probe detuning are also presented.
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 study light coherent transport in the weak localization regime using magneto-optically cooled strontium atoms. The coherent backscattering cone is measured in the four polarization channels using light resonant with a J(g) = 0-->J(e) = 1 transition of the strontium atom. We find an enhancement factor close to 2 in the helicity preserving channel, in agreement with theoretical predictions. This observation confirms the effect of internal structure as the key mechanism for the contrast reduction observed with a rubidium cold cloud [G. Labeyrie et al., Phys. Rev. Lett. 83, 5266 (1999)]. Experimental results are in good agreement with Monte Carlo simulations taking into account geometry effects.
When a quasiresonant laser beam illuminates an optically thick cloud of laser-cooled rubidium atoms, the average diffuse intensity reflected off the sample is enhanced in a narrow angular range around the direction of exact backscattering. This phenomenon is known as coherent backscattering (CBS). By detuning the laser from resonance, we are able to modify the light scattering mean-free path inside the sample and we record accordingly the variations of the CBS cone shape. We then compare the experimental data with theoretical calculations and Monte Carlo simulations including the effect of the light polarization and of the internal structure of the atoms. We confirm that the internal structure strongly affects the enhancement factor of the cone and we show that the unusual shape of the atomic medium---approximately a spherically-symmetric, Gaussian density profile---strongly affects the width and shape of the cone.
This thesis presents the author's work on multiple scattering of intense laser light by cold atoms in chapter 2 and nonlinear coherent backscattering in chapter 3. The basic concepts and most important results should be understandable from reading these chapters on their own, whereas we refer to the subsequent collection of articles (P1-P11) for more detailed treatments. In chapter 2.1, we review scattering of light by a single two-level atom, with special emphasis on the fact that the atoms are nonlinear and inelastic scatterers, which will be relevant for multiple scattering. In chapter 2.2, we treat double scattering by two distant atoms, before we generalize this technique to a dilute disordered sample of many atoms in chapter 2.3. Both 2.2 and 2.3 apply in the perturbative regime of low laser intensity, where, by analyzing scattering of two photons, we clarify the different roles of nonlinearity and inelasticity concerning the coherent backscattering interference. Chapter 2.4 discusses the master equation as a complementary approach, applicable at arbitrarily high laser intensity, but only for a small number of atoms. In addition, we present an equivalent new approach, which explicitly takes advantage of the large distance between the atoms, and thereby combines the advantages of the master equation and the scattering approach. As discussed in chapter 2.5, this new approach opens the way to a non-perturbative theory for multiple scattering of intense laser light by dilute atomic clouds. Chapter 3 presents our diagrammatic theory for nonlinear coherent backscattering of classical (or single-particle quantum) waves. In chapter 3.1, we explain the most important assumptions of the theory: weak disorder and small nonlinearity, in particular existence of a stable, stationary solution of the nonlinear wave equation. In chapter 3.2, we explain why - contrary to seemingly convincing intuitive reasoning - the nonlinearity indeed changes the height of the coherent backscattering interference peak. In order to describe this effect quantitatively, a diagrammatic theory is sketched in chapters 3.3 and 3.4, where the nonlinear Born series and the nonlinear ladder and crossed diagrams are introduced. Chapter 3.5 presents the transport equations which result from the complete summation of ladder and crossed diagrams - non-perturbatively in the strength of the nonlinearity. We discuss the conditions under which the nonlinearity reduces or enhances the coherent backscattering interference, as compared to the linear case. In order to confirm the validity of the diagrammatic analysis, we compare these results with numerical simulations in chapter 3.6. We conclude with a short account of our work on speckle instabilities for nonlinear point scatterers in chapter 3.7. Finally, chapter 4 describes some future perspectives of our work, in particular the application of the diagrammatic theory to describe the impact of nonlinearity on weak localization and Anderson localization, and possible extensions to the quantum many-particle regime.