© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:quant-ph/0506010 · Physical Review A

Coherent backscattering in nonlinear atomic media: Quantum Langevin approach

Benoît Grémaud, Thomas Wellens, Dominique Delande, Christian Miniatura

Published Sep 12, 2006• 27 citations

Abstract

In this theoretical paper, we investigate coherence properties of the near-resonant light scattered by two atoms exposed to a strong monochromatic field. To properly incorporate saturation effects, we use a quantum Langevin approach. In contrast to the standard optical Bloch equations, this method naturally provides the inelastic spectrum of the radiated light induced by the quantum electromagnetic vacuum fluctuations. However, to get the right spectral properties of the scattered light, it is essential to correctly describe the statistical properties of these vacuum fluctuations. Because of the presence of the two atoms, these statistical properties are not Gaussian: (i) the spatial two-points correlation function displays a specklelike behavior and (ii) the three-points correlation function does not vanish. We also explain how to incorporate in a simple way propagation with a frequency-dependent scattering mean-free path, meaning that the two atoms are embedded in an average scattering dispersive medium. Finally we show that saturation-induced nonlinearities strongly modify the atomic scattering properties and, as a consequence, provide a source of decoherence in multiple scattering. This is exemplified by considering the coherent backscattering configuration where interference effects are blurred by this decoherence mechanism. This leads to a decrease of the so-called coherent backscattering enhancement factor.

DOI: 10.1103/physreva.74.033808

Related papers

Coherent backscattering of light with nonlinear atomic scatterers

Thomas Wellens, Benoît Grémaud, Dominique Delande +1 more

We study coherent backscattering of a monochromatic laser by a dilute gas of cold two-level atoms in the weakly nonlinear regime. The nonlinear response of the atoms results in a modification of both the average field propagation (nonlinear refractive index) and the scattering events. Using a perturbative approach, the nonlinear effects arise from inelastic two-photon scattering processes. We present a detailed diagrammatic derivation of the elastic and inelastic components of the backscattering signal for both scalar and vectorial photons. In particular, we show that the coherent backscattering phenomenon originates in some cases from the interference between three different scattering amplitudes. This is in marked contrast with the linear regime where it is due to the interference between two different scattering amplitudes. In particular we show that, if elastically scattered photons are filtered out from the photodetection signal, the nonlinear backscattering enhancement factor exceeds the linear barrier of 2, consistently with a three-amplitude interference effect.

Physical Review A•Jan 4, 2006•27 citations

Coherent backscattering of inelastic photons from atoms and their mirror images

Paulo Hisao Moriya, R. F. Shiozaki, R Teixeira +5 more

Coherent backscattering is a coherence effect in the propagation of waves through disordered media involving two or more scattering events. Here we report on the observation of coherent backscattering from individual atoms and their mirror images. This system displays two important advantages: First, the effect can be observed at low optical densities, which allows us to work in very dilute clouds or far from resonance. Second, due to the fact that the radiation of an atom interferes constructively with that of its own image, the phenomenon is much more robust to dephasing induced by strong saturation. In particular, the contribution of inelastically scattered photons to the interference process is demonstrated.

arXiv:1604.03428•Physical Review A•Nov 7, 2016•10 citations

Coherent backscattering of light by atoms in the saturated regime

Thomas Wellens, Benoît Grémaud, Dominique Delande +1 more

We present the first calculation of coherent backscattering with inelastic scattering by saturated atoms. We consider the scattering of a quasi-monochromatic laser pulse by two distant atoms in free space. By restricting ourselves to scattering of two photons, we employ a perturbative approach, valid up to second order in the incident laser intensity. The backscattering enhancement factor is found to be smaller than two (after excluding single scattering), indicating a loss of coherence between the doubly scattered light emitted by both atoms. Since the undetected photon carries information about the path of the detected photon, the coherence loss can be explained by a which-path argument, in analogy with a double-slit experiment.

•Jan 1, 2004•0 citations

Coherent Backscattering with Nonlinear Atomic Scatterers

Thomas Wellens, Benoît Grémaud, Dominique Delande +1 more

We study coherent backscattering of a quasi-monochromatic laser by a dilute gas of cold two-level atoms. We consider the perturbative regime of weak intensities, where nonlinear effects arise from {\em inelastic} two-photon scattering processes. Here, coherent backscattering can be formed by interference between {\em three} different scattering amplitudes. Consequently, if elastically scattered photons are filtered out from the photodetection signal by means of suitable frequency-selective detection, we find the nonlinear backscattering enhancement factor to exceed the linear barrier two.

arXiv:cond-mat/0411555•Nov 22, 2004•0 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

Coherent backscattering of light by two atoms in the saturated regime

Thomas Wellens, Benoît Grémaud, Dominique Delande +1 more

We present a calculation of coherent backscattering with inelastic scattering by saturated atoms. We consider the scattering of a quasimonochromatic laser pulse by two distant atoms in free space. By restricting ourselves to scattering of two photons, we employ a perturbative approach, valid up to second order in the incident laser intensity. The backscattering enhancement factor is found to be smaller than two (after excluding single scattering), indicating a loss of coherence between the doubly scattered light emitted by both atoms. Since the undetected photon carries information about the path of the detected photon, the coherence loss can be explained by a which-path argument, in analogy with a double-slit experiment.

arXiv:quant-ph/0403057•Physical Review A•Aug 26, 2004•36 citations

In this theoretical paper, we investigate coherence properties of the near-resonant light scattered by two atoms exposed to a strong monochromatic field. To properly incorporate saturation effects, we use a quantum Langevin approach. In contrast to the standard optical Bloch equations, this method naturally provides the inelastic spectrum of the radiated light induced by the quantum electromagnetic vacuum fluctuations. However, to get the right spectral properties of the scattered light, it is essential to correctly describe the statistical properties of these vacuum fluctuations. Because of the presence of the two atoms, these statistical properties are not Gaussian: (i) the spatial two-points correlation function displays a specklelike behavior and (ii) the three-points correlation function does not vanish. We also explain how to incorporate in a simple way propagation with a frequency-dependent scattering mean-free path, meaning that the two atoms are embedded in an average scattering dispersive medium. Finally we show that saturation-induced nonlinearities strongly modify the atomic scattering properties and, as a consequence, provide a source of decoherence in multiple scattering. This is exemplified by considering the coherent backscattering configuration where interference effects are blurred by this decoherence mechanism. This leads to a decrease of the so-called coherent backscattering enhancement factor.

We study coherent backscattering of a monochromatic laser by a dilute gas of cold two-level atoms in the weakly nonlinear regime. The nonlinear response of the atoms results in a modification of both the average field propagation (nonlinear refractive index) and the scattering events. Using a perturbative approach, the nonlinear effects arise from inelastic two-photon scattering processes. We present a detailed diagrammatic derivation of the elastic and inelastic components of the backscattering signal for both scalar and vectorial photons. In particular, we show that the coherent backscattering phenomenon originates in some cases from the interference between three different scattering amplitudes. This is in marked contrast with the linear regime where it is due to the interference between two different scattering amplitudes. In particular we show that, if elastically scattered photons are filtered out from the photodetection signal, the nonlinear backscattering enhancement factor exceeds the linear barrier of 2, consistently with a three-amplitude interference effect.

Coherent backscattering is a coherence effect in the propagation of waves through disordered media involving two or more scattering events. Here we report on the observation of coherent backscattering from individual atoms and their mirror images. This system displays two important advantages: First, the effect can be observed at low optical densities, which allows us to work in very dilute clouds or far from resonance. Second, due to the fact that the radiation of an atom interferes constructively with that of its own image, the phenomenon is much more robust to dephasing induced by strong saturation. In particular, the contribution of inelastically scattered photons to the interference process is demonstrated.

We present the first calculation of coherent backscattering with inelastic scattering by saturated atoms. We consider the scattering of a quasi-monochromatic laser pulse by two distant atoms in free space. By restricting ourselves to scattering of two photons, we employ a perturbative approach, valid up to second order in the incident laser intensity. The backscattering enhancement factor is found to be smaller than two (after excluding single scattering), indicating a loss of coherence between the doubly scattered light emitted by both atoms. Since the undetected photon carries information about the path of the detected photon, the coherence loss can be explained by a which-path argument, in analogy with a double-slit experiment.

We study coherent backscattering of a quasi-monochromatic laser by a dilute gas of cold two-level atoms. We consider the perturbative regime of weak intensities, where nonlinear effects arise from {\em inelastic} two-photon scattering processes. Here, coherent backscattering can be formed by interference between {\em three} different scattering amplitudes. Consequently, if elastically scattered photons are filtered out from the photodetection signal by means of suitable frequency-selective detection, we find the nonlinear backscattering enhancement factor to exceed the linear barrier two.

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.

We present a calculation of coherent backscattering with inelastic scattering by saturated atoms. We consider the scattering of a quasimonochromatic laser pulse by two distant atoms in free space. By restricting ourselves to scattering of two photons, we employ a perturbative approach, valid up to second order in the incident laser intensity. The backscattering enhancement factor is found to be smaller than two (after excluding single scattering), indicating a loss of coherence between the doubly scattered light emitted by both atoms. Since the undetected photon carries information about the path of the detected photon, the coherence loss can be explained by a which-path argument, in analogy with a double-slit experiment.