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.
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.
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.
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.
In front of a mirror, the radiation of weakly driven large disordered clouds presents an interference fringe in the backward direction, on top of an incoherent background. Although strongly driven atoms usually present little coherent scattering, we show here that the mirror-assisted version can produce high contrast fringes, for arbitrarily high saturation parameters. The contrast of the fringes oscillates with the Rabi frequency of the atomic transition and the distance between the mirror and the atoms, due to the coherent interference between the carrier and the Mollow sidebands of the saturated resonant fluorescence spectrum emitted by the atoms. The setup thus represents a powerful platform to study the spectral properties of ensembles of correlated scatterers.
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.
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.