While Anderson is a single-particle wave effect, guaranteeing a single excitation in the system can be challenging. We here tackle this limitation in the context of light localization in three dimensions in disordered cold atom clouds, in presence of several photons. We show that the presence of these multiple excitations does not affect substantially the abnormal intensity fluctuations which characterize the Anderson localization transition, provided that the radiated light is frequency filtered. Due to their narrow linewidth, long-lived modes, and particularly the localized ones, are strongly saturated even for a weak resonant pump, leading to a large increase of the inelastic scattering and to reduced fluctuations in the total radiation. Yet the atomic coherences and the resulting elastic scattering remain a proper witness of the Anderson localization transition. Hence, frequency filtering allows one to investigate the single-excitation sector, dismissing the many-body effects showing up in the fluorescence spectrum.
While Anderson is a single-particle wave effect, guaranteeing a single excitation in the system can be challenging. We here tackle this limitation in the context of light localization in three dimensions in disordered cold atom clouds, in presence of several photons. We show that the presence of these multiple excitations does not affect substantially the abnormal intensity fluctuations which characterize the Anderson localization transition, provided that the radiated light is frequency filtered. Due to their narrow linewidth, long-lived modes, and particularly the localized ones, are strongly saturated even for a weak resonant pump, leading to a large increase of the inelastic scattering and to reduced fluctuations in the total radiation. Yet the atomic coherences and the resulting elastic scattering remain a proper witness of the Anderson localization transition. Hence, frequency filtering allows one to investigate the single-excitation sector, dismissing the many-body effects showing up in the fluorescence spectrum.
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.
A blue sky, a white cloud or a red sunset are explained by classical multiple scattering theory of light. However, these phenomena neglect interference occurrence. Once it is taken into account, interference in a disordered medium may actually put a halt to the propagation of light, an effect known as Anderson Localization. Until now, experimental reports of Anderson Localization of light in 3D systems have not been conclusive. Our goal is to understand what are the underlying obstacles, and look for new insights from a theoretical point of view. In this dissertation, the properties of a cloud of two-level atoms scattering light are investigated. The dipole-dipole interaction generates collective modes, some of them, being localized. We found that finite-size effects dominate the lifetime of the localized modes, specifically by the ratio of localization length to their distance to the system boundaries. Localized modes saturates at maximum of 20% even above phase transition. Studying the steady-state regime, the coupling between localized modes and light is weak. Both results agrees with the difficulty of experimental evidence of light localization and promote the link of experiments and theory.
In this thesis, we investigate the coherent scattering of light propagating in a random medium.We are interested in phenomena like the super-and subradiance and Anderson localization that are related to waves interferences and spatial disorder.However, the fundamental difference between subradiance and Anderson localization still needs to be clarified.This thesis gives new elements for the understanding of these phenomena and we present a new method to observe Anderson localization.A mean-field model that does not contain disorder is developed, and we show that super-and subradiance do not require disorder whereas Anderson localization does.In this theoretical work, the coupling between the light and many atoms is reduced to a coupling matrix between the atoms by tracing over the degrees of freedom of the light, which results in a linear problem for the atomic dipoles.The study of the eigenvalues and eigenmodes of this matrix then allows to determine the super-and subradiant modes, and to probe the Anderson localization phase transition with a scaling analysis.Furthermore, the link to the experiment is realized by showing that the intensity fluctuations present an increase at the localization transition.The system is studied in the steady-state regime when the medium is continuously charged by a laser until reaches a stationary regime, and the decay dynamics, when the laser is switched off, so the cloud releases the energy stored.Finally, we present a preliminary work that shows that the diagonal disorder might be a good strategy to reach Anderson localization.
The objective of this thesis is to expand our understanding of collective light-scattering phenomena, which manifest themselves in the strong suppression of radiation from the scattering medium. In particular, we are interested in subradiance, a collective effect in spontaneous emission which, as a result of the dissipative coupling of atoms through common electromagnetic modes, creates long-lived excitation modes in an ensemble of cold atoms, with lifetimes much longer than those of individual, isolated atoms. Previously, subradiance had been well-characterized for dilute cold-atom scattering media and the low-intensity limit of the driving laser (linear-optics regime). In this thesis, we study this collective phenomenon beyond the linear-optics and dilute regimes.To study experimentally subradiance beyond the linear-optics regime, we varied the saturation parameter of the excitation laser up to relatively large values and we have observed the increase of the subradiant population with increasing saturation parameter. More importantly, we have identified the super-linear scaling of the subradiant population beyond the linear-optics regime, due to a process similar to optical pumping via multi-excitation superradiant states. This study showed that the increase in the intensity of the driving laser beyond the linear-optics regime can overcome the weak coupling of subradiant modes with the external world.Moreover, we have numerically studied subradiance using the vectorial coupled-dipole model, with a focus on understanding the effect of the near-field dipole-dipole interaction. For that, we extensively compared the vectorial and scalar (which does not contain near-field interaction terms) models and studied the subradiant lifetime as a function of the density and optical thickness of the cold-atom cloud. We observed that the near-field terms are detrimental for subradiance, which was seen in the reduction of the subradiant lifetimes with increasing density. This detrimental character of near-field terms can be interpreted as being due to an effective inhomogeneous broadening induced by the near-field interaction, which reduces the subradiant lifetimes as the density increases.The detrimental character of near-field interaction has also been previously numerically identified for Anderson localization of light waves (Anderson localization is a coherent multiple-scattering wave phenomenon in a strongly scattering medium that results in a cessation of a diffusive wave transport; it also yields long-lived modes): the scalar coupled-dipole model predicts Anderson localization of light waves, but not the vectorial one. However, adding a strong magnetic field allows one to recover localized modes for vectorial light. In this context, we numerically studied a possible signature of Anderson localization of light in cold atoms, based on the measurement of intensity fluctuations of the scattered light. We have shown that at the transition to the localized regime, the fluctuations are enhanced. In particular, for vectorial light, we have demonstrated the absence and recovery of enhanced intensity fluctuations without and with the applied magnetic field, which further corroborates that the intensity fluctuations could serve as an experimental way to probe the localized states.
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.