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Anderson localization of light by cold atoms

S. E. Skipetrov

Published Oct 7, 2020• 0 citations
OpenAlex

Abstract

Large ensembles of cold, immobile atoms might serve as ideal model systems to study Anderson localization of light. In contrast to dielectric systems, atomic clouds allow for a fine experimental control and admit a precise theoretical description. In this talk, we will review the recent theoretical developments aimed at paving a path towards an experimental realization of Anderson localization of light in three-dimensional (3D) atomic systems. Because atoms are the simplest point scatterers, considering light scattering on them is a good opportunity to illustrate several basic concepts and methods of the localization theory (Thouless conductance and Ioffe-Regel criterion, the mobility edge and the critical behavior, the scaling and self-consistent theories, the finite-size scaling procedure, etc.) on a concrete example. We will show that, surprisingly, Anderson localization of light by atoms is impossible in 3D if no special efforts are made to suppress near-field interactions between atoms. The necessary suppression may be achieved by subjecting the atoms to a constant external magnetic field or by arranging them in a crystalline structure in which a small amount of disorder is introduced. However, even when spatially localized states appear in a system of immobile atoms, their experimental observation remains challenging because of the residual thermal motion of atoms.

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Search for Anderson localization of light by cold atoms in a static electric field

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We explore the potential of a static electric field to induce Anderson localization of light in a large three-dimensional cloud of randomly distributed, immobile atoms with a nondegenerate ground state (total angular momentum ${J}_{g}=0$) and a threefold-degenerate excited state (${J}_{e}=1$). We study both the spatial structure of quasimodes of the atomic cloud and the scaling of the Thouless number with the size of the cloud. Our results indicate that unlike the static magnetic field, the electric field does not induce Anderson localization of light by atoms. We explain this conclusion by the incomplete removal of degeneracy of the excited atomic state by the field and the relatively strong residual dipole-dipole coupling between atoms which is weaker than in the absence of external fields but stronger than in the presence of a static magnetic field. A joint analysis of these results together with our previous results concerning Anderson localization of scalar waves and light suggests the existence of a critical strength of dipole-dipole interactions that should not be surpassed for Anderson localization to be possible in three dimensions.

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Anderson localization – the halt of quantum transport in a strongly disordered potential – has been observed for quantum gases in optical potentials. An important stage of experiments is the creation and characterization of the optical (speckle) potential that typically features nontrivial correlations complicating the interpretation of measurements. We realize an alternative route towards Anderson localization of cold atoms using a mixture of two strongly mass-imbalanced atomic species without any externally imposed disordered potential. On short time scales, the heavy component can be considered immobile and creates a quasi-static scattering potential for the light component that experiences Anderson localization under appropriate conditions. Experimental results allow for a quantitative description based on the model of randomly distributed resonant point scatterers. This demonstrates an interesting and fruitful link between the phenomenon of (single-particle) Anderson localization and the so-called many-body localization that takes place in interacting quantum systems composed of many particles, which is the case of our experimental system.

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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2013•0 citations
Large ensembles of cold, immobile atoms might serve as ideal model systems to study Anderson localization of light. In contrast to dielectric systems, atomic clouds allow for a fine experimental control and admit a precise theoretical description. In this talk, we will review the recent theoretical developments aimed at paving a path towards an experimental realization of Anderson localization of light in three-dimensional (3D) atomic systems. Because atoms are the simplest point scatterers, considering light scattering on them is a good opportunity to illustrate several basic concepts and methods of the localization theory (Thouless conductance and Ioffe-Regel criterion, the mobility edge and the critical behavior, the scaling and self-consistent theories, the finite-size scaling procedure, etc.) on a concrete example. We will show that, surprisingly, Anderson localization of light by atoms is impossible in 3D if no special efforts are made to suppress near-field interactions between atoms. The necessary suppression may be achieved by subjecting the atoms to a constant external magnetic field or by arranging them in a crystalline structure in which a small amount of disorder is introduced. However, even when spatially localized states appear in a system of immobile atoms, their experimental observation remains challenging because of the residual thermal motion of atoms.
We explore the potential of a static electric field to induce Anderson localization of light in a large three-dimensional cloud of randomly distributed, immobile atoms with a nondegenerate ground state (total angular momentum Jg=0{J}_{g}=0Jg​=0) and a threefold-degenerate excited state (Je=1{J}_{e}=1Je​=1). We study both the spatial structure of quasimodes of the atomic cloud and the scaling of the Thouless number with the size of the cloud. Our results indicate that unlike the static magnetic field, the electric field does not induce Anderson localization of light by atoms. We explain this conclusion by the incomplete removal of degeneracy of the excited atomic state by the field and the relatively strong residual dipole-dipole coupling between atoms which is weaker than in the absence of external fields but stronger than in the presence of a static magnetic field. A joint analysis of these results together with our previous results concerning Anderson localization of scalar waves and light suggests the existence of a critical strength of dipole-dipole interactions that should not be surpassed for Anderson localization to be possible in three dimensions.
Anderson localization – the halt of quantum transport in a strongly disordered potential – has been observed for quantum gases in optical potentials. An important stage of experiments is the creation and characterization of the optical (speckle) potential that typically features nontrivial correlations complicating the interpretation of measurements. We realize an alternative route towards Anderson localization of cold atoms using a mixture of two strongly mass-imbalanced atomic species without any externally imposed disordered potential. On short time scales, the heavy component can be considered immobile and creates a quasi-static scattering potential for the light component that experiences Anderson localization under appropriate conditions. Experimental results allow for a quantitative description based on the model of randomly distributed resonant point scatterers. This demonstrates an interesting and fruitful link between the phenomenon of (single-particle) Anderson localization and the so-called many-body localization that takes place in interacting quantum systems composed of many particles, which is the case of our experimental system.
Summary form only given. The quest for Anderson localization of light is at the center of many experimental and theoretical activities. Cold atoms have emerged as interesting quantum system to study coherent transport properties of light. Initial experiments have established that dilute samples with large optical thickness allow studying weak localization of light [1]. The goal of our research is to study coherent transport of photons in dense samples. One important aspect is the quest of Anderson localization of light with cold atoms and its relation to Dicke super- or subradiance, in particular with large and dense samples of cold atoms.In this talk I will show that Dicke type cooperativity with global synchronization dominates over Anderson localisation with local interferences [2-4], even for high densities of atoms fulfilling the Ioffe-Regel criterion kl<;1. I will show that the standard approach using single parameter scaling theory does not apply for photons in resonant systems and highlight this considering on-resonance scattering of light by cold atoms.
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.
Anderson Localization - the complete halt of wave transport through multiple scattering and phase coherence - was discovered in 1958 and has been actively studied since then with several types of waves (light, µ-waves, ultrasound, acoustic waves, etc.). In three-dimensional systems, Anderson Localization manifests as a phase transition around a critical energy - the Mobility Edge - that separates the localized (insulator) states from the diffusive (metallic) states.Ultracold atoms are promising candidates for such experiments, and various groups have reported evidence of the 3D Anderson Transition, in particular, our group in 2012. Nevertheless, all these preliminary measurements were limited by the unwanted broadening of the energy distribution when the atoms were transferred into the disorder. Hence, no direct observation of the transition could be achieved.The quest for the direct observation of the 3D Anderson Transition has motivated us to develop a novel spectroscopic scheme using state-dependent disorder. The concept is to transfer, via RF coupling, a small fraction of a Bose-Einstein Condensate from a disorder-insensitive state to a disorder-sensitive state. By doing so, we selectively populate targeted energy levels in the disorder with a narrow energy distribution. This technique has paved the way for successfully achieving the direct observation of the 3D Anderson Transition in a 3D laser speckle. Moreover, it yields a precise measurement of the Mobility Edge, which is in excellent agreement with the numerical predictions.The heart of our achievement lies in the spectroscopic scheme. When transferring only a few atoms, we expect the coupling of a discrete state to a continuum, leading to a Fourier-limited energy distribution. This key assumption has so far been verified only indirectly, but never tested numerically. In the last part of my PhD, I have set up the framework for the numerical description of the RF transfer scheme. While the study remains preliminary, it already demonstrates that the dynamics can be more subtle than expected, and the model deserves further attention in the future.
Summary form only given. An ensemble of ultra cold atoms released in a well-chosen disordered optical potential is a system that offers a privileged way to directly observe Anderson Localization. Localization has been observed in 1D [1,2] and 3D [3,4], while 2D experiments are promising [5]. Theory supports the conclusion that what we observe is AL [6,7], but a smoking gun of the role of coherence is still missing. Recently, we have observed CBS [8] (see Figure), an indisputable coherent effect in quantum transport, related to the first order manifestation of localization (weak localization). Anderson Localization is a research field where many theoretical questions remain open. In particular, when there is interaction between particles, the corresponding quantum many-body problems are exceedingly difficult to solve. We thus plan to implement controlled interactions between atoms in our system, using Feschbach resonances, in order to provide answers to such problems. The system will then deserve the name of "quantum simulator" in the sense used by Feynman in his pioneering paper [9].