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Latin America Optics and Photonics Conference

Coherent Back Scattering and Anderson Localization of Ultra Cold Atoms

Alain Aspect

Published Jan 1, 2012• 0 citations
Publisher

Abstract

We use ultra cold atoms transport in a disordered potential created with a laser speckle, to study Anderson Localization (AL) and Coherent Back Scattering (CBS). Localization has been observed in 1D and 3D, and 2D experiments are promising. Theory supports the conclusion that what we observe is AL, but a smoking gun of the role of coherence is still missing. Recently, we have observed CBS (see Figure), an indisputable coherent effect in quantum transport, related to the first order manifestation of localization (weak localization).

DOI
10.1364/laop.2012.ls4b.1

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We use ultra cold atoms transport in a disordered potential created with a laser speckle, to study Anderson Localization (AL) and Coherent Back Scattering (CBS). Localization has been observed in 1D and 3D, and 2D experiments are promising. Theory supports the conclusion that what we observe is AL, but a smoking gun of the role of coherence is still missing. Recently, we have observed CBS (see Figure), an indisputable coherent effect in quantum transport, related to the first order manifestation of localization (weak localization).
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].
We report on the direct observation of coherent backscattering (CBS) of ultracold atoms in a quasi-two-dimensional configuration. Launching atoms with a well-defined momentum in a laser speckle disordered potential, we follow the progressive build up of the momentum scattering pattern, consisting of a ring associated with multiple elastic scattering, and the CBS peak in the backward direction. Monitoring the depletion of the initial momentum component and the formation of the angular ring profile allows us to determine microscopic transport quantities. We also study the time evolution of the CBS peak and find it in fair agreement with predictions, at long times as well as at short times. The observation of CBS can be considered a direct signature of coherence in quantum transport of particles in disordered media. It is responsible for the so called weak localization phenomenon, which is the precursor of Anderson localization.
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.
Weak localization of light or coherent backscattering (CBS) of light is a phenomena in which partial waves traversing momentum-reversed (time-reversed) scattering paths interfere constructively in the backscattering direction leading to an enhancement of scattered light intensity. The enhancement of intensity is proportional to a reduction of light transported in the scattering medium. Thus the CBS signal is a measure of localization of light in the scattering medium. We are building an apparatus to observe weak localization of photons in a high density sample of ultra-cold atoms. First we slow the atoms from room temperature (300 m/s) to less than 10 cm/s in a magneto-optical trap (MOT) where the atom number density is 10 11 atoms/cm 3 . In order to increase the atomic density the atoms in the MOT are transferred to a far detuned microscopic dipole trap created by a laser focused to a waist of approximately 5m. We have successfully loaded the MOT and are now in the process of loading the high density microscopic dipole trap. Once this is achieved we will look at the CBS signal as a function of the atom number density and the scattering cross section. The goal of the project is to reach the Joffe-Regel region where mean free path length is about the wavelength of the scattering radiation.
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.
Signatures of Anderson localization in the momentum distribution of a cold atom cloud after a quantum quench are studied. We consider a quasi-one-dimensional cloud initially prepared in a well-defined momentum state, and expanding for some time in a disorder speckle potential. Quantum interference generates a peak in the forward scattering amplitude which, unlike the common weak localization backscattering peak, is a signature of strong Anderson localization. We present a nonperturbative, and fully time resolved description of the phenomenon, covering the entire diffusion-to-localization crossover. Our results should be observable by present day experiments.