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arXiv:1207.4775 · Physical Review Letters

Coherent Backscattering of Ultracold Atoms

Fred Jendrzejewski, Kilian Müller, Jérémie Richard, Aditya Date, Thomas Plisson, Philippe Bouyer, Alain Aspect, Vincent Josse

Published Nov 5, 2012• 117 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.109.195302

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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.
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).
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.
We study experimentally and numerically the quasi-bidimensional transport of a 87^{87}87Rb Bose-Einstein condensate launched with a velocity v0v_0v0​ inside a disordered optical potential created by a speckle pattern. A time-of-flight analysis reveals a pronounced enhanced density peak in the backscattering direction −v0-v_0−v0​, a feature reminiscent of coherent backscattering. Detailed numerical simulations indicate however that other effects also contribute to this enhancement, including a "backscattering echo" due to the position-momentum correlations of the initial wave packet.
The Coherent Backscattering (CBS) peak is a well-known interferential signature of weak localization in disordered or chaotic systems. More recently, a second interference feature—the Coherent Forward Scattering (CFS) peak—was predicted to emerge in the regime of strong localization. However, it has never been directly observed. Here we report the direct observation of the CFS peak and demonstrate its dual role as a signature of non-ergodicity and as a probe of symmetries in quantum chaotic systems. Using a shaken rotor model realized with a Bose-Einstein condensate (BEC) of ultracold atoms in a modulated optical lattice, we investigate dynamical localization in momentum space. The CFS peak emerges in the position distribution as a consequence of non-ergodic dynamics, while its growth timescale and width reveal the underlying localization length. By finely tuning the modulation, we control time-reversal and parity symmetries and measure their distinct effects on both CBS and CFS peaks in position space. Our results highlight the strong link of both temporal growth and contrast of the coherent scattering peaks with symmetry and localization. This work opens several perspectives for investigating coherent scattering signatures in a many-body context. Ergodicity (or lack thereof) plays a major role in the relaxation of quantum systems to equilibrium, yet the search of experimentally accessible quantities acting as its signatures is still ongoing. Here, the authors observe the sought-after features of the coherent forward scattering peak from a Bose-Einstein condensate within an optical lattice.
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.