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arXiv:1108.1282 · Physical Review A

Coherent backscattering of ultracold matter waves: Momentum space signatures

Nicolas Cherroret, Tomasz Karpiuk, Cord Axel Müller, Benoît Grémaud, Christian Miniatura

Published Jan 10, 2012• 54 citations
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Abstract

Using analytical and numerical methods, it is shown that the momentum distribution of a matter wave packet launched in a random potential exhibits a pronounced coherent backscattering (CBS) peak. By analyzing the momentum distribution, key transport times can be directly measured. The CBS peak can be used to prove that transport occurs in the phase-coherent regime, and measuring its time dependence permits monitoring the transition from classical diffusion to Anderson localization.

DOI
10.1103/physreva.85.011604

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Using analytical and numerical methods, it is shown that the momentum distribution of a matter wave packet launched in a random potential exhibits a pronounced coherent backscattering (CBS) peak. By analyzing the momentum distribution, key transport times can be directly measured. The CBS peak can be used to prove that transport occurs in the phase-coherent regime, and measuring its time dependence permits monitoring the transition from classical diffusion to Anderson localization.
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 investigate the dynamics of a coherent matter wave packet launched in a random potential. As predicted by Cherroret et al. [Phys. Rev. A 85 011604(R) (2012)], the coherent backscattering signal in the momentum distribution freezes at the onset of Anderson localization. At the same time, a novel interference peak rises in the forward direction. An explanation in terms of chained maximally crossed diagrams predicts that the forward scattering peak emerges on a time scale τloc∗=2mξ2/ℏ\tau_\text{loc}^* = 2m\xi^2/\hbarτloc∗​=2mξ2/ℏ set by the localization length ξ\xiξ.
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.
We study Anderson localization in two-dimensional, disordered, spin-orbit systems belonging to the symplectic symmetry class using momentum-space signatures such as the coherent backscattering antipeak and the coherent forward-scattering peak. Significantly, these momentum-space features are readily accessible in ultracold atom experiments through absorption imaging after time-of-flight expansion. Here, the critical exponent and mobility edge of the metal-insulator transition are successfully obtained through a finite-time analysis of the coherent backscattering width. An anomalous residual diffusion, unique to two dimensions, is identified at the transition point where the system changes from a metal to an insulator. A spin localization phenomenon is also observed in the deep localized regime. Published by the American Physical Society 2024
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.
We present a detailed numerical and theoretical analysis of the recently discovered phenomenon of coherent forward scattering. This effect manifests itself as a macroscopic interference peak in the forward direction of the momentum distribution of a matter wave launched with finite velocity in a random potential. Focusing on the two-dimensional case, we show that coherent forward scattering generally arises due the confinement of the wave in a finite region of space, and explain under which conditions it can be seen as a genuine signature of Anderson localization.