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arXiv:1004.0312 · Physical Review Letters

Anisotropic 2D Diffusive Expansion of Ultracold Atoms in a Disordered Potential

Martin Robert-De-Saint-Vincent, Jean-Philippe Brantut, Baptiste Allard, Thomas Plisson, Luca Pezzè, Laurent Sanchez-Palencia, Alain Aspect, Thomas Bourdel, Philippe Bouyer

Published Jun 2, 2010• 72 citations
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Abstract

We study the horizontal expansion of vertically confined ultracold atoms in the presence of disorder. Vertical confinement allows us to realize a situation with a few coupled harmonic oscillator quantum states. The disordered potential is created by an optical speckle at an angle of 30° with respect to the horizontal plane, resulting in an effective anisotropy of the correlation lengths of a factor of 2 in that plane. We observe diffusion leading to non-gaussian density profiles. Diffusion coefficients, extracted from the experimental results, show anisotropy and strong energy dependence, in agreement with numerical calculations.

DOI
10.1103/physrevlett.104.220602

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We numerically study the dynamics of cold atoms in a twodimensional disordered potential.We consider an anisotropic speckle potential and focus on the classical dynamics, which is relevant to some recent experiments.Firstly, we study the behavior of particles with a fixed energy and identify different transport regimes.At low energy, the particles are classically localized due to the absence of a percolating cluster.At high energy, the particles undergo normal diffusion, and we show that the diffusion coefficients scale algebraically with the particle energy, with an anisotropy factor that is significantly different from that of the disordered potential.At intermediate energy, we find a transient sub-diffusive regime, which is relevant to the time scale of typical experiments.Secondly, we study the behavior of a cold atomic gas with an arbitrary energy distribution, using the above results as the groundwork.We show that the density profile of the atomic cloud in the diffusion regime is strongly peaked and, in particular, that it is not Gaussian.Its behavior at large distances allows us to extract the energy-dependent diffusion coefficients from experimental density distributions.For a thermal cloud released into the disordered potential, we show that our numerical predictions are in
The macroscopic transport properties in a disordered potential, namely diffusion and weak/strong localization, closely depend on the microscopic and statistical properties of the disorder itself.This dependence is rich in counter-intuitive consequences.It can be particularly exploited in matter wave experiments, where the disordered potential can be tailored and controlled, and anisotropies are naturally present.In this work, we apply a perturbative microscopic transport theory and the self-consistent theory of Anderson localization to study the transport properties of ultracold atoms in anisotropic two-dimensional (2D) and three-dimensional (3D) speckle potentials.In particular, we discuss the anisotropy of single-scattering, diffusion and localization.We also calculate disorder-induced shift of the energy states and propose a method to include it, which amounts to renormalizing energies in the standard on-shell approximation.We show that the renormalization of energies strongly affects the prediction for the 3D localization threshold (mobility edge).We illustrate the theoretical findings with examples which are relevant for current matter wave experiments, where the disorder is created with laser speckle.This paper provides a guideline for future experiments aiming at the precise location of the 3D mobility edge and study of anisotropic diffusion and localization effects in 2D and 3D.
We experimentally study localization and dynamics of ultracold fermions in speckle and optical lattice potentials to explore Anderson localization, many-body localization, and relaxation dynamics in strongly correlated systems. Anderson localization is probed by releasing non-interacting, spin-polarized gases into three dimensional, anisotropic disordered potentials produced from optical speckle. A fraction of the atoms are localized by the disorder, and a mobility edge is found separating localized from extended states. The length scale of the speckle is varied, and the localized state is found to scale linearly with the geometric mean of the speckle autocorrelation length. We realize the Fermi Hubbard model by loading atoms in a cubic optical lattice. Non-equilibrium momentum distributions are created via Raman transitions, and the excitation relaxation rate is measured in the lattice. Transport experiments were performed in a disordered optical lattice to explore the disordered Hubbard model. These experiments reveal localization in the presence of strong interactions and an interaction driven metal-to-insulator transition. The localized state is found to be insensitive to a doubling in the temperature of the gas and is consistent with predictions of many-body localization.
Abstract We discuss effects of anisotropic scattering in transport properties of ultracold atoms in three-dimensional optical potentials. Within the realm of the first Born approximation, we calculate the self energy, the scattering mean free time, the scattering mean free path, and the anisotropy factor. The behavior of the diffusion constant as a function of the wavenumber is also examined in diffusive and weak localization regimes. We show that these quantities are affected by quantum corrections due to the interference caused by disorder. The dimensionless conductance is evaluated using the scaling theory of localization. Our results are compared with previous theoretical and the experimental results.
We report on the impact of variable-scale disorder on 3D Anderson localization of a noninteracting ultracold atomic gas. A spin-polarized gas of fermionic atoms is localized by allowing it to expand in an optical speckle potential. Using a sudden quench of the localized density distribution, we verify that the density profile is representative of the underlying single-particle localized states. The geometric mean of the disordering potential correlation lengths is varied by a factor of 4 via adjusting the aperture of the speckle focusing lens. We observe that the root-mean-square size of the localized gas increases approximately linearly with the speckle correlation length, in qualitative agreement with the scaling predicted by weak scattering theory.
We report on the measurement of the spectral functions of noninteracting ultracold atoms in a three-dimensional disordered potential resulting from an optical speckle field. Varying the disorder strength by 2 orders of magnitude, we observe the crossover from the "quantum" perturbative regime of low disorder to the "classical" regime at higher disorder strength, and find an excellent agreement with numerical simulations. The method relies on the use of state-dependent disorder and the controlled transfer of atoms to create well-defined energy states. This opens new avenues for experimental investigations of three-dimensional Anderson localization.