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arXiv:2302.07367 · Physica Scripta

Anisotropy effects on the quantum transport of atomic matter waves

Afifa Yedjour, Abdelâali Boudjemâa

Published Feb 10, 2023• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1402-4896/acbb3c

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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.
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 study quantum transport of matter waves in anisotropic three-dimensional disorder.First, we show that structured correlations can induce rich effects, such as anisotropic suppression of the white-noise limit and inversion of the transport anisotropy.Second, we show that the localization threshold (mobility edge) is strongly affected by a disorder-induced shift of the energy states, which we calculate.Our work is directly relevant to ultracold-matter waves in optical disorder, and implications on recent experiments are discussed.It also offers scope for further studies of anisotropy effects in other systems with controlled disorder, where counterparts of the discussed effects can be expected.
We consider ultracold atoms in 2D disordered optical potentials and calculate microscopic quantities characterizing matter wave quantum transport in the noninteracting regime. We derive the diffusion constant as a function of all relevant microscopic parameters and show that coherent multiple scattering induces significant weak localization effects. In particular, we find that even the strong localization regime is accessible with current experimental techniques and calculate the corresponding localization length.
The development of atom cooling and trapping techniques and the ability to load optical lattices or disordered potentials with Bose-Einstein condensates or degenerate Fermi gases has opened a whole field of research around the strong localization of matter waves. In this theoretical work we study the coherent transport of matter waves evolving in disordered optical potentials (speckle). The influence of correlated disorder is first studied numerically in the framework of the Anderson model. Subsequently, a self-consistent diagrammatic calculation allows us to determine analytically the basic transport parameters in the regime of weak disorder: mean free path, transport mean free path, diffusion constant, localization length. A crucial quantity for these analytical calculations is the spatial correlation function of speckle fluctuations. It determines the degree of anisotropy of a scattering event. We consider in particular the transition from weak localization to strong localization. In this case the diffusion constant of matter waves decreases and approaches zero at the threshold of strong localization. We calculate the renormalization of the diffusion constant due to the interference of matter waves by explicitly considering the correlation of fluctuations of the disordered potential.
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
We report on an extensive study of the elastic scattering time τ_{s} of matter waves in optical disordered potentials. Using direct experimental measurements, numerical simulations, and comparison with the first-order Born approximation based on the knowledge of the disorder properties, we explore the behavior of τ_{s} over more than 3 orders of magnitude, ranging from the weak to the strong scattering regime. We study in detail the location of the crossover and, as a main result, we reveal the strong influence of the disorder statistics, especially on the relevance of the widely used Ioffe-Regel-like criterion kl_{s}∼1. While it is found to be relevant for Gaussian-distributed disordered potentials, we observe significant deviations for laser speckle disorders that are commonly used with ultracold atoms. Our results are crucial for connecting experimental investigation of complex transport phenomena, such as Anderson localization, to microscopic theories.