Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder

Abstract

We numerically study the dynamics of cold atoms in a two-dimensional 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. For low energy, the particles are classically localized due to the absence of a percolating cluster. For high energy, the particles undergo normal diffusion and we show that the diffusion coefficients scale algebraically with the particle energy, with an anisotropy factor which significantly differs from that of the disordered potential. For 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 a 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 agreement with experimental findings. Not only does this work give insights to recent experimental results, but it may also serve interpretation of future experiments searching for deviation from classical diffusion and traces of Anderson localization.

Dynamics of localized waves in one-dimensional random potentials: Statistical theory of the coherent forward scattering peak

“…Its unambiguous experimental observation remains difficult, often controversial, as spurious effects like absorption, dephasing or nonlinear effects should be completely suppressed. At the same time, it should be clearly distinguished from other types of localization, such as the Mott-insulator transition [21] or classical trapping in disconnected classically-allowed regions [22].…”

Anderson localization of matter waves in tailored disordered potentials

“…Then, absence of diffusion and exponential decay of density profiles can hardly be viewed as indisputable proof of AL. For instance, classical localization in some non-percolating media can lead to qualitatively similar effects, for instance in 2D speckle potentials [31]. For any model of disorder however, the classical localization length, defined as the average size of the classically-allowed patches [32], increases with the particle energy.…”

Inelastic Multiple Scattering of Interacting Bosons in Weak Random Potentials

“…1 Note that the localization length in 2D can become infinitely long such that diffusion can be studied on finite spatial and short time scales [35].…”

“…For the latter (time-dependent) scenario not too far from thermal equilibrium, different theoretical studies have extended the early results on the "dirty boson problem" [38,39] using either classical equations of motion [35] or taking the Hartree-Fock and/or Bogoliubov corrections to the Gross-Pitaevskii equation into account [40,41], see also the discussion in Section 2.2.…”

“…Since in the followingΩ + (E 0 ) will only be applied to eigen-states (or the quasi-monochromatic eigen-states alike |i N defined in (35)) ofĤ 0 , we will use the compact terminology of Møller operator for both sides of eq. (49).…”