Elastic Scattering Time of Matter Waves in Disordered Potentials

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 $k l_{s} \sim 1$ . 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.

J. Richard, L.-K. Lim, V. Denechaud, V.V Volchkov, B. Lecoutre, M. Musawwadah, F. Jendrzejewski, A. Aspect, A. Signoles, L. Sanchez-Palencia, and V. Josse.
Phys. Rev. Lett. 122, 100403 (2019) https://doi.org/10.1103/PhysRevLett.122.100403

Some other recent works from this team:
– Ultracold atoms in disordered potentials: elastic scattering time in the strong scattering regime.
A. Signoles, B. Lecoutre, J. Richard, L.-K. Lim, V. Denechaud, V. V Volchkov, V. Angelopoulou, F. Jendrzejewski, A. Aspect, and L. Sanchez-Palencia; New J. Phys. 21 105002 (2019) https://doi.org/10.1088/1367-2630/ab466f
– Twofold correlation spreading in a strongly correlated lattice Bose gas.
J. Despres, L. Villa, and L. Sanchez-Palencia
Scientific Reports 9, 4135 (2019) https://doi.org/10.1038/s41598-019-40679-3
– Critical behavior and fractality in shallow one-dimensional quasi-periodic potentials.
H. Yao, H. Khouldi, L. Bresque, and L. Sanchez-Palencia
Physical Review Letters 123, 070405 (2019) https://doi.org/10.1103/PhysRevLett.123.070405

Elastic scattering and Born approximation. (a) Scattering of a matter wave by a laser speckle disordered potential of typical correlation length $σ$ . During a scattering event, which happens on the characteristic time $τ_{s}$ , a momentum $k_{dis}$ is transferred to the initial momentum $k_{i}$ . In the Born approximation, the final momentum $k^{'} = k_{i} + k_{dis}$ lies on the elastic scattering ring (dotted circle). For positive atom-light detuning $Δ > 0$ , the laser speckle potential is repulsive. Inset: for $Δ < 0$ , it is attractive, having identical spatial properties but opposite amplitude distribution. (b) Illustrations of the 2D-momentum distributions $n (k, t)$ after a typical time $τ_{s}$ (1st row: side view, 2nd row: top view) for the isotropic ( $k_{i} ≪ σ^{- 1}$ ) and forward ( $k_{i} ≫ σ^{- 1}$ ) scattering regimes.