Matter-Wave Localization in Disordered Cold Atom Lattices

We propose to observe Anderson localization of ultracold atoms in the presence of a random potential made of atoms of another species or spin state and trapped at the nodes of an optical lattice, with a filling factor less than unity. Such systems enable a nearly perfect experimental control of the disorder, while the possibility of modeling the scattering potentials by a set of pointlike ones allows an exact theoretical analysis. This is illustrated by a detailed analysis of the one-dimensional case.

Figure 1

Atoms (“scatterers”) trapped at the nodes of a periodic optical lattice and cooled to the vibrational ground state. The average occupancy is $p$ ($\approx 1/3$ here). The test particle experiences only the delta potential (in black) created by the scatterers and is blind to the periodic optical one (in gray).

Figure 2

The localization constant $\kappa$ as a function of the incoming wave vector $k$, for average occupancies (a) $p=0.9$; (b) $p=0.1$. The coupling constant is $mgb/{\hslash }^2=2.278$. Black solid lines: numerics. Red (grey) thin line: analytical result for $1-p\ll 1$ (a), and $p\ll 1$ (b). Peaks and steps in $\kappa$ marked by arrows in the inset of (a) and in (b), with the corresponding values of $\overline{\theta }$ for (a) and of $kb$ for (b) being rational multiples of $\pi$. Blue (dark gray) line in upper frames of (a),(b): density of states. Dashed lines in (a): $\kappa$ for the periodic case $p=1$.