This project was dedicated to the study of Anderson localization (AL) using ultra-cold atoms in a well-controlled disorder potential.
Objective 1: The goal was to observe the coherent forward scattering (CFS) and link its appearance to the onset of the AL.
Objective 2: The second objective was to study the Anderson transition in the critical regime, in particular, to precisely measure the energy corresponding to the transition as well as localization lengths and diffusion constants close to transition in order to determine their critical exponents.
Work Package 1
In order to investigate the CFS of ultra-cold atoms in a disordered potential, we implemented a highly anisotropic speckle potential. We launched packets of atoms with well-defined velocities into such a potential in order to study CFS in 1D propagation. Ideally, the anisotropic speckle potential should scatter the atoms either in forward or backward directions, which would lead to a strongly enhanced CFS signal. In the experiments, we observed a non-negligible ‘out-of-the-line’ scattering. Generally, this prevents the localization in 1D, which is a possible reason why no CFS could be observed. We think that uncontrolled stray light formed an additional, weak speckle potential with geometrical properties leading to unwanted scattering outside of the propagation direction. We studied the scattering dynamics of atoms in an anisotropic disorder as a function of the disorder strength and atoms momentum and a publication of the results is in preparation.
Work package 2
As the first deliverable, we implemented a state-selective disorder potential using a near-resonant laser speckle field. Furthermore, we controlled not only the amplitude of the disorder but also its sign, giving access to two completely different disorder configurations. As planed in the Gantt chart, we successfully implemented the coherent state transfer of atoms – a central ingredient for the study of the critical regime. Using coherent transfer of atoms into the state-selective disorder allowed us to study the spectral functions of atoms in disorder, which provide essential information on the energy-momentum relation of particles in complex systems. A paper describing the results has been accepted to PRL as editor's suggestion: V. Volchkov et al. Phys. Rev. Lett. 120, 060404 (2018). Link:
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.060404(s’ouvre dans une nouvelle fenêtre).
The spectral function have been compared to numerical simulations and we found excellent agreement. This is an important result with respect to the second objective of studying the critical regime. It opens the possibility to probe the 3D Anderson transition with an unprecedented resolution compared to earlier experimental attempts.
