Anderson Localization of Matter-Waves
[This is an invited article based on recent work of the authors and their collaborators. -- 2Physics.com]
Authors: Philippe Bouyer and Vincent Josse
Affiliation: Groupe d'Optique Atomique, Laboratoire Charles Fabry, Institut d'Optique Graduate School, Palaiseau, France
How to understand the conducting properties of metals and semiconductors? From the quantum theory of conduction, in which electrons are described as matter waves, we can draw a naïve picture based on the idea that electrons with certain momenta can travel freely through the crystal, while others cannot as they diffract from the periodic structure played by the lattice.
Fifty years ago, Philip Anderson, 1977 Physics Nobel Prize winner, worked out that tiny modifications of the lattice, such as the introduction of impurities or defects, can dramatically modify this behavior : the electron that would move freely inside the solid does not simply diffuse on the defects as expected for classical particles but they can be completely stopped.
On a macroscopic scale, that would be like saying that a few blades of grass scattered haphazardly over a golf course could completely stop a full-speed golf ball in its tracks : this would be a surprising situation, since we all know that small perturbations can only slow the movement of material objects, but can never stop them. In the light of fundamental discoveries made in the 1930s about semi-conductors that led to the invention of the transistor and then to integrated circuits, this phenomenon called 'Anderson Localization' created and is still creating strong interests among physicists.
While theoretical physicists strived to understand its underlying nature and its significance, experimental physicists tried to observe the phenomenon. However, experiments in real materials had to struggle mainly against these two disturbances : residual thermal excitations inside the solid and the unavoidable strong interactions among electrons. For these reasons, even if convincing experiments existed, direct observation of these phenomena for particle matter remained an unattainable goal.
In a recent communication published in Nature, our team of researchers at the Institut d'Optique reported on the direct observation of Anderson localization of matter-waves in a controlled disorder . In our experiment, ultra-cold atoms play the role of electrons. They are chilled to a temperature close to absolute zero (-459.67 degrees Fahrenheit) to generate a Bose-Einstein condensate (BEC), in which all the atoms can be described as a single wave function.
Fig.1: Artist's view of the experimental apparatus. © A. Bernard / P. Bouyer / Institut d'Optique
We allowed these BECs to expand from a small starting spot along a single direction imposed by a laser-induced atomic waveguide. To “simulate” the disordered environment, we created a perfectly controlled disorder by shining laser light through finely ground glass onto the expanding atoms — creating then a random distribution of light and dark regions. Without disorder, the atoms propagate freely, but when disorder is present, all atomic movement stop within a fraction of a second. We then observed the atomic density profile. Its exponential form, characteristic of Anderson Localization (see figure 2 below), is the awaited direct proof that random diffusion of matter can hinder the diffusion process.
Fig. 2: The exponential atomic density profile, in green, reflects the localization of atomic waves. This immobilization is caused by minor optic disorder (represented in blue) which has stopped the movement of free atoms along the red light guide axis. © Vincent Josse / Philippe Bouyer / CNRS
Thanks to the joint effort with the team of theorists in the institute, we were able to prove the high level of accurate control that we have on all parameters in this simple model. Our results indeed show that we do have this level of control, and do not so far reveal any surprising properties. This is compliant with the fact that in 1D, Anderson localisation is rather well understood theoretically.
This is no more the case in 2D and 3D, where the role of interactions, for example, is not fully understood, and hard to calculate. We believe that our work represents a crutial step that can lead to an additional kind of quantum simulator, where, with atoms, we can build experiments with high level of control to "mimic" these complex situations. We want now to simulate these systems. Extending the technique to two and three dimensions, and better controlling interactions, it might be possible to better understand the behavior of real materials. We could experience situations that theory can not currently precisely predict in these complex systems. May be then, in the long run, these simulators can be used to improve semi-conductors devices, such as amorphous silicon-based electronic devices, for example.
Theorists and experimentalists at the Institute of optics involved in the observation of Anderson Localisation: (from L to R) Vincent Josse, Juliette Billy, Jean-Francois Schaff, Philippe Bouyer, Patrick Cheinet, Pierre Lugan, Alain Bernard, Alain Aspect, Ben Hambrecht, Laurent Sanchez-Palencia.
More information can be found in this special webpage on Anderson localization: Link>>.
 "Direct observation of Anderson localization of matter-waves in a controlled disorder”
Juliette Billy, Vincent Josse, Zhanchun Zuo, Alain Bernard, Ben Hambrecht, Pierre Lugan, David Clément, Laurent Sanchez-Palencia, Philippe Bouyer & Alain Aspect,
Nature 453, p891-894 (June 12, 2008). Abstract Link.
 "Condensed-matter physics: Paralysed by disorder"
Daniel A. Steck, Nature, 453, p866 (Jun 12, 2008). Abstract Link.
 "Anderson localization of a non-interacting Bose–Einstein condensate"
Giacomo Roati, Chiara D'Errico, Leonardo Fallani, Marco Fattori, Chiara Fort, Matteo Zaccanti, Giovanni Modugno, Michele Modugno & Massimo Inguscio,
Nature, 453, p895-898 (Jun 12, 2008). Abstract Link.
 "Transport and Anderson localization in disordered two-dimensional photonic lattices"
Tal Schwartz, Guy Bartal, Shmuel Fishman & Mordechai Segev,
Nature, 446, p52-55 (Mar 1, 2007). Abstract Link.