Direct observation of Anderson localization of matter waves in a controlled disorder

Abstract

In 1958, P.W. Anderson predicted the exponential localization 1 of electronic wave functions in disordered crystals and the resulting absence of diffusion. It has been realized later that Anderson localization (AL) is ubiquitous in wave physics 2 as it originates from the interference between multiple scattering paths, and this has prompted an intense activity. Experimentally, localization has been reported in light waves 3,4,5,6,7 , microwaves 8,9 , sound waves 10 , and electron 11 gases but to our knowledge there is no direct observation of exponential spatial localization of matter-waves (electrons or others). Here, we report the observation of exponential localization of a Bose-Einstein condensate (BEC) released into a one-dimensional waveguide in the presence of a controlled disorder created by laser speckle 12 . We operate in a regime allowing AL: i) weak disorder such that localization results from many quantum reflections of small amplitude; ii) atomic density small enough that interactions are negligible. We image directly the atomic density profiles vs time, and find that weak disorder can lead to the stopping of the expansion and to the formation of a stationary exponentially localized wave function, a direct signature of AL. Fitting the exponential wings, we extract the localization length, and compare it to theoretical calculations. Moreover we show that, in our one-dimensional speckle potentials whose noise spectrum has a high spatial frequency cut-off, exponential localization occurs only when the de Broglie wavelengths of the atoms in the expanding BEC are larger than an effective mobility edge corresponding to that cut-off. In the opposite case, we find that the density profiles decay algebraically, as predicted in ref 13. The method presented here can be extended to localization of atomic quantum gases in higher dimensions, and with controlled interactions.

Localization of correlated fermions in optical lattices with speckle disorder

“…11,12 Thereby a binary disorder potential is realized due to the interatomic interaction; ii) by superimposing two laser beams with incommensurate frequencies, 13,14 thereby generating a stationary quasiperiodic lattice; iii) by using an optical speckle field 15 superimposed onto an optical lattice. 16,17 In general, particles in a disordered lattice are exposed to an on-site potential varying from site to site, which already gives rise to localization due to coherent backscattering.…”

The random mass Dirac model and long-range correlations on an integrated optical platform

“…Disorder effects have been widely investigated in the context of non-relativistic physics, modelled by a Schrödinger equation with a disordered potential and leading to the famous Anderson localization [16][17][18][19][20] . The major difference between non-relativistic and relativistic disordered systems lies in the number of occurring length scales and the nature of the resulting correlations.…”

Lattice bosons in a quasi-disordered environment

“…In two and lower dimensions, all the single particle states are localized by non-zero disorder 2,3 . Anderson localization of matter waves was directly observed in several experiments recently [4][5][6][7] . The localization of all the single particles states in one and two dimensions occurs for random disorder (see also the note in Ref.…”