Localization of ultrasound in a three-dimensional elastic network

After exactly half a century of Anderson localization, the subject is more alive than ever. Direct observation of Anderson localization of electrons was always hampered by interactions and finite temperatures. Yet, many theoretical breakthroughs were made, highlighted by finite-size scaling, the self-consistent theory and the numerical solution of the Anderson tight-binding model. Theoretical understanding is based on simplified models or approximations and comparison with experiment is crucial. Despite a wealth of new experimental data, with microwaves, light, ultrasound and cold atoms, many questions remain, especially for three dimensions. Here we report the first observation of sound localization in a random three-dimensional elastic network. We study the time-dependent transmission below the mobility edge, and report ``transverse localization'' in three dimensions, which has never been observed previously with any wave. The data are well described by the self-consistent theory of localization. The transmission reveals non-Gaussian statistics, consistent with theoretical predictions.Comment: Final published version, 5 pages, 4 figure

Dynamics of localization in a waveguide

This is a review of the dynamics of wave propagation through a disordered N-mode waveguide in the localized regime. The basic quantities considered are the Wigner-Smith and single-mode delay times, plus the time-dependent power spectrum of a reflected pulse. The long-time dynamics is dominated by resonant transmission over length scales much larger than the localization length. The corresponding distribution of the Wigner-Smith delay times is the Laguerre ensemble of random-matrix theory. In the power spectrum the resonances show up as a 1/t^2 tail after N^2 scattering times. In the distribution of single-mode delay times the resonances introduce a dynamic coherent backscattering effect, that provides a way to distinguish localization from absorption.Comment: 18 pages including 8 figures; minor correction

Three-dimensional localization of ultracold atoms in an optical disordered potential

We report a study of three-dimensional (3D) localization of ultracold atoms suspended against gravity, and released in a 3D optical disordered potential with short correlation lengths in all directions. We observe density profiles composed of a steady localized part and a diffusive part. Our observations are compatible with the self-consistent theory of Anderson localization, taking into account the specific features of the experiment, and in particular the broad energy distribution of the atoms placed in the disordered potential. The localization we observe cannot be interpreted as trapping of particles with energy below the classical percolation threshold.Comment: published in Nature Physics; The present version is the initial manuscript (unchanged compared to version 1); The published version is available online at http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys2256.htm

Dynamic light diffusion, Anderson localization and lasing in disordered inverted opals: 3D ab-initio Maxwell-Bloch computation

We report on 3D time-domain parallel simulations of Anderson localization of light in inverted disordered opals displaying a complete photonic band-gap. We investigate dynamic diffusion processes induced by femtosecond laser excitations, calculate the diffusion constant and the decay-time distribution versus the strength of the disorder. We report evidence of the transition from delocalized Bloch oscillations to strongly localized resonances in self-starting laser processes.Comment: 4 pages, 5 figure

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

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 . 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 [Phys. Rev. Lett. 98, 210401 (2007)]. The method presented here can be extended to localization of atomic quantum gases in higher dimensions, and with controlled interactions

Controlling waves in space and time for imaging and focusing in complex media

In complex media such as white paint and biological tissue, light encounters nanoscale refractive-index inhomogeneities that cause multiple scattering. Such scattering is usually seen as an impediment to focusing and imaging. However, scientists have recently used strongly scattering materials to focus, shape and compress waves by controlling the many degrees of freedom in the incident waves. This was first demonstrated in the acoustic and microwave domains using time reversal, and is now being performed in the optical realm using spatial light modulators to address the many thousands of spatial degrees of freedom of light. This approach is being used to investigate phenomena such as optical super-resolution and the time reversal of light, thus opening many new avenues for imaging and focusing in turbid medi