Pierre Lugan

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

In 1958, Anderson predicted the localization of electronic wavefunctions in disordered crystals and the resulting absence of diffusion. It is now recognized that Anderson localization is ubiquitous in wave physics because it originates from the interference between multiple scattering paths. Experimentally, localization has been reported for light waves, microwaves, sound waves and electron gases. However, there has been no direct observation of exponential spatial localization of matter waves of any type. Here we observe exponential localization of a Bose–Einstein condensate released into a one-dimensional waveguide in the presence of a controlled disorder created by laser speckle. We operate in a regime of pure Anderson localization, that is, with weak disorder—such that localization results from many quantum reflections of low amplitude—and an atomic density low enough to render interactions negligible. We directly image the atomic density profiles as a function of time, and find that weak disorder can stop the expansion and lead to the formation of a stationary, exponentially localized wavefunction—a direct signature of Anderson localization. We extract the localization length by fitting the exponential wings of the profiles, and compare it to theoretical calculations. The power spectrum of the one-dimensional speckle potentials has a high spatial frequency cutoff, causing exponential localization to occur only when the de Broglie wavelengths of the atoms in the expanding condensate are greater than an effective mobility edge corresponding to that cutoff. 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.

Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials

We show that the expansion of an initially confined interacting 1D Bose-Einstein condensate can exhibit Anderson localization in a weak random potential with correlation length sigma(R). For speckle potentials the Fourier transform of the correlation function vanishes for momenta k>2/sigma(R) so that the Lyapunov exponent vanishes in the Born approximation for k>1/sigma(R). Then, for the initial healing length of the condensate xi(in)>sigma(R) the localization is exponential, and for xi(in)

Engineering the spatial confinement of exciton-polaritons in semiconductors

We demonstrate three-dimensional spatial confinement of exciton-polaritons in a semiconductor microcavity. Polaritons are confined within a micron-sized region of slightly larger cavity thickness, called mesa, through lateral trapping of their photon component. This results in a shallow potential well that allows the simultaneous existence of extended states above the barrier. Photoluminescence spectra were measured as a function of either the emission angle or the position on the sample. Striking signatures of confined states of lower and upper polaritons, together with the corresponding extended states at higher energy, were found. In particular, the confined states appear only within the mesa region, and are characterized by a discrete energy spectrum and a broad angular pattern. A theoretical model of polariton states, based on a realistic description of the confined photon modes, supports our observations.

Ultracold Bose Gases in 1D Disorder: From Lifshits Glass to Bose-Einstein Condensate

We study an ultracold Bose gas in the presence of 1D disorder for repulsive interatomic interactions varying from zero to the Thomas-Fermi regime. We show that for weak interactions the Bose gas populates a finite number of localized single-particle Lifshits states, while for strong interactions a delocalized disordered Bose-Einstein condensate is formed. We discuss the schematic quantum-state diagram and derive the equations of state for various regimes.

One-Dimensional Anderson Localization in Certain Correlated Random Potentials

We study Anderson localization of ultracold atoms in weak, one-dimensional speckle potentials, using perturbation theory beyond Born approximation. We show the existence of a series of sharp crossovers (effective mobility edges) between energy regions where localization lengths differ by orders of magnitude. We also point out that the correction to the Born term explicitly depends on the sign of the potential. Our results are in agreement with numerical calculations in a regime relevant for experiments. Finally, we analyze our findings in the light of a diagrammatic approach.

Anderson localization of bogolyubov quasiparticles in interacting bose-einstein condensates

We study the Anderson localization of Bogolyubov quasiparticles in an interacting Bose-Einstein condensate (with a healing [corrected] length xi) subjected to a random potential (with a finite correlation length sigma(R)). We derive analytically the Lyapunov exponent as a function of the quasiparticle momentum k, and we study the localization maximum k(max). For 1D speckle potentials, we find that k(max) proportional variant 1/xi when xi>>sigma(R) while k(max) proportional variant 1/sigma(R) when xi<<sigma(R), and that the localization is strongest when xi approximately sigma(R). Numerical calculations support our analysis, and our estimates indicate that the localization of the Bogolyubov quasiparticles is accessible in experiments with ultracold atoms.

Localization of a matter wave packet in a disordered potential

We theoretically study the Anderson localization of a matter wave packet in a one-dimensional disordered potential. We develop an analytical model which includes the initial phase-space density of the matter wave and the spectral broadening induced by the disorder. Our approach predicts a behavior of the localized density profile significantly more complex than a simple exponential decay. These results are confirmed by large-scale and long-time numerical calculations. They shed new light on recent experiments with ultracold atoms and may impact their analysis.

Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder

We study the Anderson localization of Bogoliubov quasiparticles (elementary many-body excitations) in a weakly interacting Bose gas of chemical potential

Superfluid-insulator transition of two-dimensional disordered Bose gases

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Superfluid–insulator transition in weakly interacting disordered Bose gases: a kernel polynomial approach

subjected to a disordered potential