Superfluid-insulator transition of two-dimensional disordered Bose gases

We study the two-dimensional weakly repulsive Bose gas at zero temperature in the presence of correlated disorder. Using large-scale simulations, we show that the low-energy Bogoliubov cumulative density of states remains quadratic up to a critical disorder strength, beyond which a power law with disorder-dependent exponent $\beta<2$ sets in. We associate this threshold behavior with the transition from superfluid to Bose glass, and compare the resulting mean-field phase diagram with scaling laws and the Thomas-Fermi percolation threshold of the mean-field density profile.Comment: Published version, 5 pages, 4 figure

Anderson localization of Bogoliubov excitations on quasi-1D strips

Anderson localization of Bogoliubov excitations is studied for disordered lattice Bose gases in planar quasi-one-dimensional geometries. The inverse localization length is computed as function of energy by a numerical transfer-matrix scheme, for strips of different widths. These results are described accurately by analytical formulas based on a weak-disorder expansion of backscattering mean free paths.Comment: 4 pages, 2 figure

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 > \sigma_R the localization is exponential, and for \xi < \sigma_R it changes to algebraic.Comment: published versioon (no significant change compared to last version

Extracting partial decay rates of helium from complex rotation: autoionizing resonances of the one-dimensional configurations

Partial autoionization rates of doubly excited one-dimensional helium in the collinear Zee and eZe configuration are obtained by means of the complex rotation method. The approach presented here relies on a projection of back-rotated resonance wave functions onto singly ionized $\textrm{He}^{+}$ channel wave functions and the computation of the corresponding particle fluxes. In spite of the long-range nature of the Coulomb potential between the electrons and the nucleus, an asymptotic region where the fluxes are stationary is clearly observed. Low-lying doubly excited states are found to decay predomintantly into the nearest single-ionization continuum. This approach paves the way for a systematic analysis of the decay rates observed in higher-dimensional models, and of the role of electronic correlations and atomic structure in recent photoionization experiments

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

Anderson localization of Bogolyubov quasiparticles in disordered Bose-Einstein condensates

séminaireSeminar of the Institute for Quantum Optics and Quantum Information (Innsbruck, Austria

Gaz de bosons ultra-froids dans des potentiels désordonnés : excitations collectives et effets de localisation

In this thesis, we theoretically investigate the localization properties of weakly-interacting Bose gases in the presence of one-dimensional disorder. We focus on three aspects of those disordered systems. First, we study the case of a non-interacting gas. According to general results, all single-particle states are localized in one dimension. We show that for certain classes of correlated disorder, the dependence of the localization length of the atoms on their energy undergoes sharp crossovers for weak disorder. These findings allow for the interpretation of recent experiments beyond previous analyses. Then, we examine the ground state of an interacting gas, and establish a diagram of the quantum states as a function of the strength of disorder and interactions. We analyze the density modulations imposed on the gas by the disorder, in order to describe the crossover from the regime of delocalized Bose-Einstein condensate to the regime of fragmented condensate. For the regime of very weak interactions, we develop a microscopic description of the system on the basis of the eigenstates of the single-particle Hamiltonian. These results contribute to characterizing the Bose-glass phase at weak interactions, which has yet to be explored thoroughly. Finally, we study the localization of the elementary excitations of the Bose gas in the (quasi-) condensate regime. We show that the suppressed localization of the excitations of lowest energy is due to an efficient screening by the (quasi-) condensate of the long-wavelength variations of the external potential.Ce mémoire présente une étude théorique des propriétés de localisation de gaz de Bose avec interactions faibles, en présence de désordre uni-dimensionnel. Nous abordons trois aspects de ces systèmes désordonnés. En premier lieu, nous étudions le cas d'un gaz sans interactions. Des résultats généraux stipulent que tous les états à une particule sont localisés en une dimension. Nous montrons que pour certaines classes de désordre corrélé, la dépendance de la longueur de localisation des atomes vis-à-vis de leur énergie est marquée par d'abruptes transitions à faible désordre. Ceci permet l'interprétation de résultats expérimentaux récents, au-delà des analyses précédentes. Dans un deuxième temps, nous étudions l'état fondamental d'un gaz avec interactions répulsives, et établissons un diagramme des états quantiques du système en fonction de l'amplitude du désordre et des interactions. Nous analysons les modulations de densité imposées au gaz par le désordre afin de décrire le passage du régime de condensat de Bose-Einstein délocalisé à celui de condensat fragmenté. Pour le régime des très faibles interactions, nous développons une description microscopique du système sur la base des états propres de basse énergie du hamiltonien à une particule. Ces résultats contribuent à la caractérisation de la phase de verre de Bose encore peu explorée aux faibles interactions. Enfin, nous étudions la localisation des excitations élémentaires du gaz de Bose dans le régime de (quasi-) condensat. Nous montrons que la localisation réduite des excitations de plus faible énergie est imputable à un écrantage efficace par le (quasi-) condensat des variations de grande longueur d'onde du potentiel extérieur

Anderson localization of ultracold 1D Bose gases

séminaireSeminar of the Department of Condensed Matter Physics, University of Geneva (Geneva, Switzerland