Collective localization transitions in interacting disordered and quasiperiodic Bose superfluids

Samuel Lellouch 1
1 Laboratoire Charles Fabry / Optique atomique
LCF - Laboratoire Charles Fabry
Abstract : In this thesis, we theoretically investigate the collective localization properties of weakly-Interacting Bose superfluids subjected to disordered or quasiperiodic potentials. While disorder has been recognized since Anderson to induce single-Particle localization, the interplay between disorder and interactions in quantum systems is today among the most challenging questions in the field, and underlies fascinating phase transitions and non-Trivial localization effetcs. Focusing on Bose gases in the weakly-Interacting regime for which the Bogoliubov theory proves a successful tool, we study the localization transitions of collective excitations in several contexts. First, in the case of a continuous true disorder, we develop a strong-Disorder formalism going beyond previous studies, providing us with a complete description of the localization behaviour of collective excitations in arbitrary dimension. A generic localization diagram is obtained and the transport of excitations in the disorder is microscopically interpreted. Secondly, we consider the case of one-Dimensional quasiperiodic potentials, which are known to display intermediate properties between periodic and disordered ones. We perform a numerical and analytical treatment of the localization problem of collective excitations, allowing us to quantitatively characterize and interpret the localization transition in terms of an effective multiharmonic problem. Finally, we set up the general inhomogeneous formalism to address such issues in multicomponent Bose gases, and enlighten the basic physic of such systems, which are known to exhibit their own specific features.
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Samuel Lellouch. Collective localization transitions in interacting disordered and quasiperiodic Bose superfluids. Optics [physics.optics]. Institut d’Optique Graduate School, 2014. English. ⟨NNT : 2014IOTA0017⟩. ⟨tel-01127165⟩

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