Localization of Bose-Einstein condensates in one-dimensional random potentials

Hochschulschrift

Abstract: Within the present thesis, we investigate, analytically and numerically, the expansion of initially strongly confined wave packets in one-dimensional, correlated random potentials.In the first part, we focus on single-particle wave packets, i. e. without considering interactions between particles. At long times, the expansion of the wave packet comes to a halt due to destructive interferences leading to Anderson localization. The resulting stationary density profile has been measured in experiments on Bose-Einstein condensates in one-dimensional random potentials, but existing theories are unable to explain the behaviour of the density profile at the center. To improve this situation, we develop an analytical description for the disorder averaged localized density profile. For this purpose, we employ the diagrammatic method of Berezinskii, which we generalize to the case of wave packets, present an analytical expression of the localization length which is valid for small as well as for high energies and finally, develop a self-consistent Born approximation in order to analytically calculate the energy distribution of our wave packet. By comparison with numerical simulations, we show that our theory describes well the complete localized density profile, not only in the tails but also in the center.In the second part, we discuss the influence of interactions on the spatial expansion of Bose-Einstein condesates in one-dimensional random potentials. We show, by comparison with numerical data, that the quasi stationary state reached at intermediate times can be well described within the theory developed for the non-interacting case, provided that the interactions are taken into account through the choice of an effective initial state

Angaben zum Objekt

• Standort: Deutsche Nationalbibliothek Frankfurt am Main
• Umfang: Online-Ressource
• Sprache: Englisch
• Anmerkungen: IN COPYRIGHT http://rightsstatements.org/page/InC/1.0 rs ; Albert-Ludwigs-Universität Freiburg, Dissertation, 2017

Klassifikation und Themen

• Klassifikation: Physik

Beteiligte, Orts- und Zeitangaben

• Ereignis: Veröffentlichung
• (wo): Freiburg
• (wer): Universität
• (wann): 2017
• Urheber: Ramírez Valdes, Juan Pablo
• Beteiligte Personen und Organisationen: Wellens, Thomas ; Fakultät für Mathematik und Physik ; Physikalisches Institut ; Albert-Ludwigs-Universität Freiburg

Weitere Informationen

• DOI: 10.6094/UNIFR/12326
• URN: urn:nbn:de:bsz:25-freidok-123266
• Rechteinformation: Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Letzte Aktualisierung: 25.03.2025, 13:52 MEZ