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- Bogoliubov Excitations of Inhomogeneous Bose-Einstein Condensates (2010)
- In this thesis, different aspects of interacting ultracold bosons in presence of inhomogeneous external potentials are studied. The first part deals with repulsively interacting Bose-Einstein condensates in speckle disorder potentials. In the Bogoliubov approach, the many-body problem is split into the Gross-Pitaevskii condensate (mean-field) and the Bogoliubov excitations, which are bosonic quasiparticles. The disorder potential causes an imprint in the condensate, which makes the Hamiltonian for the Bogoliubov excitations inhomogeneous. The inhomogeneous Bogoliubov Hamiltonian is the starting point for a diagrammatic perturbation theory that leads to the renormalized Bogoliubov dispersion relation. From this effective dispersion relation, physical quantities are derived, e.g. the mean free path and disorder corrections to the speed of sound and the density of states. The analytical results are supported by a numerical integration of the Gross-Pitaevskii equation and by an exact diagonalization of the disordered Bogoliubov problem. In the second part, Bloch oscillations of Bose-Einstein condensates in presence of time-dependent interactions are considered. In general, the interaction leads to dephasing and destroys the Bloch oscillation. Feshbach resonances allow the atom-atom interaction to be manipulated as function of time. In particular, modulations around zero are considered. Different modulations lead to very different behavior: either the wave packet evolves periodically with time or it decays rapidly. The former is explained by a periodic time-reversal argument. The decay in the other cases can be described by a dynamical instability with respect to small perturbations, which are similar to the Bogoliubov excitations in the first part.