Dresden 2011 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 2: Quantum Gases: Bosons 1

Q 2.4: Talk

Monday, March 14, 2011, 11:15–11:30, HÜL 386

Bogoliubov theory of disordered Bose-Einstein condensates — •Christopher Gaul¹ and Cord A. Müller² — ¹GISC, Departamento de Física de Materiales, Universidad Complutense, E-28040 Madrid, Spain — ²Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore

We describe repulsively interacting Bose-Einstein condensates in spatially correlated disorder potentials of arbitrary dimension. The first effect of disorder is to deform the mean-field condensate. Secondly, the quantum excitation spectrum and condensate population are affected. By a saddle-point expansion of the many-body Hamiltonian around the deformed mean-field ground state, we find the fundamental quadratic Hamiltonian of quantum fluctuations, in a basis where excitations remain always orthogonal to the deformed condensate. Via Bogoliubov-Nambu perturbation theory, we compute the effective excitation dispersion, including the disorder-corrected sound velocity and localization lengths. Finally, we are able to calculate analytically, for the first time and in all dimensions, the true disorder-induced quantum depletion, i.e. the fraction of particles out of the deformed condensate, which is found to depend strongly on the disorder correlation.

C. Gaul and C.A. Müller, arXiv:1009.5448