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Bogoliubov Excitations of Disordered Bose-Einstein Condensates

Authors
  • Gaul, Christopher
  • Müller, Cord A.
Type
Published Article
Publication Date
Jan 25, 2011
Submission Date
Jan 25, 2011
Identifiers
DOI: 10.1103/PhysRevA.83.063629
Source
arXiv
License
Yellow
External links

Abstract

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 derive the fundamental quadratic Hamiltonian of quantum fluctuations. Importantly, a basis is used such that excitations are orthogonal to the deformed condensate. Via Bogoliubov-Nambu perturbation theory, we compute the effective excitation dispersion, including mean free paths and localization lengths. Corrections to the speed of sound and average density of states are calculated, due to correlated disorder in arbitrary dimensions, extending to the case of weak lattice potentials.

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