Bogoliubov Excitations of Disordered Bose-Einstein Condensates

Details Bogoliubov Excitations of Disordered Bose-Einstein Condensates Bogoliubov Excitations of Disordered Bose-Einstein Condensates

2011-01-25

arxiv.org/abs/1101.4781v1

Phys. Rev. A 83, 063629 (2011)

Physics

Condensed Matter

Quantum Gases

23 pages, 11 figures

Scientific paper

10.1103/PhysRevA.83.063629

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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