Condensate deformation and quantum depletion of Bose–Einstein condensates in external potentials

Abstract

structural properties. Abstract. The one-body density matrix of weakly interacting, condensed bosons in external potentials is calculated using inhomogeneous Bogoliubov theory. We determine the condensate deformation caused by weak external potentials on the mean-field level. The momentum distribution of quantum fluctuations around the deformed ground state is obtained analytically, and finally the resulting quantum depletion is calculated. The depletion due to the external potential, or potential depletion for short, is a small correction to the homogeneous depletion, validating our inhomogeneous Bogoliubov theory. Analytical results are derived for weak lattices and spatially correlated random potentials, with simple, universal results in the Thomas-Fermi limit of very smooth potentials. 1. Penrose-Onsager criterion and Bogoliubov theory for inhomogeneous condensates The phenomenon of Bose-Einstein condensation (BEC) underlies bosonic superfluidity and thus plays a pivotal role in condensed-matter physics. In recent years, the unique experimental possibilities offered by dilute ultracold atomic gases have triggered a renewed interest in Bose-Einstein condensates. These are loaded into external potentials of a large variety,