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arXiv:1911.09429 · Chaos Solitons & Fractals

Effects of weak disorder on two-dimensional bilayered dipolar Bose–Einstein condensates

Abdelâali Boudjemâa, Redaouia Keltoum

Published Nov 26, 2019• 5 citations
arXivHTMLPDF
DOI
10.1016/j.chaos.2019.109543

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We investigate the combined effects of weak disorder and a two-dimensional (2D) optical lattice on the collective excitations of a harmonically trapped Bose-Einstein condensate (BEC) at zero temperature. Accordingly, we generalize the hydrodynamic equations of superfluid for a weakly interacting Bose gas in a 2D optical lattice to include the effects of weak disorder. Our analytical results for the collective frequencies beyond the mean-field approximation reveal the peculiar role of disorder, interplaying with the 2D optical lattice and interatomic interaction, on elementary excitations along the 3D to 1D crossover. In particular, consequences of disorder on the phonon propagation and surface modes are analyzed in detail. The experimental scenario is also proposed.
We investigate a Bose-Einstein condensate (BEC) trapped in a two-dimensional optical lattice in the presence of weak disorder within the framework of the Bogoliubov theory. In particular, we analyze the combined effects of disorder and an optical lattice on quantum fluctuations and superfluid density of the BEC system. Accordingly, the analytical expressions of the ground-state energy and quantum depletion of the system are obtained. Our results show that the lattice still induces a characteristic three-dimensional (3D) to one-dimensional crossover in the behavior of quantum fluctuations, despite the presence of weak disorder. Furthermore, we use the linear response theory to calculate the normal fluid density of the condensate induced by disorder. Our results in the 3D regime show that the combined presence of disorder and lattice induce a normal fluid density that asymptotically approaches 4/3 of the corresponding condensate depletion. Conditions for possible experimental realization of our scenario are also proposed.