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

We investigate properties of two-dimensional bilayered dipolar Bose condensed gases in a weak random potential with Gaussian correlation at zero temperature. Here the dipoles are oriented perpendicularly to the layers and in parallel/antiparallel configurations. We calculate analytically and numerically the condensate depletion, the one-body density-matrix, and the superfluid fraction in the framework of the Bogoliubov theory. Our analysis not only provides fascinating new results do not exist in the literature but also shows that the intriguing interplay between the disorder, the interlayer coupling and the polarization orientation may lead to localize/delocalize the condensed particles results in the formation of glassy/superfluid phases. For a pure short-range interaction and a vanishing correlation length and a small interlayer distance, we reproduce the seminal results of Huang and Meng. While for a vanishing interlayer distance, our results reduce to the those obtained for single layer systems.