  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.
