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We consider a Bose-Einstein condensate (BEC), which is characterized bylong-range and anisotropic dipole-dipole interactions and vanishing s-wavescattering length, in a double-well potential. The properties of this systemare investigated as functions of the height of the barrier that splits theharmonic trap into two halves, the number of particles (or dipole-dipolestrength) and the aspect ratio $\lambda$, which is defined as the ratio betweenthe axial and longitudinal trapping frequencies $\omega_z$ and $\omega_{\rho}$.The phase diagram is determined by analyzing the stationary mean-fieldsolutions. Three distinct regions are found: a region where the energeticallylowest lying stationary solution is symmetric, a region where the energeticallylowest lying stationary solution is located asymmetrically in one of the wells,and a region where the system is mechanically unstable. For sufficiently largeaspect ratio $\lambda$ and sufficiently high barrier height, the systemconsists of two connected quasi-two-dimensional sheets with density profileswhose maxima are located either at $\rho=0$ or away from $\rho=0$. Thestability of the stationary solutions is investigated by analyzing theBogoliubov de Gennes excitation spectrum and the dynamical response to smallperturbations. These studies reveal unique oscillation frequencies and distinctcollapse mechanisms. The results derived within the mean-field framework arecomplemented by an analysis based on a two-mode model.

Aligned dipolar Bose-Einstein condensate in a double-well potential: From cigar-shaped to pancake-shaped