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We consider the ground state and the low-lying excitations of dipolarBose-Einstein condensates in a bubble trap, i.e., a shell-shaped sphericallysymmetric confining potential. By means of an appropriate Gaussian ansatz, wedetermine the ground-state properties in the case where the particles interactby means of both the isotropic and short-range contact and the anisotropic andlong-range dipole-dipole potential in the thin-shell limit. Moreover, with theground state at hand, we employ the sum-rule approach to study the monopole,the two-, the three-dimensional quadrupole as well as the dipole modes. We findsituations in which neither the virial nor Kohn's theorem can be applied. Ontop of that, we demonstrate the existence of anisotropic particle densityprofiles, which are absent in the case with repulsive contact interaction only.These significant deviations from what one would typically expect are thentraced back to both the anisotropic nature of the dipolar interaction and thenovel topology introduced by the bubble trap.

Ground state and collective excitations of a dipolar Bose-Einstein condensate in a bubble trap