Effective dipole-dipole interactions in multilayered dipolar Bose-Einstein condensates

We propose a two-dimensional model for a multilayer stack of dipolar Bose-Einstein condensates formed by a strong optical lattice. We derive effective intra- and interlayer dipole-dipole interaction potentials and provide simple analytical approximations for a given number of lattice sites at arbitrary polarization. We find that the interlayer dipole-dipole interaction changes the transverse aspect ratio of the ground state in the central layers depending on its polarization and the number of lattice sites. The changing aspect ratio should be observable in time of flight images. Furthermore, we show that the interlayer dipole-dipole interaction reduces the excitation energy of local perturbations, affecting the development of a roton minimum.