Vortex lattices in binary Bose-Einstein condensates with dipole-dipole interactions

Abstract

We study the structure and stability of vortex lattices in two-component rotating Bose-Einstein condensates with intrinsic dipole-dipole interactions and contact interactions. To address experimentally accessible coupled systems, we consider $^{164}\mathrm{Dy}\ensuremath{-}^{162}\mathrm{Dy}$ and $^{168}\mathrm{Er}\ensuremath{-}^{164}\mathrm{Dy}$ mixtures, which feature different miscibilities. The corresponding dipole moments are ${\ensuremath{\mu}}_{\mathrm{Dy}}=10{\ensuremath{\mu}}_{\mathrm{B}}$ and ${\ensuremath{\mu}}_{\mathrm{Er}}=7{\ensuremath{\mu}}_{\mathrm{B}}$, where ${\ensuremath{\mu}}_{\mathrm{B}}$ is the Bohr magneton. For comparison we also discuss a case where one of the species is nondipolar. Under a large aspect ratio of the trap, we consider mixtures in the pancake-shaped format, which are modeled by effective two-dimensional coupled Gross-Pitaevskii equations, with a fixed polarization of the magnetic dipoles. Then, the miscibility and vortex-lattice structures are studied by varying the coefficients of the contact interactions (assuming the use of the Feshbach-resonance mechanism) and the rotation frequency. We present phase diagrams for several types of lattices in the parameter plane of the rotation frequency and the ratio of inter- and intraspecies scattering lengths. The vortex structures are found to be diverse for the more miscible $^{164}\mathrm{Dy}\ensuremath{-}^{162}\mathrm{Dy}$ composition, with a variety of shapes, whereas for the less miscible case of $^{168}\mathrm{Er}\ensuremath{-}^{164}\mathrm{Dy}$, the lattice patterns mainly feature circular or square formats.