Vortex patterns in rotating dipolar Bose-Einstein condensate mixtures with squared optical lattices

Vortex-lattice patterns with transitions from regular to other variety vortex shapes are predicted in rotating binary mixtures of dipolar Bose-Einstein condensates loaded in squared optical lattices (OLs). We focus our investigation on the experimentally accessible dipolar isotopes of dysprosium (Dy-162,Dy-164), erbium (Er-168), chromium (Cr-52), and rubidium (Rb-87), by considering the binary mixtures (Dy-164-Dy-162, Er-168-Dy-164, Dy-164-Cr-52 and Dy-164-Rb-87), which are confined in strong pancake-shaped traps and loaded in squared two-dimensional (2D) OLs, where we vary the polarization angle of the dipoles, the inter-species contact interactions and the rotation frequency. The ratio between inter- to intra-species contact interaction is used for altering the miscibility properties, with the polarization of the dipolar species used for tuning the dipole-dipole interactions to repulsive or attractive. For enough higher rotation, where the inter- to intra-species scattering length ratio is larger than one, in which a richer variety of vortex-lattice patterns are predicted, including vortex sheets and 2D rotating droplet formations. The patterns can be controlled by changing the OL parameters, as shown for the symmetric Dy-164-Dy-162 dipolar mixture. For mixtures with stronger differences in the dipole moments, such as Dy-164-Cr-52 and Dy-164-Rb-87, only half the quantum vortices and circular ones have been observed, which will depend on the dipole orientations.