Many of the static and dynamic properties of an atomic Bose-Einstein condensate (BEC) are usually studied by solving the mean-field Gross-Pitaevskii (GP) equation, which is a nonlinear partial differential equation for short-range atomic interaction. More recently, BEC of atoms with long-range dipolar atomic interaction are used in theoretical and experimental studies. For dipolar atomic interaction, the GP equation is a partial integro-differential equation, requiring complex algorithm for its numerical solution. Here we present numerical algorithms for both stationary and non-stationary solutions of the full threedimensional (3D) GP equation for a dipolar BEC, including the contact interaction. We also consider the simplified one-(1D) and two-dimensional (2D) GP equations satisfied by cigar-and disk-shaped dipolar BECs. We employ the split-step Crank-Nicolson method with real-and imaginary-time propagations, respectively, for the numerical solution of the GP equation for dynamic and static properties of a dipolar BEC. The atoms are considered to be polarized along the z axis and we consider ten different cases, e.g., stationary and non-stationary solutions of the GP equation for a dipolar BEC in 1D (along x and z axes), 2D (in x-y and x-z planes), and 3D, and we provide working codes in Fortran 90/95 and C for these ten cases (twenty programs in all). We present numerical results for energy, chemical potential, rootmean-square sizes and density of the dipolar BECs and, where available, compare them with results of other authors and of variational and Thomas-Fermi approximations. Program summary Program title: (i) imag1dZ, (ii) imag1dX, (iii) imag2dXY, (iv) imag2dXZ, (v) imag3d, (vi) real1dZ, (vii) real1dX, (viii) real2dXY, (ix) real2dXZ, (x) real3d

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We perform a full three-dimensional study on miscible-immiscible conditions for coupled dipolar and non-dipolar Bose-Einstein condensates (BEC), confined in anisotropic traps. In view of recent experimental studies, our focus was the atomic erbium-dysprosium ( 168 Er-164 Dy) and dysprosiumdysprosium ( 164 Dy-162 Dy) mixtures. The miscibility is quantified by the overlap of the twocomponent densities, using an appropriate defined parameter. By verifying that stable regimes for pure-dipolar coupled BECs are only possible in pancake-type traps, we obtain some non-trivial local minimum biconcave-shaped states with density oscillations in both components. For non-dipolar systems with repulsive interactions, we show that immiscible stable configurations are also possible in cigar-type geometries. The main role of the trap aspect ratio and inter-species contact interaction for the miscibility is verified for different configurations, from non-dipolar to pure dipolar systems.

We study the structure and stability of vortex lattices in two-component rotating Bose-Einstein condensates with intrinsic dipole-dipole interactions (DDIs) and contact interactions. To address experimentally accessible coupled systems, we consider 164 Dy-162 Dy and 168 Er-164 Dy mixtures, which feature different miscibilities. The corresponding dipole moments are µDy = 10µB and µEr = 7µB, where µB is the Bohr magneton. For comparison we also discuss a case where one of the species is non dipolar. 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 Feshbachresonance mechanism) and the rotation frequency. We present phase diagrams for several types of lattices in the parameter plane of the rotation frequency and ratio of inter-and intra-species scattering lengths. The vortex structures are found to be diverse for the more miscible 164 Dy-162 Dy mixture, with a variety of shapes, whereas for the less miscible case of 168 Er-164 Dy, the lattice patterns mainly feature circular or square formats. PACS numbers: 67.85.-d, 03.75.-b, 67.85.Fg arXiv:1712.04719v1 [cond-mat.quant-gas]