We report results for the Thomas-Fermi ground state of a spin-polarized dipolar interacting Bose-Einstein condensate for the case when the external magnetic field B is not orientated parallel to a principal axis but is aligned parallel to a symmetry plane of a harmonic anisotropic trap. For a dipole interaction strength parameter ε D = 0 the release energy of the condensate depends on the trap orientation angle ϑ T between the principal axis e z,T of the trap and the field B. From the quasiclassical Josephson equation of macroscopic quantum physics we determine the low-lying eigenfrequencies of small-amplitude collective modes of the condensate density for various trap frequencies ω a and trap orientation angles ϑ T . For the special case of a spherical harmonic trap with trap frequency ω it is rigorously shown for − 1 2 < ε D < 1 that a pure s-wave symmetry breather excitation of the condensate density exists, that oscillates at a constant frequency s = √ 5ω around the ground-state cloud, despite the well-known fact that the shape of the ground-state cloud of a spin-polarized dipolar condensate is for ε D = 0 not isotropic. For ϑ T = 0 the small-amplitude modes of the particle density with isotropic and quadrupolar symmetry consist of two groups. There exist four modes that are combinations of basis functions, with s-wave, d x 2 -y 2 -and d z 2 -wave, and d xz -wave symmetry, and two modes that are combinations of basis functions with d yz -and d xy -wave symmetry. A characteristic difference in the dependence of the frequencies of these six collective modes on the dipole interaction strength parameter ε D for prolate and oblate harmonic triaxial traps, respectively, is suggested to be used as an experimental method to measure the s-wave scattering length a s of the atoms.

We study center-of-mass oscillations of a dipolar Bose-Einstein condensate in the vicinity of a superconducting surface. We show that the magnetic field of the magnetic dipoles induces eddy currents in the superconductor, which act back on the Bose-Einstein condensate. This leads to a shift of its oscillation frequency and to an anharmonic coupling of the Bose-Einstein condensate with the superconductor. The anharmonicity creates a coupling to one of the collective modes of the condensate that can be resonantly enhanced if the parameters of the condensate are chosen properly. This provides a new physical mechanism to couple a Bose-Einstein condensate and a superconductor, which becomes significant for 52 Cr, 168 Er or 164 Dy condensates in superconducting microtraps.

We study the dynamics of a dipolar Bose-Einstein condensate, like for example a 52 Cr or 164 Dy condensate, interacting with a superconducting surface. The magnetic dipole moments of the atoms in the Bose-Einstein condensate induce eddy currents in the superconductor. The magnetic field generated by eddy currents modifies the trapping potential such that the center-of-mass oscillation frequency is shifted. We numerically solve the Gross-Pitaevskii equation for this system and compare the results with analytical approximations. We present an approximation that gives excellent agreement with the numerical results. The eddy currents give rise to anharmonic terms, which leads to the excitation of shape fluctuations of the condensate. We discuss how the strength of the excitation of such modes can be increased by exploiting resonances, and we examine the strength of the resonances as a function of the center-of-mass oscillation amplitude of the condensate. Finally, we study different orientations of the magnetic dipoles and discuss favorable conditions for the experimental observation of the eddy current effect.