  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 52Cr, 168Er or 164Dy condensates in superconducting
mircotraps.
