Interaction of a Bose-Einstein condensate and a superconductor via eddy currents

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