Modeling and fabrication of chip-based superconducting traps for levitation of micrometer-sized superconducting particles.

We describe the finite-element modeling and fabrication of chip-based superconducting traps for levitating micrometer-sized superconducting particles. Such experiments promise to lead to a new generation of macroscopic quantum experiments and of force and acceleration sensors. An accurate modeling of the utilized trap architectures is crucial for predicting parameters of the traps, such as trap stability, frequency and levitation height, in realistic situations accounting for the finite extent of the involved superconducting objects. To this end, we apply a modeling method that is applicable to arbitrary superconducting structures in the Meissner state. It is based on Maxwell-London equations in the static regime using the A-V formulation. The modeling allows us to simulate superconducting objects with arbitrary geometry subject to arbitrary magnetic field distributions and captures finite volume effects like magnetic field expulsion. We use this modeling to simulate two chip-based trap architectures: an anti-Helmholtz coil-type trap and a planar double-loop trap. We calculate important parameters of the superconducting traps for the cases of levitating micrometer-sized particles of either spherical, cylindrical or ring shape. We compare our modeling results to analytical test cases for idealized geometries. We also model detection of the motion of the levitated particle by measurement of flux-changes induced in a nearby pick-up loop. We demonstrate the fabrication of these chip-based traps and particles using thin Nb films. Our modeling is generic and has applications beyond the one considered, such as for designing superconducting magnetic shields or for calculating filling factors in superconducting resonators.