Modelling magnetically-levitated superconducting ellipsoids, cylinders and cuboids for quantum magnetomechanics

We theoretically investigate the properties of magnetically-levitated superconducting rotors confined in anti-Helmholtz traps, for application in magnetomechanical experiments. We study both the translational modes and a librational mode. The librational mode gives an additional degree of freedom that levitated spheres do not have access to. We compare rotors of different shapes: ellipsoids, cylinders and cuboids. We find that the stable orientations of the rotors depend on the rotors' aspect ratios.