A new model for characterizing stable magnetic levitation in SRF cavities of non-trivial geometry

The coupling of a levitated magnet’s mechanical oscillations to a radio frequency (RF) mode inside of a superconducting cavity may lay the groundwork for coupling to quantum objects whose states can be probed and controlled, such as magnons or transmons. We have previously reported levitation of a strong, mm-scale neodymium magnet within a cm-scale coaxial microwave resonator. In trying to better understand the behavior of the system, we have developed a finite element model that allows us to calculate the potential energy landscape of the cavity-magnet system. This can be done for a wide array of cavity and magnet specifications as well as any magnet orientation. By identifying the stable points, we can design the cavity such that levitation can be forced in regions of interest, such as regions of maximum electric or magnetic fields. We can also control the system’s sensitivity to the magnet’s motion and approximate the mechanical frequency at which the magnet vibrates about equilibrium. The calculated potential energy landscapes are used, in combination with other geometry-based FEM simulations, in comparison with experimental measurements of the shift in resonance frequency with the motion of the magnet when there is no optical access inside of the cavity at cryogenic temperatures.