Magnet Strength Dependence of Levitated Magnets in a Microwave Cavity

We report on the behavior of a superconducting microwave cavity containing levitated permanent magnets having a range of magnet strengths. By observing the changes in the cavity's loaded quality factor and resonance frequency as functions of temperature and magnet remanence, we gain an understanding of the transient motion of the magnet as well as its steady-state levitation height when the temperature drops below 1 K. Experimental measurements of Meissner-effect levitation within a 10 GHz superconducting aluminum coaxial quarter-wave stub cavity are performed for a sequence of identically shaped millimeter-scale neodymium magnets having varying strengths. Magnet levitation within the cavity is accompanied by both gradual and abrupt shifts in the resonance frequency (with a height sensitivity as large as 400 MHz/mm) as well as changes in the total quality factor (8%-17%) as a function of temperature during the superconducting transition of the aluminum cavity. Prior to magnet motion and levitation, the Q of the cavity changes quadratically with temperature, as expected, as the walls of the cavity undergo the superconducting transition. We observe, however, a deviation from the quadratic trend which is attributable to magnet movement within the cavity. Such an electromechanical system is a transducer between mechanical and microwave oscillators enabling coupling of low-frequency mechanical motion of the magnet to other quantum objects, such as magnons and transmons, which are used for sensing and quantum information processing.