Characterization of magnetic levitation within a microwave cavity

A mechanical coupling within a microwave cavity shows rich physics from the test of fundamental physics to semi-classical to quantum to novel physics. Such coupling to the levitated mechanical oscillator is promising for reducing losses that come about from clamping and reduced thermal contact. We experimentally, theoretically, and analytically characterized Meissner-effect levitation within a 10 GHz superconducting aluminum coaxial quarter-wave stub cavity for a sequence of identically shaped millimeter-scale neodymium magnets having varying strengths (1.22-1.47 T). In the microwave spectra collected from 5 K (well above the transition temperature of aluminum) to 50 mK (base temperature of the dilution refrigerator), we observed shifts in the spectra corresponding with the change in the total quality factor of the cavity. A large change in the resonance frequency with height, exhibiting a sensitivity as large as 400 MHz/mm and a sharp rise in the quality factor of 8%-17%, is observed during magnetic levitation. There is an excellent agreement between our experimental measurements and the expected results from a circuit model for the system. 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 as a function of temperature which is attributable to magnet movement within the cavity.