Power Dependent Resonant Frequency of a Microwave Cavity Due to Magnetic Levitation

The fact that a magnet levitates above a superconductor is a fascinating consequence of the interaction between electromagnetic fields and the macroscopic quantum state of the superconductor. Such field-matter interactions, which include the Meissner and Josephson effects, combined with superconducting devices, such as low-loss superconducting microwave cavities, are emerging as key elements used in quantum computers. One technique that can be used to monitor the levitation of a magnet is to place the magnet within a superconducting microwave cavity and monitor the microwave resonance of that cavity. Here, we report measurements of the change in resonance frequency of the microwave cavity with the Meissner-levitated permanent magnet. The cavity resonance changes because the magnet perturbs the radio-frequency field inside the microwave cavity. The changes in resonant frequency and quality factor were measured as functions of input power and temperature. The observed power-dependent variations are explained in terms of the power dependence of the London penetration depth.