Capacitative measurement of an Andreev bound state in a quantum dot coupled to a floating superconducting island

We study the response of a resonator attached to a gate of a floating quantum dot coupled to a superconducting island, defined in an InAs nanowire with an epitaxial Al shell. The reflectometry signal distinguishes between the superconducting island hosting no subgap states and discrete subgap states. In the case of the superconducting island hosting no subgap states, we vary the applied magnetic field and tunnel coupling. The resonance frequency shift and changes in the quality factor at the charge transitions are simulated using a projected numerical renormalization group method, and show good quantitative agreement with the experiment. The established measurement method, as well as the simulation framework, are suitable for the study of devices consisting of multiple superconducting islands and quantum dots, such as Andreev molecules or a Kitaev chain.