Frequency spectrum of a superconducting metadevice

We report on a systematic analysis of the frequency spectrum of a system often considered for quantum computing purposes, metadevice applications, and high-sensitivity sensors, namely a superconducting loop interrupted by Josephson junctions, the core of an rf-SQUID. We analyze both the cases in which a single junction closes the superconducting loop and the one in which the single junction is replaced by a superconducting interferometer. Perturbation analysis is employed to display the variety of the solutions of the system and the implications of the results for the present interest in fundamental and applied research are analyzed.