An analysis method for two superconducting resonators with common defects

We report on a novel device consisting of a pair of superconducting circuit resonators with nearly degenerate resonances. The resonators share the same capacitor C which is engineered as an electrical capacitor bridge such that the capacitances for the resonators share the same defects. One of the resonators is made tunable using the nonlinearity of titanium nitride’s kinetic inductance and is current biased, such that the detuning from degeneracy can be controlled. The design allows us to study virtually the same ensemble of atomic-sized two-level tunneling systems (TLSs) coupled to both resonators when degenerate. Slightly off resonance they should be affected by correlated noise but also allow measurement through separate readout lines. In this talk we analyze the device with a new 4 port, 2 resonator scattering theory. This will allow the extraction of two related TLS losses, many resonator couplings related by device symmetry, and an analysis of the noise.