An Effective Reflection Mode for Hanger Coupled Superconducting Microwave Resonators

Superconducting microwave resonators are frequently used to study two-level system (TLS) loss in superconducting quantum devices. Fano asymmetry — or a nonzero asymmetry angle phi in the diameter correction method (DCM) — generally results from the necessary coupling scheme, introducing an additional fitting parameter which contains no physically interesting information. The underlying cause of this Fano asymmetry is only partially understood, making it difficult to avoid in design. However, the tee-junction symmetry nominally present in these resonator devices provides an avenue for the elimination of Fano asymmetry. We show that the eigenvalue associated with the common mode excitation of the resonator has the same form as an ideal reflection mode response: i.e. this eigenvalue is an effective reflection mode, eliminating the Fano asymmetry from the measurement. Practically, this entails measurements of both reflection and transmission. We explore perturbation theory applied to the coupling network to extend the applicability of this result.