Resonator measurements are a simple but powerful tool to characterize a material’s microwave response. The losses of a resonant mode are quantified by its internal quality factorQi, which can be extracted from the scattering coefficient in a microwave reflection or transmission measurement. Here we show that a systematic error on Qi arises from Fano interference of the signal with a background path. Limited knowledge of the interfering paths in a given setup translates into a range of uncertainty for Qi, which increases with the coupling coefficient. We experimentally illustrate the relevance of Fano interference in typical microwave resonator measurements and the associated pitfalls encountered in extracting Qi. On the other hand, we also show how to characterize and utilize the Fano interference to eliminate the systematic error.
Mesoscopic Josephson junctions (JJs), consisting of overlapping superconducting electrodes separated by a nanometer thin oxide layer, provide a precious source of nonlinearity for superconductingquantum circuits and are at the heart of state-of-the-art qubits, such as the transmon and fluxonium. Here, we show that in a fluxonium qubit the role of the JJ can also be played by a lithographically defined, self-structured granular aluminum (grAl) nano-junction: a superconductor-insulator-superconductor (SIS) JJ obtained in a single layer, zero-angle evaporation. The measured spectrum of the resulting qubit, which we nickname gralmonium, is indistinguishable from the one of a standard fluxonium qubit. Remarkably, the lack of a mesoscopic parallel plate capacitor gives rise to an intrinsically large grAl nano-junction charging energy in the range of 10−100GHz, comparable to its Josephson energy EJ. We measure average energy relaxation times of T1=10μs and Hahn echo coherence times of Techo2=9μs. The exponential sensitivity of the gralmonium to the EJ of the grAl nano-junction provides a highly susceptible detector. Indeed, we observe spontaneous jumps of the value of EJ on timescales from milliseconds to days, which offer a powerful diagnostics tool for microscopic defects in superconducting materials.