We describe a unified quantum approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. We also generalize the method to a chain of resonators with time delays, and reveal several transport properties similar to a photonic crystal. It is shown that both the quantum and classical analyses provide consistent results, and they together reveal different decay and decoherence mechanisms in a general microwave resonator. These results form a solid basis for understanding the scattering spectrums of networks of microwave resonators, and pave the way for applying superconducting microwave resonators in complex circuits.
@article{arxiv.2109.07766,
title = {The scattering coefficients of superconducting microwave resonators: II. System-bath approach},
author = {Qi-Ming Chen and Matti Partanen and Florian Fesquet and Kedar E. Honasoge and Fabian Kronowetter and Yuki Nojiri and Michael Renger and Kirill G. Fedorov and Achim Marx and Frank Deppe and Rudolf Gross},
journal= {arXiv preprint arXiv:2109.07766},
year = {2022}
}