Abstract
We describe a unified quantum approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries, and demonstrate its consistency with the classical approach [Q.-M. Chen et al., Phys. Rev. B 106, 214505 (2022)]. We also generalize the result to a chain of resonators with time delays, and reveal several transport properties similar to a photonic crystal and can be used to design high-quality resonators. These results form a firm theoretical ground for analyzing the scattering coefficients of an arbitrary resonator network. They set a step forward to designing and characterizing superconducting microwave resonators in a complex superconducting quantum circuit.
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