Coupling-induced microwave transmission transparency with quarter-wavelength superconducting resonators

The electromagnetic induced transparency (EIT) to atomic systems and its various applications have beenextensively investigated, both theoretically and experimentally. In this paper, we study how to similarly verify these phenomena in the waveguide coupled to the transmission line resonators. By making use of real spacequantum scattering theory, we calculate the transmission spectrum of the waveguide photons scattered by a single quarter-wavelength transmission line resonator. Our experimental results show that the resonantmicrowave transporting along the feedline is completely reflected by the resonator. This is similar to the situation of the light absorbed by the resonant atomic medium, and thus its transmission is significantly suppressed. Like the EIT phenomena in atomic gas, wherein the resonant absorption can be significantly suppressed by applying a strong pumping light to control the optical properties of medium, the transport properties of theresonant microwave can be investigated by coupling it into an auxiliary quarter-wavelength resonator in this paper. If the frequency of the auxiliary quarter-wavelength resonator is different from the resonant frequency ,the calculated transmission spectrum shows that the coupling with auxiliary quarter-wavelength resonatorinduces the complete transmission of the resonant microwave. This is one of the features of the EIT-like effect,and can be simply explained as the frequency renormalization of the coupling resonators. Also, by adjusting thecoupling strength between the resonators, the width of the microwave transmission spectrum window can bemanipulated. Our experimental observations verify such an argument, but the phase shift mutation (anothertypical signs of the EIT effect) of the resonant microwave cannot be observed. In physics, this is because the interference between the transmitted microwave and the reflected micowave with different frequencies does not take place in the coupling region between the two resonators. It is expected that the effects with the complete EIT-like phenomena can be observed, in future, by fabricating the sample of two quarter-wavelength transmission line resonators with the same frequency, and thus the coupling between the two resonators can be controlled.