High Impedance Josephson Junction Resonators in the Transmission Line Geometry

In this article we present an experimental study of microwave resonators made out of Josephson junctions. The junctions are embedded in a transmission line geometry so that they increase the inductance per length for the line. By comparing two devices with different input/output coupling strengths, we show that the coupling capacitors, however, add a significant amount to the total capacitance of the resonator. This makes the resonators with high coupling capacitance to act rather as lumped element resonators with inductance from the junctions and capacitance from the end sections. Based on a circuit analysis, we show that the input and output couplings of the resonator are limited to a maximum value of $\omega_r Z_0 /4 Z_r$ where $\omega_r$ is the resonance frequency and $Z_0$ and $Z_r$ are the characteristic impedances of the input/output lines and the resonator respectively.