High quality factor coplanar resonators are critical elements in superconducting quantum circuits. We describe the design, fabrication and measurement of stepped impedance resonators (SIRs), which have more compact size than commonly used uniform impedance resonators (UIRs). With properly chosen impedance ratio, SIRs can be much shorter in total length than that of UIRs. Two kinds of designs containing both SIRs and UIRs are fabricated and measured. The power dependence of the extracted internal quality factors (Qi) for all the resonators indicated that SIRs and UIRs had comparable performance at high incident power. However, as the incident power decreased, the internal quality factor of SIRs decreased much slower than that of UIRs. All the SIRs in design I kept near half-million Qi at single-photon level, while the two UIRs on the same chip decreased heavily to less than 2× 10^5 . These results indicate potential advantages of SIRs in quantum computer architectures: they consume less space than UIRs, while perform excellent under single-photon level.
The resonators in design II were measured under a large residual magnetic field. The measured results showed that the internal quality factor of all the SIRs and UIRs were more or less suppressed. Such behavior confirmed that trapped vortices in the coplanar resonators provide another loss channel.
Index Terms—Circuit-QED, coplanar resonator, stepped impedance resonator, superconducting quantum circuit.