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The Japan Society of Applied Physics

Current and Magnetic Field Dependence of Resonant Frequency and Quality Factor of the Superconducting Coplanar Waveguide Resonator and its Hysteresis due to the Motion of Vortices

Hodaka Kurokawa, Fuyuki Nabeshima, Atsutaka Maeda

Published Feb 8, 2018• 0 citations
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Abstract We fabricated a superconducting coplanar waveguide resonator with leads for dc bias, which enables an ac conductivity measurement under dc bias. The current and magnetic field dependences of resonance properties were measured, and hysteretic behavior was observed as a function of the dc driving current. The observed shifts in the inverse of the quality factor, Q −1 , and the center frequency, f 0 , were explained by considering both motion of vortices and suppression of the order parameter by the dc current. Our investigation revealed that the strongly pinned vortices have a small influence on f 0 , while they still affect Q −1 . Our results indicate that the accurate understanding of the dynamics of driven vortices is indispensable for a control of the resonance properties with a high precision.
Superconducting coplanar waveguide resonators that can operate in strong magnetic fields are important for a variety of high-frequency superconducting devices. Magnetic fields degrade resonator performance by creating Abrikosov vortices that cause resistive losses and frequency fluctuations, or suppress the superconductivity entirely. To mitigate these effects, the authors investigate how device geometry and lithographically defined artificial defects can control vortex dynamics. These techniques allow the resonators to retain single-photon quality factors of about 105{}^{5}5 at ${B}_{\ensuremath{\parallel}}$ \ensuremath{\simeq} 6 T, for fast charge readout of a gate-defined double quantum dot at ${B}_{\ensuremath{\parallel}}$ = 1 T.
We performed transmission spectroscopy experiments on coplanar half-wavelength niobium resonators at temperature T=4.2T=4.2\phantom{\rule{0.16em}{0ex}}T=4.2K. We observe not only a strong dependence of the quality factor QQQ and the resonance frequency fres{f}_{\mathrm{res}}fres​ on an externally applied magnetic field but also on the magnetic history of our resonators, i.e., on the spatial distribution of trapped Abrikosov vortices in the device. This is valid for a broad range of frequencies and angles between the resonator plane and the magnetic field direction and holds for resonators with and without antidots near the edges of the center conductor and the ground planes. In a detailed analysis, we show that characteristic features of the experimental data can only be reproduced by calculations if we assume a highly inhomogeneous rf current density and a flux density gradient with maxima at the edges of the superconductor. We furthermore demonstrate that the hysteretic behavior of the resonator properties can be used to considerably reduce the vortex-induced losses and to fine-tune the resonance frequency by the proper way of cycling to a desired magnetic field value.