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arXiv:1805.05131 · Japanese Journal of Applied Physics

Current and magnetic field dependences of a superconducting coplanar waveguide resonator

Hodaka Kurokawa, Fuyuki Nabeshima, Atsutaka Maeda

Published Feb 11, 2019• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.7567/1347-4065/aafb65

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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.
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.
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 report on the design, fabrication, and characterization of superconducting coplanar waveguide resonators with nanoscopic constrictions. By reducing the size of the center line down to 50 nm, the radio frequency currents are concentrated and the magnetic field in its vicinity is increased. The device characteristics are only slightly modified by the constrictions, with changes in resonance frequency lower than 1% and internal quality factors of the same order of magnitude as the original ones. These devices could enable the achievement of higher couplings to small magnetic samples or even to single molecular spins and have applications in circuit quantum electrodynamics, quantum computing, and electron paramagnetic resonance.
Superconducting microwave resonators based on coplanar waveguides (CPWs), which allow for on-chip implementation, have a wide variety of uses, from the coupling of qubits to the detection of photons from interstellar clouds. With the integration of a bias circuitry, the already versatile resonator will become even more so. However, applying a DC voltage or current bias to the resonator without significantly degrading its quality factor Q is no trivial task. One of the first superconducting microwave resonators with the ability to allow for the application of a DC bias, made use of symmetry points. In order to not rely on those symmetry points, our group came up with a different design that used a shunted capacitor instead. However, this design needs a more extensive and in particular more complicated fabrication process. As the groups focus is now completely away from the original design, we go back in this thesis, to honestly evaluate such a resonator by applying a bias to its center. We present a design with the cavity length l to be a full wavelength (l = λ) terminated on both ends to ground, fed in by a capacitively coupled AC-feedline at λ/4 and a DC-bias line at its center (λ/2). After the first fabrication trial we were unable to successfully judge the performance of the microwave resonator as it suffered from bad internal loss, leading to a low internal Q ~ 300 at 4 K. The only thing that this showed us, is that its design is perhaps not as straightforward. On the other hand, interesting results specific to the design were obtained from QUCS simulations (using a combination of lumped and distributed elements). These simulations showed that the quality of the resonator is highly sensitive to the position of its galvanically connected bias line, with respect to the center of the cavity (voltage node). Where Qint drops down to 10 % of its maximum for < 0.1 mm (= l/320) away from the center. Furthermore, we saw that asymmetry in the ports causes the maximum Qint (voltage node) to be off-center by 9 μm, and that adding an extra feedline in symmetry to the existing one puts it back on-center. Demonstrating the voltage node susceptibility to asymmetries of the cavity mode. Despite the unpromising signs the results show, suggestions have been put forward about better isolation of the bias line that have the potential to still make the design attractive. While these isolations still baring the traits of a faster and less complex fabrication.