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AIP Advances

Cavity and ground effects on a superconducting microstrip resonator

Wei-Tao Lv, Jiang‐Qiao Ding, Qiang Zhi, Zheng Wang, Jing Li, Sheng‐Cai Shi

Published Sep 1, 2021• 2 citations
Publisher

Abstract

Superconducting planar-transmission-line resonators play an increasingly important role in applications such as astronomical detection and circuit quantum electrodynamics. When measuring the transmission response of an array of resonators, however, one often observes some spurious resonances besides the intrinsic ones. In this letter, the effect of the cavity accommodating a half-wavelength superconducting microstrip resonator is investigated. An attenuation pole associated with the intrinsic resonance of the half-wavelength resonator is clearly observed and found to be resulted from the mutual coupling between the microstrip resonator and the cavity. In addition, it is demonstrated that adding a superconducting ground layer for such a microstrip resonator can avoid the frequency shift owing to an ever-present thin air gap between the microstrip resonator and the cavity and can also improve the Q factor of the microstrip resonator.

DOI
10.1063/5.0063498

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Superconducting planar-transmission-line resonators play an increasingly important role in applications such as astronomical detection and circuit quantum electrodynamics. When measuring the transmission response of an array of resonators, however, one often observes some spurious resonances besides the intrinsic ones. In this letter, the effect of the cavity accommodating a half-wavelength superconducting microstrip resonator is investigated. An attenuation pole associated with the intrinsic resonance of the half-wavelength resonator is clearly observed and found to be resulted from the mutual coupling between the microstrip resonator and the cavity. In addition, it is demonstrated that adding a superconducting ground layer for such a microstrip resonator can avoid the frequency shift owing to an ever-present thin air gap between the microstrip resonator and the cavity and can also improve the Q factor of the microstrip resonator.
We report our development on design, fabrication and characterization of various superconducting resonators for quantum device applications. The resonators are developed mainly for superconducting qubit implementation in circuit QED structure, but future application will include photon detectors such as microwave kinetic inductance detectors. First we designed and fabricated half-wavelength coplanar waveguide resonators with niobium thin film on a high resistive silicon wafer, with the fundamental frequencies in the range of 1 to 8 GHz. The loaded quality factors are controlled by the coupling capacitors, and the lower bound of the intrinsic quality factor was measured down to 7 mK in the dilution refrigerator. We have also designed quarter-wavelength resonators and lumped LC resonators coupled to a transmission line, and characterized multiple resonators in a single transmission line. For the 3D transmon qubit application, we designed and fabricated a rectangular box resonator with superconducting aluminum. The intrinsic quality factor of the box resonator exceeds three million at 7 mK. We will also present basic results on the integration of a transmon qubit in the superconducting resonator.
The simplest model of nonlinear response of a superconducting thin film is used for modeling the nonlinear phenomena in a superconducting transmission line and a microstrip resonator. The specified characteristic power of the transmission line is suggested to use as a fitting parameter for numerical description of the microstrip line nonlinearity at microwaves. Quantitative agreement of simulated and experimental data has been obtained for the incident power dependent transmission coefficient of a microstrip line section and a high quality microstrip resonator. Numerical results have also been obtained for the power of the third harmonic radiated from the nonlinear resonator.
Investigations into the propagation characteristics, specifically loss and wave velocity, of superconducting coplanar waveguides and microstrip lines were conducted at a 2 mm wavelength. This was achieved through the measurement of on-chip half-wavelength resonators, employing superconductor-insulator-superconductor tunnel junctions as detectors. A continuous wave millimeter wave probe signal was introduced to the chip via a silicon membrane-based orthomode transducer. This setup not only facilitated the injection of the probe signal but also provided a reference path essential for differential measurements. The observed resonance frequencies aligned closely with theoretical predictions, exhibiting a discrepancy of only several percent. However, the measured losses significantly exceeded those anticipated from quasi-particle loss mechanisms, suggesting the presence of additional loss factors. Notably, the measurement results revealed that the tangential loss attributable to the dielectric layer, specifically silicon dioxide, was approximately7±2×10−3{\text{7}\pm \text{2} \times \text{10}^{-\text{3}}}7±2×10−3. This factor emerged as the dominant contributor to overall loss at temperatures around4 K\text{4}\,{\text{K}}4K.
The frequency dependence of the coupling of niobium superconducting transmission lines is measured for frequencies up to and above the superconducting gap frequency. For this purpose superconducting microstrips are integrated in log-periodic planar antennas and the spectral response is measured by means of a Fourier transform spectrometer with 1 μm2 Nb/Al2O3/Nb SIS junctions as detectors. Resonances of microstrips are observed up to 650 GHz, the superconducting gap frequency of niobium, but above that frequency no resonances have been detected. The measured resonance frequencies are in good agreement with a dispersive model for superconducting transmission lines based on the Mattis–Bardeen theory. The radiation coupling is lower than calculated, indicating significant dielectric losses.
The use of a transmission line resonator offers the possibility for different sensor readout methods, e.g. flux qubit and kinetic inductance detectors. Both cases require a high quality factor, Q L , of the cavity circuit to detect small deviations in the resonance frequency. Various superconducting niobium coplanar waveguide resonators of λ/4 and λ/2 wavelength for 3 and 6 GHz were developed. Different layouts for the coplanar resonators were designed, simulated and measured on common silicon and sapphire substrates at 4.2 K. We found a very good agreement between simulation and measurement results, with Q L between 10 4 and 10 5 at helium temperatures. The presented results show the dependences on the chosen cross section geometries, the coupling factor and the complex layout of the transmission line.