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arXiv:2303.15914 · AIP Advances

Characterization of harmonic modes and parasitic resonances in multi-mode superconducting coplanar resonators

Cenk Beydeda, Konstantin Nikolaou, Marius Tochtermann, Nikolaj G. Ebensperger, Gabriele Untereiner, Ahmed Farag, Philipp Karl, Monika Ubl, Harald W. Giessen, Martin Dressel, Marc Scheffler

Published Oct 1, 2023• 3 citations

Abstract

Planar superconducting microwave transmission line resonators can be operated at multiple harmonic resonance frequencies. This allows covering wide spectral regimes with high sensitivity, as it is desired, e.g., for cryogenic microwave spectroscopy. A common complication of such experiments is the presence of undesired “spurious” additional resonances, which are due to standing waves within the resonator substrate or housing box. Identifying the nature of individual resonances (“designed” vs “spurious”) can become challenging for higher frequencies or if elements with unknown material properties are included, as is common for microwave spectroscopy. Here, we discuss various experimental strategies to distinguish designed and spurious modes in coplanar superconducting resonators that are operated in a broad frequency range up to 20 GHz. These strategies include tracking resonance evolution as a function of temperature, magnetic field, and microwave power. We also demonstrate that local modification of the resonator, by applying minute amounts of dielectric or electron spin resonance-active materials, leads to characteristic signatures in the various resonance modes, depending on the local strength of the electric or magnetic microwave fields.

DOI: 10.1063/5.0152461

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We performed transmission spectroscopy experiments on coplanar half-wavelength niobium resonators at temperature

T=4.2\phantom{\rule{0.16em}{0ex}}

K. We observe not only a strong dependence of the quality factor

Q

and the resonance frequency

{f}_{\mathrm{res}}

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.

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The electromagnetic environment can have a significant effect on the resonant line-shape and loadedQ-factor of superconducting coplanar waveguides in the low temperature (<; 100 mK) and low microwave power regime. Here, electromagnetic simulations are used to visualize the electric field strength throughout the resonator environment, highlighting situations in which parasitic modes lead to increased dissipation. Methods used to suppress parasitic coupling include increasing the density of wire bonds and vias, reducing the width of the transmission line (whilst maintaining the characteristic impedance at 50 Ω) and establishing strong grounding to the sample enclosure. The effect of reducing the parasitic coupling on the microwave transmission spectrum is reported.