The overall, loaded quality factor QL quantifies the loss of energy stored in a resonator. Here we discuss on general grounds how QL of a planar microwave resonator made of a conventionalsuperconductor should depend on temperature and frequency. We consider contributions to QL due to dissipation by thermal quasiparticles (QQP), due to residual dissipation (QRes), and due to coupling (QC). We present experimental data obtained with superconducting stripline resonators fabricated from lead (Pb), with different center conductor widths and different coupling gaps. We probe the resonators at various harmonics between 0.7 GHz and 6 GHz and at temperatures between 1.5 K and 7 K. We find a strongly frequency- and temperature-dependent QL, which we can describe by a lumped-element model. For certain resonators at lowest temperatures we observe a maximum in the frequency-dependent QL when QRes and QC match, and here the measured QL can exceed 2×105.
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 ESR-active materials, lead to characteristic signatures in the various resonance modes, depending on the local strength of the electric or magnetic microwave fields.
We present an experimental approach for cryogenic dielectric measurements on ultra-thin insulating films. Based on a coplanar microwave waveguide design we implement superconductingquarter-wave resonators with inductive coupling, which allows us to determine the real part ε1 of the dielectric function at GHz frequencies and for sample thicknesses down to a few nm. We perform simulations to optimize resonator coupling and sensitivity, and we demonstrate the possibility to quantify ε1 with a conformal mapping technique in a wide sample-thickness and ε1-regime. Experimentally we determine ε1 for various thin-film samples (photoresist, MgF2, and SiO2) in the thickness regime of nm up to μm. We find good correspondence with nominative values and we identify the precision of the film thickness as our predominant error source. Additionally we demonstrate a measurement of ε1(T) vs. temperature for a SrTiO3 bulk sample, using an in-situ reference method to compensate for the temperature dependence of the superconducting resonator properties.