We examine the transmission through nonideal microwave resonant circuits. The general analytical resonance line shape is derived for both inductive and capacitive coupling with mismatched input and output transmission impedances, and it is found that for certain non-ideal conditions the line shape is asymmetric. We describe an analysis method for extracting an accurate internal quality factor (Q i ), the Diameter Correction Method (DCM), and compare it to the conventional method used for millikelvin resonator measurements, the φ Rotation Method (φRM). We analytically find that the φRM deterministically overestimates Q i when the asymmetry of the resonance line shape is high, and that this error is eliminated with the DCM. A consistent discrepancy between the two methods is observed when they are used to analyze both simulations from a numerical linear solver and data from asymmetric coplanar superconducting thin-film resonators.

Tunneling two level systems (TLS), present in dielectrics at low temperatures, have been recently studied for fundamental understanding and superconducting device development. According to a recent theory by Burin et al., the TLS bath of any amorphous dielectric experiences a distribution of Landau-Zener transitions if exposed to simultaneous fields. In this experiment we measure amorphous insulating films at millikelvin temperatures with a microwave field and a swept electric field bias using a superconducting resonator. We find that the maximum dielectric loss per microwave photon with the simultaneous fields is approximately the same as that in the equilibrium state, in agreement with the generic material theory. In addition, we find that the loss depends on the fields in a way which allows for the separate extraction of the TLS bath dipole moment and density of states. This method allows for the study of the TLS dipole moment in a diverse set of disordered films, and provides a technique for continuously inverting their population.In quantum computing, two-level systems (TLS) in dielectrics have been found to function as an environmental bath for superconducting quantum elements 1-4 and as quantum memory bits in a hybrid quantum computer 5 . The environmental impact of the deleterious bath has led to improved materials 6-8 for superconducting qubits. In recent qubit designs 9,10 the geometrical architecture allows only for a small amount of electrical energy storage in the deleterious amorphous metal oxides. Over four decades ago, a now standard model of TLS was introduced which describes charged nanoscale systems moving independently in a distribution of double well potentials, presumably created by undercoordinated bonds 11,12 . Recent measurements of individual TLSs under application of a strain field are in agreement with this model 13 . Although the TLS effects are generally known, the precise identity of the atomic defects or bonds that comprise the TLS and dipole moments from a given material are generally not known [14][15][16] . Furthermore, it was found that the sudden application of strain or electric fields can result in an immediate change in the TLS density, followed by a slow glassy relaxation to the equilibrium state 17-19 , possibly caused by weak TLS-TLS interactions 20,21 .In the case of resonant microwave measurements, the loss tangent is proportional to the weighted TLS densitythe TLS density times the dipole moment squared. Experiments on individual TLS provide important quantum properties 5,22-24 , but have previously been restricted to an alumina tunneling barrier and must characterize many TLS, one at a time, in order to extract an average dipole moment of the film. The Landau-Zener effect has been used to study a wide variety of qubit systems, including superconducting circuits 25-27 , silicon-dopants 28 , and quantum dots 29 . A recent theory using this effect predicts that TLS can be characterized using the quantum dynamics created by two simultaneous fields 30 . Experimental real...

We have fabricated and measured Josephson junction defect spectrometers (JJDSs), which are frequency-tunable, nearly-harmonic oscillators that probe strongly-coupled two-level systems (TLSs) in the barrier of a Josephson junction (JJ). The JJDSs accommodate a wide range of junction inductances, $L_{J}$, while maintaining a resonance frequency, $f_{0}$, in the range of 4-8 GHz. By applying a magnetic flux bias to tune $f_{0}$, we detect strongly-coupled TLSs in the junction barrier as splittings in the device spectrum. JJDSs fabricated with a via-style Al/thermal AlOx/Al junction and measured at 30 mK with single-photon excitation levels show a density of TLSs in the range $\sigma_{TLS}h = 0.4-0.5 /GHz {\mu}m^2$, and a junction loss tangent of $\tan \delta_{J} = 2.9x10^{-3}$.Comment: 4 pages, 3 figure