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 textit{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.
Two-level system (TLS) defects in dielectrics are known to limit the performance of electronic devices. We study TLS using millikelvin microwave loss measurements of three atomic layer deposited (ALD) oxide films--crystalline BeO ($rm{c-BeO}$), amorp
hous $rm{Al_2O_3}$ ($rm{a-Al_2O_3}$), and amorphous $rm{LaAlO_3}$ ($rm{a-LaAlO_3}$)--and interpret them with room temperature characterization measurements. We find that the bulk loss tangent in the crystalline film is 6 times higher than in the amorphous films. In addition, its power saturation agrees with an amorphous distribution of TLS. Through a comparison of loss tangent data to secondary ion mass spectrometry (SIMS) impurity analysis we find that the dominant loss in all film types is consistent with hydrogen-based TLS. In the amorphous films excess hydrogen is found at the ambient-exposed surface, and we extract the associated hydrogen-based surface loss tangent. Data from films with a factor of 40 difference in carbon impurities revealed that carbon is currently a negligible contributor to TLS loss.
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 $phi$ Rotation Method ($phi$RM). We analytically find that the $phi$RM 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.
