Loss Dependence on Geometry and Applied Power in Superconducting Coplanar Resonators

The loss in superconducting microwave resonators at low-photon number and low temperatures is not well understood but has implications for achievable coherence times in superconducting qubits. We have fabricated single-layer resonators with a high quality factor by patterning a superconducting aluminum film on a sapphire substrate. Four resonator geometries were studied with resonant frequencies ranging from 5 to 7 GHz: a quasi-lumped element resonator, a coplanar strip waveguide resonator, and two hybrid designs that contain both a coplanar strip and a quasi-lumped element. Transmitted power measurements were taken at 30 mK as a function of frequency and probe power. We find that the resonator loss, expressed as the inverse of the internal quality factor, decreases slowly over four decades of photon number in a manner not merely explained by loss from a conventional uniform spatial distribution of two-level systems in an oxide layer on the superconducting surfaces of the resonator.Comment: 4 pages, 5 figures, Submitted to ASC 2010 conference proceeding

Universal dielectric loss in amorphous solids from simultaneous bias and microwave field

We derive the ac dielectric loss in glasses due to resonant processes created by two-level systems and a swept electric field bias. It is shown that at sufficiently large ac fields and bias sweep rates the nonequilibrium loss tangent created by the two fields approaches a universal maximum determined by the bare linear dielectric permittivity. In addition this nonequilibrium loss tangent is derived for a range of bias sweep rates and ac amplitudes and show that the loss tangent creates a predicted loss function that can be understood in a Landau-Zener theory and which can be used to extract the TLS density, dipole moment, and relaxation rate.Comment: To appear in Physical Review Letters, 4 pages, 3 figure

Probing Hundreds of Individual Quantum Defects in Polycrystalline and Amorphous Alumina

Quantum two-level systems (TLSs) are present in the materials of qubits and are considered defects because they limit qubit coherence. For superconducting qubits, the quintessential Josephson junction barrier is made of amorphous alumina, which hosts TLSs. However, TLSs are not understood generally -- either structurally or in atomic composition. In this study, we greatly extend the quantitative data available on TLSs by reporting on the physical dipole moment in two alumina types: polycrystalline γ−Al$_2$O$_3$ and amorphous a−AlO$_x$. To obtain the dipole moments p$_z$, rather from the less-structural coupling parameter g, we tune individual TLSs with an external electric field to extract the p$_z$ of the TLSs in a cavity QED system. We find a clear difference in the dipole moment distribution from the film types, indicating a difference in TLS structures. A large sample of approximately 400 individual TLSs are analyzed from the polycrystalline film type. Their dipoles along the growth direction p$_z$ have a mean value of 2.6±0.3 Debye (D) and standard deviation σ = 1.6±0.2 D . The material distribution fits well to a single Gaussian function. Approximately 200 individual TLSs are analyzed from amorphous films. Both the mean p$_z$ =4.6±0.5 D and σ =2.5±0.3 D are larger. Amorphous alumina also has some very large p$_z$, > 8.6 D, in contrast to polycrystalline which has none of this moment. These large moments agree only with oxygen-based TLS models. Based on data and the candidate models (delocalized O and hydrogen-based TLSs), we find polycrystalline alumina has smaller ratio of O-based to H-based TLS than amorphous alumina