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Register a new userInductances and attenuation constant for a thin-film superconducting coplanar waveguide resonator
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John R. Clem
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The geometric, kinetic, and total inductances and the attenuation constant are theoretically analyzed for a thin-film superconducting coplanar waveguide (CPW) resonator consisting of a current-carrying central conductor, adjacent slots, and ground planes that return the current. The analysis focuses on films of thickness $d$ obeying $d < 2lambda$ ($lambda$ is the London penetration depth), for which the material properties are characterized by the two-dimensional screening length $Lambda = 2 lambda^2/d$. Introducing a cut-off procedure that guarantees that the magnitudes of the currents in the central conductor and the ground planes are equal, new and simpler results are obtained for the kinetic inductance and the attenuation constant for small $Lambda$. Exact results for arbitrary $Lambda$ are presented for the geometric, kinetic, and total inductances in the limit of tiny slot widths, and approximate results are presented for arbitrary slot widths.
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We fabricated superconducting coplanar waveguide resonator with leads for dc bias, which enables the ac conductivity measurement under dc bias. The current and the magnetic field dependences of resonance properties were measured, and hysteretic behavior was observed as a function of the dc driving current. The observed shift in the inverse of the quality factor and the center frequency were understood by considering both the motion of vortices and the suppression of the order parameter with dc current. Our investigation revealed that the strongly pinned vortices have little infuluence on the change in the center frequency, while it still affects that of the quality factor. Our results indicate that an accurate understanding of the dynamics of driven vortices is indispensable when we attempt to control the resonance properties with high precision.
We report on the design, fabrication and characterization of superconducting coplanar waveguide resonators with nanoscopic constrictions. By reducing the size of the center line down to 50 nm, the radio frequency currents are concentrated and the magnetic field in its vicinity is increased. The device characteristics are only slightly modified by the constrictions, with changes in resonance frequency lower than 1% and internal quality factors of the same order of magnitude as the original ones. These devices could enable the achievement of higher couplings to small magnetic samples or even to single molecular spins and have applications in circuit quantum electrodynamics, quantum computing and electron paramagnetic resonance.
Thin films of TiN were sputter-deposited onto Si and sapphire wafers with and without SiN buffer layers. The films were fabricated into RF coplanar waveguide resonators, and internal quality factor measurements were taken at millikelvin temperatures in both the many photon and single photon limits, i.e. high and low power regimes, respectively. At high power, internal quality factors ($Q_i$s) higher than $10^7$ were measured for TiN with predominantly a (200)-TiN orientation. Films that showed significant (111)-TiN texture invariably had much lower $Q_i$s, on the order of $10^5$. Our studies show that the (200)-TiN is favored for growth at high temperature on either bare Si or SiN buffer layers. However, growth on bare sapphire or Si(100) at low temperature resulted in primarily a (111)-TiN orientation. Ellipsometry and Auger measurements indicate that the (200)-TiN growth on the bare Si substrates is correlated with the formation of a thin, $approx 2$ nm, layer of SiN during the pre-deposition procedure. In the single photon regime, $Q_i$ of these films exceeded $8times10^5$, while thicker SiN buffer layers led to reduced $Q_i$s at low power.
We have measured noise in thin-film superconducting coplanar waveguide resonators. This noise appears entirely as phase noise, equivalent to a jitter of the resonance frequency. In contrast, amplitude fluctuations are not observed at the sensitivity of our measurement. The ratio between the noise power in the phase and amplitude directions is large, in excess of 30 dB. These results have important implications for resonant readouts of various devices such as detectors, amplifiers, and qubits. We suggest that the phase noise is due to two-level systems in dielectric materials.
We have designed and fabricated superconducting coplanar waveguide resonators with fundamental frequencies from 2 to $9 rm{GHz}$ and loaded quality factors ranging from a few hundreds to a several hundred thousands reached at temperatures of $20 rm{mK}$. The loaded quality factors are controlled by appropriately designed input and output coupling capacitors. The measured transmission spectra are analyzed using both a lumped element model and a distributed element transmission matrix method. The experimentally determined resonance frequencies, quality factors and insertion losses are fully and consistently characterized by the two models for all measured devices. Such resonators find prominent applications in quantum optics and quantum information processing with superconducting electronic circuits and in single photon detectors and parametric amplifiers.
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