With improved understanding of loss mechanisms in superconducting resonant circuits (SRC), it is possible to design a variety of devices which take advantage of the high Q. Superconducting surface resistance, trapped-flux loss, and residual losses which are annealable can all be related to the superconductor itself. Dielectric dissipation is well enough understood to permit this source of loss to be minimized. Coupling and radiation losses can be made negligible. SRC's are described with a variety of geometries to fill the range from 10 MHz to 10 GHz. Type-I superconductors provide the highest Q's and are readily fabricated by several techniques. The superconducting resonator can be tuned accurately in frequency by temperature control of the surface reactance as well as the dielectric constant of liquid helium. An external magnetic field can be used to tune the bandwidth as well as the resonant frequency. A quarter-wave reentrant cavity is ideally suited for use as an optically tuned frequency-control element. This is accomplished using the photodielectric effect in high-resistivity semiconductor wafers which terminate the stub. Wide-bandwidth optical communication detectors are described using semiconductors with short recombination lifetime. Oscillators have been built which are optically tuned, and others which have frequency stabilities as good as commercial frequency counters. Use of SRC's to study material properties at low temperature is emphasized.
With improved understanding of loss mechanisms in superconducting resonant circuits (SRC), it is possible to design a variety of devices which take advantage of the high Q. Superconducting surface resistance, trapped-flux loss, and residual losses which are annealable can all be related to the superconductor itself. Dielectric dissipation is well enough understood to permit this source of loss to be minimized. Coupling and radiation losses can be made negligible. SRC's are described with a variety of geometries to fill the range from 10 MHz to 10 GHz. Type-I superconductors provide the highest Q's and are readily fabricated by several techniques. The superconducting resonator can be tuned accurately in frequency by temperature control of the surface reactance as well as the dielectric constant of liquid helium. An external magnetic field can be used to tune the bandwidth as well as the resonant frequency. A quarter-wave reentrant cavity is ideally suited for use as an optically tuned frequency-control element. This is accomplished using the photodielectric effect in high-resistivity semiconductor wafers which terminate the stub. Wide-bandwidth optical communication detectors are described using semiconductors with short recombination lifetime. Oscillators have been built which are optically tuned, and others which have frequency stabilities as good as commercial frequency counters. Use of SRC's to study material properties at low temperature is emphasized.
Superconducting quantum devices have gained increasing interest over the past 15 years because of their role as promising candidates for implementing a large-scale quantum computer and as ultra-sensitive detectors. Superconducting resonators are one type of superconducting device which are used in a variety of applications including quantum computing and radioastronomy. They can achieve large quality factors which are important for these applications and a variety of others. Specific examples of these applications include the readout and coupling of superconducting qubits and also microwave kinetic inductance detector arrays for sub-mm wavelength astronomical measurements. High quality factors also enable the study of very subtle features in the electromagnetic response of the resonator. This feature in turn offers provides a method to characterize loss mechanisms which affect the performance of superconducting qubits, by measuring the quality factor of a resonator. Dielectric loss is an example of such a loss mechanism, and is considered to be one of, if not \\it the \\rm major obstacle to overcome in order to construct scalable quantum technologies based on superconducting devices. This type of loss arises from the coupling of the electric field in the device to spurious degrees of freedom which arise naturally the dielectric environment of the device. The fast-growing interest in the physics and applications of superconducting resonators has renewed interest in an improving our fundamental understanding of dielectric loss. This interest involves the study of a much bigger and older question in condensed matter physics; namely, what is the microscopic physics which governs the behaviour and of an amorphous material at low-temperatures? \n \nIn this thesis, we present a systematic study of dielectric loss in amorphous aluminum oxide using superconducting microwave resonators. Measurements of the intrinsic loss tangent over a large temperature range of 40~mK to 1~K are presented and analyzed in detail. Some aspects of the data are well understood in terms of the standard tunnelling two-level system model, while others require a deeper analysis of the electrodynamics of the resonator and insights from more advanced theories. We employ a consistent approach using numerical simulations of the resonator to understand loss mechanisms arising from both an inhomogeneous electric field and multiple dielectric layers. We measure saturation effects which provide insight into coherent properties of two-level system ensembles and the mutual interaction between them. Excellent agreement with the two-level system model is found for intrinsic losses, however the strong dependence on temperature which we observe for saturation effects is not predicted in the standard form of the model. We find that this dependence can be understood in terms of the theory of spectral diffusion which is consistent with a strong mutual interaction between two-level systems contributes to broadening of their spectral linewidths.
The performance of superconducting circuits for quantum computing is limited by materials losses. In particular, coherence times are typically bounded by two-level system (TLS) losses at single photon powers and millikelvin temperatures. The identification of low loss fabrication techniques, materials, and thin film dielectrics is critical to achieving scalable architectures for superconducting quantum computing. Superconducting microwave resonators provide a convenient qubit proxy for assessing performance and studying TLS loss and other mechanisms relevant to superconducting circuits such as non-equilibrium quasiparticles and magnetic flux vortices. In this review article, we provide an overview of considerations for designing accurate resonator experiments to characterize loss, including applicable types of losses, cryogenic setup, device design, and methods for extracting material and interface losses, summarizing techniques that have been evolving for over two decades. Results from measurements of a wide variety of materials and processes are also summarized. Finally, we present recommendations for the reporting of loss data from superconducting microwave resonators to facilitate materials comparisons across the field.
Superconducting qubits are fabricated "loss-free" electrical circuits on a chip with size features of tens of nanometers. If cooled to cryogenic temperatures below -273 °C they behave as quantum elements, similar to atoms and molecules. Such a qubit can be manipulated by fast-oscillating magnetic fields and its resulting quantum state can be measured using a proper magnetic detector. These qubits could be the basic elements for a quantum processor. To that order, multiple qubits have to controllably interact, and to that purpose very high quality resonators are fabricated on the same chip. Effectively the interaction results from the phase-coherent exchange of a single photon between qubit and resonator. In this way it is highly analogous to the so-called cavity QED in atomic physics where single atoms couple to a single trapped photon, all inside a cavity resonator. In this thesis, a superconducting flux qubit has been coupled to an LC resonator and coherent exchange of a single photon between qubit and resonator has been achieved. A striking option in these superconducting circuits, not attainable in "common" atomic cavity-QED, is that the interaction between qubit and photon can be made very large, up to the limit that one no longer can talk about the qubit and resonator as such. This limit requires a fully different description and it leads to novel effects, e.g. in the energy spectrum of the qubit-resonator composite. The Bloch-Siegert spectral shift is experimentally demonstrated in this thesis. As a small but critical technical aside a new type of control line filter has been developed, which allows strong suppression of excess electrical noise that forms a threat for qubit coherence. Having two modes of operation, it shorts all low-frequency noise if control is idle while being transparent if control is active, where short or open is determined by the control line signal level itself.
Microwave resonators fabricated from superconducting thin films are playing a critical role with recent advances in superconducting quantum computing technology and photon detectors. There has been an intensive worldwide effort to study the sources of loss that limit the quality factors of these resonators. In this thesis, I have focused on the measurements of the microwave response of vortices in Al and Re superconducting thin film resonators cooled in magnetic fields comparable to or less than that of the Earth. Previous work on vortex dynamics at microwave frequencies has involved large magnetic fields, orders of magnitude larger than the Earth's fields. Al and Re are common materials used in superconducting resonant circuits for qubits and detectors. Despite the similarities of Al and Re superconductors, the microwave vortex response is strikingly different in the two materials from my resonator measurements. I present a quantitative model for the dissipation and reactance contributed by the vortices in terms of the elastic pinning forces and the viscous damping from the vortex cores. The differences in the vortex response in Al and Re were due to the vortex pinning strength in the two films The critical role played by pinning in determining the microwave response motivated us to try to modify the pinning in our Al films by nanostructuring the film surface. A single narrow slot along the center line of a resonator was used to increase the pinning in the resonator traces and resulted in a reduction of the loss from vortices by over an order of magnitude. Such patterned pinning techniques could be used on resonators in systems with insufficient shielding or pulsed control fields to reduce the loss from unwanted trapped vortices. Finally, we explored the possibility for using measurements of the power dependence of the resonators to determine if trapped vortices are present.
Superconducting microwave circuits with and without Josephson inductances are the Swiss Army knife for many experiments and technologies from quantum information science to astrophysical particle detectors. Despite a large variety of existing circuit types, thin film materials and Josephson junction technologies, a flexible and reliable platform for high-magnetic-field and high-temperature applications is yet to be found. In this manuscript, we investigate coplanar waveguide cavities made of the high-temperature cuprate superconductor YBa2Cu3O7 (YBCO), integrated with Josephson inductances and quantum interferometers that are generated by the controlled local irradiation of the YBCO with a focused helium ion beam. We obtain strongly flux-tunable microwave resonators, which not only display periodic interferometer oscillations of resonance frequency and decay rate, but also a superimposed Fraunhofer-like modulation pattern. The latter originates from the magnetic field tuning of the individual Josephson junction critical currents due to the out-of-plane junction barriers. It allows adjusting resonance frequency and flux responsivity independently of each other, potentially enabling tunable microwave circuits with low sensitivity to external magnetic-field noise over a broad range of frequencies. Finally, we investigate the temperature dependence of the cavities, show that they have promising characteristics up to 14K, and present a model for the junction-induced cavity losses.
In this thesis, we first demonstrate that a disordered superconductor with high kinetic inductance can realise a microwave low-loss, non-dissipative circuit element with impedance greater than the quantum resistance. This element, known as a superinductor, can suppress the fluctuations of charge in a quantum circuit.For this purpose, we fabricated and characterised 20 nm thick, 40 nm wide niobium-nitride nanowires and determined the impedance to 6.795 kΩ. We demonstrate internal quality factors Qi = 2.5e4 in nanowire resonators at single photon excitation, which is significantly higher than values reported in devices with similar materials and geometries. Moreover, we show that the dominant dissipation in our nanowires is not an intrinsic property of the disordered films, but can instead be fully understood within the framework of two-level systems.To further characterise these losses, we then explore the geometrical scaling, toward nanowire dimensions, of dielectric losses in superconducting microwave resonators fabricated with the same techniques and from the same NbN thin-film as the nanowire superinductors. For this purpose, we perform an experimental and numerical study of dielectric loss at low temperatures. Using 3D finite-element simulation of the Maxwell--London equations, we compute the geometric filling factors of the lossy regions in our resonator structures and fit the experimental data to determine the intrinsic loss tangents of its interfaces and dielectrics. Finally, we study the effect of two-level systems on the performance of various superconducting quantum circuits. For this purpose, we measure coherence-time fluctuations in qubits and frequency fluctuations in resonators. In all devices, through statistical analysis, we identify the signature of individual Lorentzian fluctuators in the noise. We find that fluctuations in qubit relaxation are local to the qubit and are caused by instabilities of near-resonant two-level-systems. Furthermore, when examining the low-frequency noise of three different types of superconducting resonator - one NbN nanowire, one Al coplanar waveguide, and one Al 3D cavity - we observe a similar power-law dependence of the Lorentzian switching time and amplitude on the circulating power in the resonators, suggesting a common noise mechanism in the three different types of devices.