Magnetic-field and current-density distributions in thin-film superconducting rings and disks

We show how to calculate the magnetic-field and sheet-current distributions for a thin-film superconducting annular ring (inner radius a, outer radius b, and thickness d<<a) when either the penetration depth obeys lambda < d/2 or, if lambda > d/2, the two-dimensional screening length obeys Lambda = 2 lambda^2/d << a for the following cases: (a) magnetic flux trapped in the hole in the absence of an applied magnetic field, (b) zero magnetic flux in the hole when the ring is subjected to an applied magnetic field, and (c) focusing of magnetic flux into the hole when a magnetic field is applied but no net current flows around the ring. We use a similar method to calculate the magnetic-field and sheet-current distributions and magnetization loops for a thin, bulk-pinning-free superconducting disk (radius b) containing a dome of magnetic flux of radius a when flux entry is impeded by a geometrical barrier.Comment: 10 pages, 13 figure

Electromagnetic Modelling of Superconducting Sensor Designs

The problem of design optimisation of thin film direct current Superconducting QUantum Interference Device (SQUID) magnetometers made of YBCO (YBa2Cu3O7-x) was considered. The inductances and effective areas were calculated using the software package 3D-MLSI. Resolution and reliability issues were first tested on simple superconducting systems, showing good agreement with analytical formulae and experimental results, and demonstrating that a remarkable precision can be obtained though at the expense of CPU time and memory. The software was then used to simulate a SQUID magnetometer fabricated in the Device Materials Group of the Department of Materials Science and Metallurgy, proving that 3D-MLSI can be used to predict the parameters of real systems with acceptable accuracy

Effect of partially ionized impurities and radiation on the effective critical electric field for runaway generation

We derive a formula for the effective critical electric field for runaway generation and decay that accounts for the presence of partially ionized impurities in combination with synchrotron and bremsstrahlung radiation losses. We show that the effective critical field is drastically larger than the classical Connor-Hastie field, and even exceeds the value obtained by replacing the free electron density by the total electron density (including both free and bound electrons). Using a kinetic equation solver with an inductive electric field, we show that the runaway current decay after an impurity injection is expected to be linear in time and proportional to the effective critical electric field in highly inductive tokamak devices. This is relevant for the efficacy of mitigation strategies for runaway electrons since it reduces the required amount of injected impurities to achieve a certain current decay rate.Comment: 17 pages, 6 figures. Minor revisions of original manuscrip

Understanding the saturation power of Josephson Parametric Amplifiers made from SQUIDs arrays

We report on the implementation and detailed modelling of a Josephson Parametric Amplifier (JPA) made from an array of eighty Superconducting QUantum Interference Devices (SQUIDs), forming a non-linear quarter-wave resonator. This device was fabricated using a very simple single step fabrication process. It shows a large bandwidth (45 MHz), an operating frequency tunable between 5.9 GHz and 6.8 GHz and a large input saturation power (-117 dBm) when biased to obtain 20 dB of gain. Despite the length of the SQUID array being comparable to the wavelength, we present a model based on an effective non-linear LC series resonator that quantitatively describes these figures of merit without fitting parameters. Our work illustrates the advantage of using array-based JPA since a single-SQUID device showing the same bandwidth and resonant frequency would display a saturation power 15 dB lower.Comment: 12 pages, 9 figures, Appendices include

Experimental study of the quantum phase-slip effect in NbN nanowires

Coherent quantum phase-slip (QPS) in a superconducting nanowire is the dual phenomenon to the well-known Josephson effect. Josephson junctions form the basis of superconducting electronic circuits with a wide range of applications, and each of those circuits has a corresponding dual quantum phase-slip device with a dual purpose. Examples that draw particular attention are a new quantum standard of electric current, and a quantum phase-slip qubit. The aim of this project is to develop methods of design, fabrication, and measurement of quantum phase-slip nanowires, and to demonstrate the potential of these devices for technological application. In our experiments we incorporate NbN nanowires into a superconducting loop and bias the loop with a magnetic flux. The state of the nanowire-embedded loop is then read out by coupling to a high quality coplanar waveguide resonator. In this thesis we present the results of two such experiments. First, we fabricated NbN nanowires using a neon focused-ion-beam, and measured their properties at T=300 mK. Periodic tuning of the resonant frequency of the readout resonator revealed that magnetic flux is transferred to the interior of the loop with flux-quantum-periodicity. Our measurements confirm that the flux-quantum transfer is mediated by incoherent quantum phase-slips occurring in the nanowires, and that these incoherent QPS can be fully controlled with an external bias. In the second experiment, nanowire-embedded NbN loops were fabricated by electron-beam lithography and cooled to T=10 mK. The resonant frequency tuning exhibited avoided crossings, which is evidence of coherent coupling between the resonator and a coherent quantum two-level system. We numerically fit these avoided crossings to the Jaynes-Cummings model to extract the properties of the two-level system, and find a good fit with the design parameters of our nanowire qubit. Finally we discuss whether the observation of coherent dynamics is evidence of coherent QPS in the EBL-fabricated nanowire

Superconducting quantum circuits for hybrid architectures

Im Bestreben nach neuen Quantentechnologien gehören supraleitende Quantenschaltkreise (SQS) zu den weltweit führenden Hardware-Plattformen, und finden bereits Anwendung in den Bereichen der Quanteninformationsverarbeitung, Quantenkommunikation und –kryptographie, sowie in der Quantensensorik. Obwohl die Kohärenz solcher Schaltkreise in den vergangenen zwei Jahrzehnten enorm gesteigert werden konnte, existieren konkurrierende Plattformen, die teilweise in bedeutenden Aspekten noch immer überlegen sind. Gerade deshalb erscheint eine Verknüpfung unterschiedlicher Implementierungen zu einer Quantenhybridarchitektur reizvoll, mit dem Ziel, die Stärken der individuellen Plattformen zu kombinieren und gleichzeitig vorhandene Schwächen auszugleichen. In diesem Zusammenhang habe ich im Rahmen meiner Dissertation eine nichtlineare Induktivität für die Verwendung in SQSs entwickelt, die, basierend auf dem ungeordneten Supraleiter „granulares Aluminium“ (grAl), auch in hohen Magnetfeldern verwendet werden kann, was eine Grundvoraussetzung für die Anwendbarkeit in Hybridstrukturen darstellt. Als Machbarkeitsnachweise habe ich den konventionellen Josephson-Kontakt in einem Transmon-Qubit mit dieser grAl-Induktivität ausgetauscht, und die Mikrowelleneigenschaften des Systems im Magnetfeld charakterisiert. Um das Signal-Rausch-Verhältnis der Messung zu verbessern, habe ich zudem einen nicht-entarteten parametrischen Verstärker entwickelt, der auf langen Ketten von Josephson-Kontakten basiert. Die Neuheit des zugrundeliegenden Konzeptes ist dabei die Verwendung von mehreren Eigenmodpaaren der Josephson-Kette, um den Frequenzbereich zwischen 1 und 10 GHz möglichst mit einem einzigen Verstärker abzudecken