Physical processes and applications of linear arrays of small Josephson junctions

Samuel A. Wilkinson

Josephson junction arrays (JJAs) are engineered many-body quantum systems consisting of several superconducting islands connected by thin tunnel barriers - Josephson junctions (JJs). They are of interest both from a fundamental point of view (e.g. addressing questions of macroscopic quantum physics, providing model systems in which to study complex many-body phenomena) and from the prospect of technological applications (e.g. quantum computing, metrology, metamaterials). In this thesis we present various tools and techniques for the theoretical study of JJAs, and then put these tools to use in the modelling of two particular experiments on JJAs. In our presentation of the physics of JJAs, we emphasise phenomena unique to arrays (i.e. not seen in single junction devices such as qubits). We investigate charge transport through the the bilinear array, consisting of two linear chains of JJs, and show that it exhibits both Coulomb drag and depinning. We predict new phenomena arising from the interplay between Coulomb drag and depinning at voltages higher than have so far been experimentally reported. We then turn our attention to recent experiments in which planar JJAs were placed in 3-D microwave cavities, with vortices being injected via an externally applied magnetic eld. We calculate the impedance spectrum using linear response theory, which enables us to see when new vortices enter the system in the form of sharp changes in the resonance frequency.

Victor K. Kornev, Igor I. Soloviev, N. V. Klenov +1 more

J. Kent Harbaugh, D. Stroud

Oliver Kieler, Ruediger Wendisch, Rolf-Werner Gerdau +3 more

We developed a fabrication process to establish large arrays of up to 5-stacked Josephson junctions for the Josephson Arbitrary Waveform Synthesizer (JAWS). SNS-type Josephson junctions with NbxSi1-xbarriers are used for this application. By modifying our standard window process, e.g. to add a CMP (chemical mechanical polishing) and an ALD (atomic layer deposition) step, the yield of this process was increased. An output voltage of 1 V RMS could be achieved by using 4 JAWS arrays in series with a total number of 60,000 5-stacked junctions. The investigation of the current-voltage characteristics (IVC) showed an interesting and potentially useful feature. The required pulse amplitude per junction for getting the maximum Shapiro step width reduces for higher junction stacks. We found that the pulse power linearly reduces with the square of the junction number in the array. The origin of this effect might be a strong neighbour-neighbour interaction of the junctions, which are closely arranged within the stacked configuration. This might generate a strong self-synchronization of the junctions.

Herbert R. Shea

Juha Hassel

Properties of weak links between two superconductors, or Josephson junctions, make them interesting for fundamental physics research. Since their discovery over four decades ago, they have provided a unique way to study the behavior of the superconducting quantum phase. More recently, ultra small, or mesoscopic, Josephson junctions with substantial single Cooper pair charging energy have gained interest due to their behavior as macroscopic quantum objects. In addition to the theoretical interest, Josephson junctions can be used as active elements in circuit applications. Particularly, in this Thesis we study two different devices. We develop the required theoretical treatments, derive device properties, and compare the results with experimental data. The first application is a Josephson voltage standard based on externally damped Superconductor - Insulator - Superconductor junctions. It consists of an array of large Josephson junctions connected in series and irradiated with a 70 GHz microwave signal. Phase locking the Josephson dynamics into the signal leads to the quantization of the voltage. This is utilized in metrology. We introduce a new circuit solution based on frequency dependent damping of the junctions. Optimization and some designs for practical arrays are presented. The purpose is to find such a design that the array is fast, has low power consumption and is as stable as possible. Arrays able to generate DC voltages of order 1 volt with metrological accuracy are demonstrated experimentally and their applicability in AC voltage calibrations is analyzed. The second application is the Bloch Oscillating Transistor (BOT). The BOT is based on controlling the Cooper pair current in an ultra small Josephson junction by means of quasiparticles tunneling through a normal junction. As part of the thesis work, the principle of operation is first demonstrated computationally. The model is then refined to yield quantitative predictions of the characteristics. Finally, an analytic theory for the device is developed and the properties as an amplifier are derived.