Bloch inductance in small-capacitance Josephson junctions

We show that the electrical impedance of a small-capacitance Josephson junction includes besides the capacitive term $-i/\omega C_B$ also an inductive term $i\omega L_B$. Similar to the known Bloch capacitance $C_B(q)$, the Bloch inductance $L_B(q)$ also depends periodically on the quasicharge $q$, and its maximum value achieved at $q=e (\textrm{mod} 2e)$ always exceeds the value of the Josephson inductance of this junction $L_J(\phi)$ at fixed $\phi=0$. The effect of the Bloch inductance on the dynamics of a single junction and a one-dimensional array is described.Comment: 5 pages incl. 3 fig

Assessing T cell clonal size distribution: a non-parametric approach

Clonal structure of the human peripheral T-cell repertoire is shaped by a number of homeostatic mechanisms, including antigen presentation, cytokine and cell regulation. Its accurate tuning leads to a remarkable ability to combat pathogens in all their variety, while systemic failures may lead to severe consequences like autoimmune diseases. Here we develop and make use of a non-parametric statistical approach to assess T cell clonal size distributions from recent next generation sequencing data. For 41 healthy individuals and a patient with ankylosing spondylitis, who undergone treatment, we invariably find power law scaling over several decades and for the first time calculate quantitatively meaningful values of decay exponent. It has proved to be much the same among healthy donors, significantly different for an autoimmune patient before the therapy, and converging towards a typical value afterwards. We discuss implications of the findings for theoretical understanding and mathematical modeling of adaptive immunity.Comment: 13 pages, 3 figures, 2 table

Josephson tunnel junctions with nonlinear damping for RSFQ-qubit circuit applications

We demonstrate that shunting of Superconductor-Insulator-Superconductor Josephson junctions by Superconductor-Insulator-Normal metal (S-I-N) structures having pronounced non-linear I-V characteristics can remarkably modify the Josephson dynamics. In the regime of Josephson generation the phase behaves as an overdamped coordinate, while in the superconducting state the damping and current noise are strikingly small, that is vitally important for application of such junctions for readout and control of Josephson qubits. Superconducting Nb/AlO${_x}$/Nb junction shunted by Nb/AlO${_x}$/AuPd junction of S-I-N type was fabricated and, in agreement with our model, exhibited non-hysteretic I-V characteristics at temperatures down to at least 1.4 K.Comment: 4 pages incl. 3 figure

Thue-Morse constant is not badly approximable

We prove that Thue–Morse constant τTM=0.01101001…2 is not a badly approximable number. Moreover, we prove that τTM(a)=0.01101001…a is not badly approximable for every integer base a≥2 such that a is not divisible by 15. At the same time, we provide a precise formula for convergents of the Laurent series f~TM(z)=z−1∏∞n=1(1−z−2n), thus developing further the research initiated by Alf van der Poorten and others

Aluminum Single Electron Transistors with Islands Isolated from a Substrate

The low-frequency noise figures of single-electron transistors (electrometers) of traditional planar and new stacked geometry were compared. We observed a correlation between the charge noise and the contact area of the transistor island with a dielectric substrate in the set of Al transistors located on the same chip and having almost similar electric parameters. We have found that the smaller the contact area the lower the noise level of the transistor. The lowest noise value 8*10E-6 e/sqrt(Hz) at f = 10 Hz. has been measured in a stacked transistor with an island which was completely isolated from a substrate. Our measurements have unambiguously indicated that the dominant source of the background charge fluctuations is associated with a dielectric substrateComment: Review paper, latex, 10 pages, 7 figures, to be publ. in JLTP, 2000; Proceeding of "Electron Transport in Mesoscopic Systems", August 12-15, 1999 Geteborg, Sweden, http://fy.chalmers.se/meso_satellite/index.html See also LT22 manuscript: http://lt22.hut.fi/cgi/view?id=S1113

Single-charge devices with ultrasmall Nb/AlOx/Nb trilayer Josephson junctions

Josephson junction transistors and 50-junction arrays with linear junction dimensions from 200 nm down to 70 nm were fabricated from standard Nb/AlOx/Nb trilayers. The fabrication process includes electron beam lithography, dry etching, anodization, and planarization by chemical-mechanical polishing. The samples were characterized at temperatures down to 25 mK. In general, all junctions are of high quality and their I-U characteristics show low leakage currents and high superconducting energy gap values of 1.35 meV. The characteristics of the transistors and arrays exhibit some features in the subgap area, associated with tunneling of Cooper pairs, quasiparticles and their combinations due to the redistribution of the bias voltage between the junctions. Total island capacitances of the transistor samples ranged from 1.5 fF to 4 fF, depending on the junction sizes. Devices made of junctions with linear dimensions below 100 nm by 100 nm demonstrate a remarkable single-electron behavior in both superconducting and normal state. We also investigated the area dependence of the junction capacitances for transistor and array samples.Comment: 19 pages incl. 2 tables and 11 figure

Cooper pair cotunneling in single charge transistors with dissipative electromagnetic environment

We observed current-voltage characteristics of superconducting single charge transistors with on-chip resistors of R about R_Q = h/4e^2 = 6.45 kOhm, which are explained in terms of Cooper-pair cotunneling. Both the effective strength of Josephson coupling and the cotunneling current are modulated by the gate-induced charge on the transistor island. For increasing values of the resistance R we found the Cooper pair current at small transport voltages to be dramatically suppressed.Comment: 4 pages and 2 figure

Josephson charge-phase qubit with radio frequency readout: coupling and decoherence

The charge-phase Josephson qubit based on a superconducting single charge transistor inserted in a low-inductance superconducting loop is considered. The loop is inductively coupled to a radio-frequency driven tank circuit enabling the readout of the qubit states by measuring the effective Josephson inductance of the transistor. The effect of qubit dephasing and relaxation due to electric and magnetic control lines as well as the measuring system is evaluated. Recommendations for operation of the qubit in magic points producing minimum decoherence are given.Comment: 11 pages incl. 6 fig

Structurally optimized shells.

Shells, i.e., objects made of a thin layer of material following a surface, are among the most common structures in use. They are highly efficient, in terms of material required to maintain strength, but also prone to deformation and failure. We introduce an efficient method for reinforcing shells, that is, adding material to the shell to increase its resilience to external loads. Our goal is to produce a reinforcement structure of minimal weight. It has been demonstrated that optimal reinforcement structures may be qualitatively different, depending on external loads and surface shape. In some cases, it naturally consists of discrete protruding ribs; in other cases, a smooth shell thickness variation allows to save more material. Most previously proposed solutions, starting from classical Michell trusses, are not able to handle a full range of shells (e.g., are restricted to self-supporting structures) or are unable to reproduce this range of behaviors, resulting in suboptimal structures. We propose a new method that works for any input surface with any load configurations, taking into account both in-plane (tensile/compression) and out-of-plane (bending) forces. By using a more precise volume model, we are capable of producing optimized structures with the full range of qualitative behaviors. Our method includes new algorithms for determining the layout of reinforcement structure elements, and an efficient algorithm to optimize their shape, minimizing a non-linear non-convex functional at a fraction of the cost and with better optimality compared to standard solvers. We demonstrate the optimization results for a variety of shapes, and the improvements it yields in the strength of 3D-printed objects