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The dominant source of decoherence in contemporary frequency-tunable superconducting qubits is 1/$f$ flux noise. To understand its origin and find ways to minimize its impact, we systematically study flux noise amplitudes in more than 50 flux qubits with varied SQUID geometry parameters and compare our results to a microscopic model of magnetic spin defects located at the interfaces surrounding the SQUID loops. Our data are in agreement with an extension of the previously proposed model, based on numerical simulations of the current distribution in the investigated SQUIDs. Our results and detailed model provide a guide for minimizing the flux noise susceptibility in future circuits., 14 pages, 6 figures

Solid-state qubits with transition frequencies in the microwave regime, such as superconducting qubits, are at the forefront of quantum information processing. However, high-fidelity, simultaneous control of superconducting qubits at even a moderate scale remains a challenge, partly due to the complexities of packaging these devices. Here, we present an approach to microwave package design focusing on material choices, signal line engineering, and spurious mode suppression. We describe design guidelines validated using simulations and measurements used to develop a 24-port microwave package. Analyzing the qubit environment reveals no spurious modes up to 11GHz. The material and geometric design choices enable the package to support qubits with lifetimes exceeding 350 {\mu}s. The microwave package design guidelines presented here address many issues relevant for near-term quantum processors., Comment: 15 pages, 9 figures

Extending qubit lifetime through a shaped environment Qubits are the quantum two-level systems that encode and process information in quantum computing. Kept in isolation, qubits can be stable. In a practical setting, however, qubits must be addressed and interact with each other. Such an environment is typically viewed as a source of decoherence and has a detrimental effect on a qubit's ability to retain encoded information. Gustavsson et al. used a sequence of pulses as a source of “environment shaping” that could substantially increase the coherence time of a superconducting qubit. Science , this issue p. 1573

© 2019 IEEE. Over the past two decades, the performance of superconducting quantum circuits has tremendously improved. The progress of superconducting qubits enabled a new industry branch to emerge from global technology enterprises to quantum computing startups. Here, an overview of superconducting quantum circuit microwave control is presented. Furthermore, we discuss one of the persistent engineering challenges in the field - how to control the electromagnetic environment of increasingly complex superconducting circuits such that they are simultaneously protected and efficiently controllable.

The aim of this review is to provide quantum engineers with an introductory guide to the central concepts and challenges in the rapidly accelerating field of superconducting quantum circuits. Over the past twenty years, the field has matured from a predominantly basic research endeavor to one that increasingly explores the engineering of larger-scale superconducting quantum systems. Here, we review several foundational elements -- qubit design, noise properties, qubit control, and readout techniques -- developed during this period, bridging fundamental concepts in circuit quantum electrodynamics (cQED) and contemporary, state-of-the-art applications in gate-model quantum computation., Comment: 67 pages, 28 figures

Detuning a superconducting qubit from its rotating frame is one means to implement a Z-gate operation. In this work, we implement a Z gate by pulsing a current through the qubit’s readout dc SQUID. While the dc SQUID acts as a magnetic flux sensor for qubit readout, we in turn may use it as a flux actuator with tunable strength to impose a qubit frequency shift. Using this approach, we demonstrate Ramsey-type free-induction experiments with time constants as long as 280 ns and rotation frequencies as high as 1.4 GHz. We experimentally demonstrate an inferred Z-gate fidelity of approximately 90%, limited largely by the bandwidth of our system. In the absence of this limitation, we argue that the inferred fidelity may be improved to as high as 99%.

We implement dynamical decoupling techniques to mitigate noise and enhance the lifetime of an entangled state that is formed in a superconducting flux qubit coupled to a microscopic two-level system. By rapidly changing the qubit's transition frequency relative to the two-level system, we realize a refocusing pulse that reduces dephasing due to fluctuations in the transition frequencies, thereby improving the coherence time of the entangled state. The coupling coherence is further enhanced when applying multiple refocusing pulses, in agreement with our $1/f$ noise model. The results are applicable to any two-qubit system with transverse coupling, and they highlight the potential of decoupling techniques for improving two-qubit gate fidelities, an essential prerequisite for implementing fault-tolerant quantum computing.

We have measured vortex motion in a long one‐dimensional array of small underdamped niobium tunnel junctions which are coupled in parallel by superconducting wires. In the current‐voltage characteristic, a resonant step occurs similar to the Eck peak in long continuous junctions. Due to the discrete nature of our samples, the voltage of this resonant step follows a sinusoidal dependence on the magnetic field rather than the linear dependence found in long continuous junctions. With a control current applied parallel to the array of junctions, the device can be operated as a vortex‐flow transistor or as a tunable vortex‐flow oscillator. Compared to long continuous junctions, the performance of discrete transistors is better with regard to the threshold current and transresistance, but worse with regard to the output resistance. Discrete oscillators have the advantage over their continuous counterparts in that the output impedance is of the order of 10 Ω. Numerical simulations indicate power levels around 0...

A closed-form expression is presented for the current distribution in an isolated strip made from a superconducting thin film with thickness less than a few penetration depths. This equation gives a good approximation within certain limits for the resistance and inductance per unit length of superconducting striplines and microstrip lines. Both the ac resistance of an isolated superconducting strip and the resistance per unit length of a superconducting stripline calculated using this closed-form expression agree well with the numerical results generated by the modified Weeks' method. The possibility of using this expression along with the integral equation method to develop an efficient full-wave method for analyzing superconducting planar transmission lines is discussed. >

Smooth, superconducting films of Bi 2 Sr 2 CaCu 2 O 8+° have been prepared by reactive sputtering from elemental targets in the presence of ozone. The influence of substrate temperature, deposition rate, and ozone pressure on the resulting films are discussed. Films deposited on SrTiO 3 substrates are c -axis oriented and featureless for substrate temperatures below 710°C. Above this temperature, small inclusions of CuO appear. Films on MgO exhibit mixed a -axis and c -axis orientation below about 710°C, and inclusions of CuO above this temperature. The temperature at which this transition occurs increases with increasing deposition rate. T c increases and then decreases sharply with decreasing oxygen content. The oxygen partial pressure corresponding to the maximum T c of 77 K is well above the thermodynamic stability limit for Bi 2 Sr 2 CaCu 2 O 8+° , suggesting that an optimum carrier concentration has been achieved for these films.

The traditional two-fluid model of superconducting conductivity was modified to reflect the BCS coherence effects in the conductivity of a superconductor, which are incorporated through an effective ratio of normal-to-superconducting electrons. The ratio is a simple analytical expression which depends on frequency, temperature, and material parameters. This modified two-fluid model allows accurate and rapid calculation of the microwave surface impedance of a superconductor in the clean and dirty limits and in the weak- and strong-coupled regimes. The model compares well with surface resistance data for Nb. Numerical calculations of surface impedance with the modified two-fluid model are one to five orders of magnitude faster than equivalent BCS calculations. >

We measured the phase stability of the Bi 2 Sr 2 CaCu 2 O 8+δ and Bi 2 Sr 2 Ca 2 Cu 3 O 10+δ superconductors as a function of temperature and oxygen pressure. Below the solidus temperature of ∼790°C, Bi 2 Sr 2 CaCu 2 O 8+δ is stable at oxygen pressures one fourth of those where CuO becomes metastable, while Bi 2 Sr 2 Ca 2 Cu 3 O 10+δ is stable at the same pressures where CuO is stable. Above the solidus temperature, the pressure required to stabilize either phase increases rapidly with temperature. The major solid-state decomposition products of Bi 2 Sr 2 CaCu 2 O 8+δ are Bi 2 Sr 3− x Ca x O 6+δ and Cu 2 O, and also Bi 2 Sr 2− x Ca x O 5 for bismuth-rich samples. For Bi 2 Sr 2 Ca 2 Cu 3 O 10+δ the major decomposition products are Bi 2 Sr 2 CaCu 2 O 8+δ , Ca 2− x Sr x CuO 3 , and Cu 2 O. The solid-state decomposition reaction is reversible for the Bi-2212 phase, but not for the Bi-2223 phase.

We have observed ballistic motion of vortices in arrays of superconducting tunnel junctions. In a special geometry vortices are accelerated in one region, then launched into a second region without driving forces. At low temperatures, where damping is small, the vortices are found to propagate in a beam across the force-free region.

The voltage generated by moving ballistic vortices with a mass ${\mathit{m}}_{\ensuremath{\nu}}$ in a two-dimensional superconducting ring is quantized, and this quantization depends on the amount of charge enclosed by the ring. The quantization of the voltage is the dual to flux quantization in a superconductor, and is a manifestation of the Aharonov-Casher effect. The quantization is obtained by applying the Bohr-Sommerfeld criterion to the canonical momentum of the ballistic vortices. The results of this quantization condition can also be used to understand the persistent voltage predicted by van Wees for an array of Josephson junctions.

This project dealt with nanofabrication by metal-trilayer evaporation and liftoff. It included fabrication of Josephson-junction structures, and development of novel methods for metal liftoff at the sub-10-nm length scale. The ultra-narrow features developed in this project also have direct relevance to the nanofabrication of nanowire phase-slip qubits, which would provide an interesting alternative approach to superconducting qubits.

Superconducting transition temperatures between 0.7 and 1.5 K are reported for the stage-1 potassium-mercury graphite intercalation compound (GIC) C{sub 4}KHg. A number of experiments have been performed to investigate the differences between the C{sub 4}KHg samples at either extreme in {ital T}{sub {ital c}}. The only structural difference appears to be that the {beta} phase (characterized by a {ital c}-axis lattice constant {ital I}{sub {ital c}}=10.83 A) is consistently found in the lower-{ital T}{sub {ital c}} samples, while the higher-{ital T}{sub {ital c}} samples always contain only the {alpha} phase ({ital I}{sub {ital c}}=10.24 A). Adding a minute amount of hydrogen to the {ital T}{sub {ital c}}=0.8 K samples raises their transition temperature to 1.5 K. Measurements of the angular dependence of the critical-field suggest that the higher-{ital T}{sub {ital c}} samples have type-I character for a range of applied field orientations near {bold H}{parallel}{bold {cflx c}}. The temperature dependence of the upper critical field of C{sub 4}KHg shows extended linearity of {ital H}{sub {ital c}2}(T) for both types of samples. The critical field data of C{sub 4}KHg and other GIC's are discussed in light of multiband and anisotropic Fermi-surface models of superconductivity. The thermodynamic parameters obtained from the critical-fieldmore » experiments are compared to the specific-heat data of Alexander {ital et} {ital al}. A charge-density-wave hypothesis first proposed by DeLong and Eklund is suggested to explain the hydrogen-induced enhancement of {ital T}{sub {ital c}}.« less

We measured the intrawell energy relaxation time \tau_{d} between macroscopic quantum levels in the double well potential of a Nb persistent-current qubit. Interwell population transitions were generated by irradiating the qubit with microwaves. Zero population in the initial well was then observed due to a multi-level decay process in which the initial population relaxed to the lower energy levels during transitions. The qubit's decoherence time, determined from \tau_{d}, is longer than 20 microseconds, holding the promise of building a quantum computer with Nb-based superconducting qubits., Comment: 18 pages, 5 figures

We describe a new biasing scheme for single photon detectors based on superconducting tunnel junctions. It replaces a single detector junction with a circuit of three junctions and achieves biasing of a detector junction at subgap currents without the use of an external magnetic field. The biasing occurs through the nonlinear interaction of the three junctions, which we demonstrate through numerical simulation. This nonlinear state is numerically stable against external fluctuations and is compatible with high fidelity electrical readout of the photon-induced current. The elimination of the external magnetic field potentially increases the capability of these types of photon detectors and eases constraints involved in the fabrication of large detector arrays., Comment: 15 pages, including 3 figures

Measurements of thermal activation are made in a superconducting, niobium Persistent-Current (PC) qubit structure, which has two stable classical states of equal and opposite circulating current. The magnetization signal is read out by ramping the bias current of a DC SQUID. This ramping causes time-ordered measurements of the two states, where measurement of one state occurs before the other. This time-ordering results in an effective measurement time, which can be used to probe the thermal activation rate between the two states. Fitting the magnetization signal as a function of temperature and ramp time allows one to estimate a quality factor of 10^6 for our devices, a value favorable for the observation of long quantum coherence times at lower temperatures., 14 pages, 4 figures

DC measurements are made in a superconducting, persistent current qubit structure with a time-ordered meter. The persistent-current qubit has a double-well potential, with the two minima corresponding to magnetization states of opposite sign. Macroscopic resonant tunneling between the two wells is observed at values of energy bias that correspond to the positions of the calculated quantum levels. The magnetometer, a Superconducting Quantum Interference Device (SQUID), detects the state of the qubit in a time-ordered fashion, measuring one state before the other. This results in a different meter output depending on the initial state, providing different signatures of the energy levels for each tunneling direction. From these measurements, the intrawell relaxation time is found to be about 50 microseconds., Comment: 17 pages, 7 figures

We report a significant increase in the pinning energy of vortices in single‐crystal Bi2Sr2CaCu2O8 when irradiated with heavy ions such as Ar+. This is in contrast with the results of light ion (H+, He+) irradiations which give pinning energies comparable with those of unirradiated crystals. The stronger pinning is attributed to defects larger than point defects, e.g., clusters or amorphized regions. As a result of higher pinning energies, critical currents persist at markedly higher temperatures and fields.

We present a study of nonlinear localized excitations called discrete breathers in a superconducting array. These localized solutions were recently observed in Josephson-junction ladder arrays by two different experimental groups. We review the experiments made by Trias et al. We report the detection of different single-site and multi-site breather states and study the dynamics when changing the array bias current. By changing the temperature we can control the value of the damping (the Stewart-McCumber parameter) in the array, thus allowing an experimental study at different array parameters. We propose a simple DC circuit model to understand most of the features of the detected states. We have also compared this model and the experiments with simulations of the dynamics of the array. We show that the study of the resonances in the ladder and the use of harmonic balance techniques allow for understanding of most of the numerical results. We have computed existence diagrams of breather solutions in our arrays, found resonant localized solutions and described the localized states in terms of vortex and antivortex motion., Accepted in Physica D

Highly oriented Bi‐Sr‐Ca‐Cu‐oxide thin films with Tc≥100 K and large (10–20 μm) grains were used to produce thin‐film dc superconducting quantum interference devices (SQUIDs). The best SQUID, which operated up to 75 K, had an inside loop diameter of ∼18 μm and an estimated loop inductance of 30 pH. The device was patterned by standard photolithography and had weak links that were likely due to existing grain boundaries around the loop. The effective loop area, calculated from the period of the SQUID modulation, is roughly consistent with the geometrical area of the SQUID loop. Significant hysteresis was observed in the flux‐voltage characteristic which depended on the amplitude of the magnetic field sweep. The 1/f noise levels measured at 100 Hz in this device gave a flux noise Sφ of 1.0×10−8 Φ20/Hz at 4.8 K and 2.3×10−7 Φ20/Hz at 60 K. The detailed noise measurements which we report for this SQUID are the first for any Bi‐Sr‐Ca‐Cu‐oxide based SQUID.

We present analytical and numerical studies of pinned superconducting states of open-ended Josephson ladder arrays, neglecting inductances but taking edge effects into account. Treating the edge effects perturbatively, we find analytical approximations for three of these superconducting states -- the no-vortex, fully-frustrated and single-vortex states -- as functions of the dc bias current $I$ and the frustration $f$. Bifurcation theory is used to derive formulas for the depinning currents and critical frustrations at which the superconducting states disappear or lose dynamical stability as $I$ and $f$ are varied. These results are combined to yield a zero-temperature stability diagram of the system with respect to $I$ and $f$. To highlight the effects of the edges, we compare this dynamical stability diagram to the thermodynamic phase diagram for the infinite system where edges have been neglected. We briefly indicate how to extend our methods to include self-inductances., RevTeX, 22 pages, 17 figures included; Errata added, 1 page, 1 corrected figure

Superconducting systems built of underdamped Josephson junctions are of interest for ballistic and quantum vortex experiments. The dissipation in a Josephson tunnel junction can be extremely small because its subgap resistance can easily be made of the order of 1 MΩ which for a typical junction translates into a McCumber parameter as high as 107. In a Josephson system with such little dissipation, the vortex velocity can be high enough so that the energy stored in the electric field generated by the moving vortex has to be taken into account. This electric field contribution to the energy acts like a kinetic-energy term and the vortex mass is found to be proportional to the junction capacitance [1, 2, 3]. Measurements have indicated the existence of a mass term in the equation of motion for a vortex [4, 5]. The concept of a massive vortex has also been tested in quantum experiments: there is evidence for quantum tunneling of vortices [4, 5], for a collective, quantum phase transition triggered by a Bose-condensation of vortices [6], and for vortex interference (Aharonov-Casher effect) [7].

We have observed ballistic motion of vortices in arrays of superconducting tunnel junctions. In a special geometry vortices are accelerated with a current in one region, then launched through a channel into a second region where no current is applied. At low temperatures where damping is small, and for low vortex densities, we found that the vortices propagate in a beam across the force-free region.

We present an extensive study of the magnetization properties of high quality YBa 2 Cu 3 O 7 and conventional low-temperature superconducting single crystals using a vibrating sample magnetometer. The experimental conditions cover a wide range of temperatures, applied fields (up to 30 T), and sweep rates. The experimentally measured linear relationship between the magnetization and the logarithm of the sweep rate is examined in detail. A simple picture of vortex motion as a combination of drift and diffusion components provides a particularly useful model for analyzing the experimental results.

Spin-polarized tunneling is used to measure the energy difference delta between spin-up and spin-down electrons in a magnetic field in thin films of superconducting Al. delta decreases from 2..mu../sub B/H at low temperature and field to 0.8 (2..mu../sub B/H) as the phase boundary T/sub c/(H) is approached. This change in delta provides the first measurement of the l = 0 antisymmetric Fermi-liquid parameter G/sup 0/ in a real metal and the first direct evidence for the renormalization of the Pauli field in high-field superconductivity.

The upper critical fields ${B}_{c2}(T)$ were measured up to 28 T for ${R}_{1}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}y}$, where $R=\mathrm{N}\mathrm{d},\phantom{\rule{0ex}{0ex}}\mathrm{E}\mathrm{u},\phantom{\rule{0ex}{0ex}}\mathrm{G}\mathrm{d},\phantom{\rule{0ex}{0ex}}\mathrm{D}\mathrm{y},\phantom{\rule{0ex}{0ex}}\mathrm{H}\mathrm{o},\phantom{\rule{0ex}{0ex}}\mathrm{E}\mathrm{r},\phantom{\rule{0ex}{0ex}}\mathrm{a}\mathrm{n}\mathrm{d}\phantom{\rule{0ex}{0ex}}\mathrm{T}\mathrm{m}$, and for $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}y}$. The midpoints ${(\frac{d{B}_{c2}}{\mathrm{dT}})}_{T={T}_{c}}$ cluster about (2.8\ifmmode\pm\else\textpm\fi{}0.2) T/K, the ${T}_{c}'\mathrm{s}=(93\ifmmode\pm\else\textpm\fi{}2)$ K show a slight systematic decrease from Nd to Tm, and the extrapolated values of ${B}_{c2}(0)$ cluster about (160\ifmmode\pm\else\textpm\fi{}20) T. The wide range of normal-state resistivities indicates that they are not intrinsic to the superconductor. The anisotropy $A=\frac{{B}_{c2\ensuremath{\parallel}}}{{B}_{c2}\ensuremath{\perp}}$ is estimated to be less than 12 based on the data for the resistive transition. Criteria for the midpoint resistive transition are also reexamined.

Thin films of the Chevrel phase superconductor AgMo6S8 have been prepared by simultaneous sputtering of silver and molybdenum onto sapphire substrates held at temperatures between 800°C and 1000°C using H2S as a reactive gas. The best films have a superconducting critical temperature of 9.2 K and a transition width of 0.2 K. Depending on the deposition conditions the microstructure can be varied from films that are smooth on a sub-micron scale to films that have a grain size of fractions of a micron. The smooth films have a resistivity comparable to that measured for single crystals and a resistance ratio of twenty. The films with smaller grains resistivities which are anorder of magnitude higher and show very little temperature dependence. Critical field measurements of the films with high transition temperatures give a slope of the upper critical field of 1.7 T/K and a critical field extrapolated to zero temperature of 14 T.

By electron tunneling we have studied the superconducting properties of granular aluminum as one approaches the metal-insulator transition. We find that with increasing sample resistivity, the superconducting energy-gap edge broadens because of lifetime effects until that broadening becomes comparable to the gap. At this point, superconductivity disappears.

Fermi-liquid effects are incorporated into the quasiclassical theory of superconductivity to give a quantitative theory for understanding tunneling experiments on real metals in high magnetic fields. The theory is formulated for arbitrary impurity scattering and anisotropy. Numerical calculations are done for the dirty, isotropic limit. The calculations for low spin-orbit scattering show that the energy difference in a magnetic field between spin-up and spin-down electrons is proportional to the l=0 antisymmetric Fermi-liquid parameter as confirmed by recent experiments. Furthermore, this same Fermi-liquid parameter is shown to renormalize the Pauli-limiting field in the calculation of the upper critical field. Recent experiments on thin films of Al are compared with the theoretical calculations.

Preferentially oriented thin films of the Chevrel‐phase superconductor AgMo6S8 were prepared by reactive sputtering. Ag and Mo were simultaneously sputtered from separate guns onto sapphire substrates held at about 850 °C with H2S gas injected near the substrate. The films have superconducting critical temperatures up to 9.2 K and narrow‐phase transitions. The reactive sputtering process chosen for the preparation of our films makes it possible to change the superconducting properties and the microstructure of the samples in a systematic way by changing individual preparation parameters and to study which of the preparation conditions are the most crucial for the formation of the Chevrel phase. We find that the superconducting transition temperature of the Chevrel phase is very sensitive to both substrate temperature and to the flow of H2S but insensitive to the background pressure in the chamber before deposition. The microstructure can be changed by controlling the H2S pressure. X‐ray measurements show ...

Low‐frequency (∼1 Hz) ac loss measurements were made at applied fields up to 20 T with field modulation amplitudes of up to 1 T. Results for the alternative in situ and powder metallurgy (P/M) processed Nb3Sn and Nb–Al wires are presented for single‐strand and multistrand geometries. Loss measurements for commercial continuous‐fiber Nb3Sn wires manufactured by Holec and Supercon also are presented and show that the effective fiber size determined by these ac‐loss measurements corresponds to that measured optically. The effective fiber size for alternative processed wires was intermediate between the wire size and the fiber size, and the losses (and effective fiber size) were reduced by twisting. Multistrand geometries showed further reductions in losses. The smallest effective fiber size at high field was measured for P/M processed Nb–Al. The losses were fully hysteretic and the ac losses were used to determine the critical‐current density at low fields where it was difficult to measure directly.

Two independent methods are used to measure the spin-orbit scattering rate in thin films of Al. Superconducting tunneling gives a rate that agrees reasonably well with normal-state magnetoresistance measurements interpreted by use of weak-localization theory. This agreement is good considering that the theory of superconducting tunneling does not include localization effects.

The upper critical fields B/sub c//sub 2/(T) of La/sub 2-//sub x/Sr/sub x/CuO/sub 4/(x = 0.15 and x = 0.20) were measured near T/sub c/ in dc fields to 23 T and at 4.2 K with pulsed fields to 45 T. Resistive midpoint transitions for the x = 0.15 sample yield (dB/sub c//sub 2//dT)/sub T //sub = //sub =/ = 2.2 T/K, T/sub c/ = 38.1 K, and B/sub c//sub 2/(0) = 58 T assuming a dirty type-II superconductor with no Pauli paramagnetic limiting. Data for the onset yield 4.5 +- 0.5 K/sup -1/, 40.1 K, and 125 +- 15 T, respectively. Pulsed-field data show that fractions of both materials are superconducting above 45 T at 4.2 K. Calculations of limits of B/sub c//sub 2/(T) are presented and experimental limitations of measurements in these high-field superconductors are indicated.

We have measured the upper critical field ${B}_{c2}$(T) of ${\mathrm{Y}}_{2\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ba}}_{\mathrm{x}}$${\mathrm{CuO}}_{4\mathrm{\ensuremath{-}}\mathrm{y}}$ with x=0.4 near ${T}_{c}$ in dc fields up to 20 T and at 77 K with pulsed fields to 45 T. The data yield (${\mathrm{dB}}_{c2}$/dT${)}_{T={T}_{c}}$=1.3 T/K and ${T}_{c}$=89.5 K for the midpoint of the resistive transitions, and (${\mathrm{dB}}_{c2}$/dT${)}_{T={T}_{c}}$=5\ifmmode\pm\else\textpm\fi{}1 T/K and ${T}_{c}$=95.1 K for the onset. The estimates for ${B}_{c2}$(0) range from 80 to 320 T. Pulsed-field data suggest that a fraction of the material is still superconducting above 45 T at 77 K.

The Zeeman energy splitting \ensuremath{\delta} of the superconducting tunneling conductances measured in a magnetic field gives a measure of both the g factor of the conduction electrons and also the l=0 antisymmetric Fermi-liquid parameter ${G}^{0}$. We show how a technique of Fourier analysis, known as cepstral analysis, can be used to measure the Zeeman splitting directly from the total conductance. This technique allows measurement of Fermi-liquid effects which are thought to be of particular importance in high-${T}_{c}$ vanadium-based compounds. We present some results on the recent data of Bending, Beasley, and Tsuei on ${\mathrm{V}}_{3}$Ga in which the g factor is found to be nearly 2.0.

The powder metallurgy (P/M) process and the In Situ process are alternative technologies for producing fine fiber, multifilamentary, A15 superconductors with high overall critical current densities, Jc, at high fields and with good strain tolerance. Several papers were presented at the 1983 Applied Superconductivity Conference by our group.These papers, references cited therein, and related papers should be consulted for progress to that date. Because of space limitations, in this paper we will refer to these papers briefly, examine some fundamental limits to further improved performance, report on new developments in processing, outline recent results, and give some overall assessments of future directions. At this time it is clear that the performance of Nb3Sn can be improved within rather well defined limits, whereas the Jc of Nb3Al, which now surpasses Nb3Sn at high fields, is expected to show further substantial increases in performance. The discussion here is directed toward highest field applications.

We study the dynamics of one-dimensional arrays of Josephson junctions connected in parallel by superconducting wires. These arrays are model systems for the discrete, damped sine-Gordon equation and excellent agreement between theory and experiment is obtained. The influence of boundary conditions and the coupling between two discrete sine-Gordon systems have also been investigated. In Josephson ladders, superconducting islands are connected to other islands by three Josephson junctions. The dynamics of Josephson ladders is more complicated than that of the purely 1D sine-Gordon systems.

New resonance steps are found in the experimental current-voltage characteristics of long, discrete, one-dimensional Josephson junction arrays with open boundaries and in an external magnetic field. The junctions are underdamped, connected in parallel, and DC biased. Numerical simulations based on the discrete sine-Gordon model are carried out, and show that the solutions on the steps are periodic trains of fluxons, phase-locked by a finite amplitude radiation. Power spectra of the voltages consist of a small number of harmonic peaks, which may be exploited for possible oscillator applications. The steps form a family that can be numbered by the harmonic content of the radiation, the first member corresponding to the Eck step. Discreteness of the arrays is shown to be essential for appearance of the higher order steps. We use a multi-mode extension of the harmonic balance analysis, and estimate the resonance frequencies, the AC voltage amplitudes, and the theoretical limit on the output power on the first two steps., Comment: REVTeX, 17 pages, 7 figures, psfig; to appear in J. Applied Physics

We have prepared highly oriented thin films of Bi Sr Ca Cu Oxide by reactive magnetron sputtering on MgO substrates. Deposition of films with a Bi:Sr:Ca:Cu ratio of 2:2:2:4.5 together with long anneals in low oxygen partial pressures at ≈880°C yields films with R=0 as high as 106 K and a large fraction of the 110 K superconducting phase (2223) relative to the 85 K phase (2212) as judged by x-ray diffraction. A dc SQUID was was patterned based on the large (10–20 μm) grains in these films and operated up to 75 K. The detailed noise measurements which we report for this SQUID are the first for any Bi Sr Ca Cu Oxide based SQUID.