Fabrication of high-quality submicron Nb/Al--AlOx/Nb tunnel junctions

Nb/Al-AlOx/Nb tunnel junctions are often used in the studies of macroscopic quantum phenomena and superconducting qubit applications of the Josephson devices. In this work, we describe a convenient and reliable process using electron beam lithography for the fabrication of high-quality, submicron-sized Nb/Al-AlOx/Nb Josephson junctions. The technique follows the well-known selective Nb etching process and produces high-quality junctions with Vm=100 mV at 2.3 K for the typical critical current density of 2.2 kA/cm^2, which can be adjusted by controlling the oxygen pressure and oxidation time during the formation of the tunnelling barrier. We present the results of the temperature dependence of the sub-gap current and in-plane magnetic-field dependence of the critical current, and compare them with the theoretical predictions.     

Nb/Al-AlOx/Nb junctions with controllable critical current density for qubit application

Nb/Al-AlOx/Nb tunnel junctions with controllable critical current density Jc are fabricated using the standard selective Nb etching process.Tunnel barriers are formed in different oxygen exposure conditions (oxygen pressure P and oxidation time t),giving rise to Jc ranging from 100 A/cm2 to above 2000 A/cm2.Jc shows a familiar linear dependence on P × t in logarithmic scales.We calculate the energy levels of the phaseand flux-type qubits using the achievable junction parameters and show that the fabricated Nb/Al-AlOx/Nb tunnel junctions can be used conveniently for quantum computation applications in the future.     

Macroscopic quantum tunneling in differently loaded Josephson junctions

In relation to the problem of quantum measurement, macroscopic quantum tunneling (MQT) in Josephson junctions is one of the most investigated topics. Although many theoretical studies have been devoted to this argument, the agreement on a single theoretical model has not yet been reached. The purpose of the present work is to analyze the load “seen” by the junction, in order to evaluate the contribution of the dissipation that modifies the decay-rate of the metastable state of the junction. The present work reports some theoretical results in relation to different kinds of loading systems, namely, the cases of capacitive, inductive and purely resistive load. The resistive load is considered also in relation to an experimental test.     

Chaos in Josephson junctions

A detailed analysis of the control space characterization of phase locked states and chaotic attractors in Josephson junctions is presented, based on a model that includes both quadratic damping and cosine interference terms. In addition, some novel features of the nonlinear characteristics of the junction like evolution of basin boundaries, bifurcation structure analysis and scaling behaviour of Lyapunov exponent are discussed.     

约瑟夫森器件中的宏观量子现象及超导量子计算

超导体中的电子结成库珀对，凝聚到可以用一个宏观波函数来描绘的能量基态，该波函数的位相是代表了成百万库珀对集体运动的宏观变量．以约瑟夫森结为基础元件的超导约瑟夫森器件，使人们能够控制并测量一个超导体的位相和库珀对数目，因此是研究宏观量子现象的理想系统．文章回顾了约瑟夫森器件中的宏观量子现象研究的发展历程，介绍了当前超导约瑟夫森器件在量子计算中的重要应用，并对它们的未来作了简要的展望．     

Fabrication of rhenium Josephson junctions

Rhenium is a superconductor with a relatively weak tendency to oxidize, which is advantageous in superconducting quantum circuit and qubit applications. In this work, Re/A1-A1Ox/Re Josephson tunnel junctions were fabricated using a selective film-etching process similar to that developed in Nb trilayer technology. The Re films had a superconducting transition temperature of 4.8 K and a transition width of 0.2 K. The junctions were found to be highly reproducible using the fabrication process and their characteristics had good quality with a low leakage current and showed a superconducting gap of 0.55 meV.     

Flux qubit with a large loop size and tunable Josephson junctions

We present the design of a superconducting flux qubit with a large loop inductance. The large loop inductance is desirable for coupling between qubits. The loop is configured into a gradiometer form that could reduce the interference from environmental magnetic noise. A combined Josephson junction, i.e., a DC-SQUID is used to replace the small Josephson junction in the usual 3-JJ (Josephaon junction) flux qubit, leading to a tunable energy gap by using an independent external flux line. We perform numerical calculations to investigate the dependence of the energy gap on qubit parameters such as junction capacitance, critical current, loop inductance, and the ratio of junction energy between small and large junctions in the flux qubit. We suggest a range of values for the parameters.     

Fabrication and characterization of all-Nb lumped-element Josephson parametric amplifiers

Josephson parametric amplifiers (JPAs) with nearly quantum-limited noise performance have become indispensable devices for the measurements of superconducting quantum information. We have developed an all-Nb lumped-element flux-driven JPA operating in the three-wave mixing mode. Our Nb-based JPA comprises Nb/Al-AlO_x/Nb Josephson junctions, a parallel-plate capacitor with SiO₂ dielectric sandwiched between two Nb layers, a bottom coplanar waveguides layer, and a top Nb wiring layer. We experimentally demonstrate a 20 dB gain over a 190 MHz bandwidth, a mean 1 dB compression of -123 dBm, and near quantum-limited noise performance. This fabrication process can be further used to design impedance transformed parametric amplifiers for multiple-qubit readout.     

Scattering of quasi-one-dimensional solitons on impurities in large Josephson junctions

Fluxon transmission through impurities of different shape in a quasi-one-dimensional long Josephson junction is investigated. The junction width is significantly less than its length but, at the same time, is of the order of the Josephson penetration length _λJ${\lambda }_J$ or exceeds it. The retrapping current on the impurities of the point, line and rectangular shape is computed as a function of the junction width both numerically and analytically. Good agreement between the analytic formulae and the numerical simulation results for the intermediate (several _λJ${\lambda }_J$) junction width is observed.     

Aspects of macroscopic quantum tunnelling in small Josephson junctions

Summary We study the effect of temperature on the lifetime of the resonant macroscopic quantum tunnelling voltage state. In view of experiments we consider a merit factor in order to balance between measuring extremely small signals of longer duration or larger signals of shorter duration.     

YBCO/Nb bulk junctions: Observation of the Josephson effect

Summary The fabrication procedure of reliable YBCO-based bulk junctions with a Nb film as a counterelectrode is described. Typical currentvoltage characteristics are presented, clearly showing the presence of the Josephson effect.     

The Phase Space Model of Nonrelativistic Quantum Mechanics

We focus on several questions arising during the modelling of quantum systems on a phase space. First, we discuss the choice of phase space and its structure. We include an interesting case of discrete phase space. Then, we introduce the respective algebras of functions containing quantum observables. We also consider the possibility of performing strict calculations and indicate cases where only formal considerations can be performed. We analyse alternative realisations of strict and formal calculi, which are determined by different kernels. Finally, two classes of Wigner functions as representations of states are investigated.     

Energy gap suppression and excess current in Tl_2Ba_2CaCu_2O_8 intrinsic Josephson junctions

Intrinsic Josephson junctions in misaligned Tl2Ba2CaCu2O8 thin film were fabricated on LaAlO3 substrate. The temperature dependence of the critical current is investigated around liquid nitrogen temperature. In the current voltage characteristic, large voltage jump and lack of resistive branch are observed, which shows good consistency with the intrinsic Josephson junctions. By analyzing the large gap voltage in the curve, great suppression of the energy gap is found. Through discussing the temperature dependence of the gap voltage in liquid nitrogen temperature, it is shown that this phenomenon can be caused by the non-equilibrium quasiparticle injection. The temperature influence on the excess current also confirms the non-equilibrium effect.     

Quantum Dynamics of Two Capacitively Coupled Superconducting Islands via Josephson Junctions

In this paper, we consider a system consisting of two capacitively coupled superconducting islands viaJosephson junctions. We show that it can be reduced to two coupling harmonic oscillators under certain conditions,and can be solved exactly in terms of a displacing transformation, a beam-splitter-like transformation, and a squeezingtransformation. It is found that the system evolves by a rotated-squeezed-coherent state when the system is initially in acoherent state. Quantum dynamics of the Cooper pairs in the two superconducting islands are investigated. It is shownthat the number of the Cooper pairs in the two islands evolves periodically.     

Detecting quantum signatures of optical fields by ultrasmall Josephson junctions

We prove that a mesoscopic Josephson junction, irradiated with a quantum superposition of two -out of phase optical coherent states, exhibits an experimentally observable sensitivity to the quantum coherences of the field state. Received 1 June 1999 and Received in final form 30 July 1999     

Aspects of dissipation effects in experiments on macroscopic quantum tunnelling in Josephson junctions

Summary The effect of dissipation in experiments on macroscopic quantum tunnelling in Josephson tunnel junctions are discussed. The frequency-dependent, nonlinear dynamic resistance of the junction makes it difficult to understand which effective linear resistance has to be chosen to compare the experimental results with the theory developed in the framework of the RSJ model. Various experiments reported in the literature lead to different conclusions and are presently discussed. Recently obtained experimental results on the thermal regime allow us to propose a new experimental strategy which ultimately should remove any ambiguity on the possibility to observe MQT process in the presence of dissipation in Josephson structures. To speed up publication, the authors have agreed not to receive proofs which have been supervised by the Scientific Committee.     

Hyperchaotic behaviours and controlling hyperchaos in an array of RCL-shunted Josephson junctions

This paper deals with dynamical behaviours in an array composed of two resistive-capacitive-inductive-shunted (RCL-shunted) Josephson junctions (RCLSJJs) and a shunted resistor. Numerical simulations show that periodic, chaotic and hyperchaotic states can coexist in this array. Moreover, a scheme for controlling hyperchaos in this array is presented by adjusting the external bias current. Numerical results confirm that this scheme can be effectively used to control hyperchaotic states in this array into stable periodic states, and different stable periodic states with different period numbers can be obtained by appropriately choosing the intensity of the external bias current.     

Current-voltage characteristics of voltage-biased Tl2Ba2CaCu2O8 intrinsic Josephson junctions

The voltage-biased current-voltage (I–V) characteristics of intrinsic Josephson junctions (IJJs), which are fabricated with misaligned high temperature superconducting Tl₂Ba₂CaCu₂O₈ (Tl-2212) thin film, are investigated experimentally. Three characteristic regions in the I–V curve are observed at 47 K. In the low voltage part, the current firstly increases and then decreases slowly with increasing the biased voltage, which is shown as a bump. In the next region, the current slightly increases with increasing the biased voltage until a sudden decrease of the current appears. Thereafter, branch structure forms with increasing the voltage on the I–V characteristic. The influence of the self-heating on the I–V characteristics is investigated and the temperature dependence of the I–V characteristics is measured to explore these characteristics in detail.     

Unusual constraints in the quantum statistical mechanics of Josephson junction systems

In order to apply quantum statistical mechanics to systems composed of Josephson junctions, the unconventional constraint of fixed macroscopic wave function magnitudes on either side of a junction must be accommodated. In order to use this information, the density matrix formalism must be extended to deal directly with probability distributions over general quantum states. As a result, in thermal equilibrium, the explicit temperature dependence becomes modified from the trivial 1/kT factors.