Design optimization for microwave coupling structures of a digital-to-analog converter based on series arrays of high-temperature superconducting Josephson junctions

A new coupling scheme of the external microwave signal for a digital-to-analog converter based on series arrays of high-temperature superconducting Josephson junctions has been proposed. It is suggested to couple the meander-like array inductively to a parallel microwave transmission line. Within the resistively shunted junction model different types of microwave coupling structures were analyzed with the goal to reduce the mutual phase locking and to achieve high output power and phase-locking stability. A harmonic balance technique was used to derive an analytic expression connecting the amplitudes of microwave voltages and currents in the array and the frequency of the external signal. Numerical simulations were performed to determine the boundaries of stable locking as a function of circuit parameters.     

嵌入到Fabry-Perot谐振腔的双晶约瑟夫森结阵列的阻抗匹配和相位锁定研究

在He等人所做的嵌入到Fabry-Perot谐振腔中约瑟夫森结阵列的微波辐照研究基础上,提出了同时实现约瑟夫森结阵列阻抗匹配和相位锁定的方法,进行了相关的电磁仿真和数值计算.双晶约瑟夫森结阵列被制作在YSZ双晶基片上,同时被嵌入到Fabry-Perot谐振腔内.通过在基片上制作与结阵列集成的串联馈电半波偶极天线阵,并对其结构进行优化实现了结与天线的匹配,数值计算表明结的辐射效率达到94%;利用天线阵辐射场的特征和对模型合理的设计,使Fabry-Perot谐振腔和基片同时谐振在合适的模式下,从而使结阵列与谐 关键词： 约瑟夫森结阵列 阻抗匹配 相位锁定 Fabry-Perot谐振腔     

Development of highly integrated RSFQ circuits on the basis of intrinsically shunted Josephson junctions

At PTB, for application in rapid single flux quantum (RSFQ) and voltage standard circuits, the development of highly integrated SDE circuits is focused on devices based on intrinsically shunted Josephson junctions in the SINIS and SNS technologies. In SINIS technology, the fabrication process has been optimized to values of the critical current density of j_C=500 A/cm² and the characteristic voltage of V_C=190 μV. To raise the circuit integration level, successive steps of development are shown by the example of the layout of an elementary RSFQ cell designed for higher values of j_C. In SNS technology, a fabrication process has been developed to produce small ramp-type junctions with contact areas smaller than 0.4 μm² and with values for j_C and V_C of about j_C=200 kA/cm² and V_C=20 μV. The design allows the SNS junction size to be further reduced down to the deep sub-micron range.     

约瑟夫森结与阵列的非线性混沌行为及研究进展

约瑟夫森结是一种利用超导材料制备的新型量子电子器件,它的一个显著特性是具有高度的非线性,因而会出现明显的混沌行为。约瑟夫森结与阵列的混沌行为具有重要的研究和应用价值,受到了广泛的关注。文中对约瑟夫森结与阵列的非线性混沌行为及研究进展做一些介绍。     

Mutual inductance effects in rf driven planar Josephson junctions arrays

In this paper we investigate the behavior of moderate size two-dimensional classical arrays of Josephson junctions in presence of an external oscillating field. We have included in the model the effects due to mutual inductance terms, and we have employed an explicit set of differential equations. We have found that the discretization parameter - i.e. the coupling term due to the inductance of the loops - is the most important parameter to determine the height of the Shapiro steps for a given amplitude and frequency of the rf-bias. The amplitude of the Shapiro steps in the case of zero frustration as a function of the coupling term shows a remarkable minimum for intermediate values when we retain all terms of the full model with mutual inductances, while the limits for very large and very small values of they are the same of the single Josephson junction. For the case of frustration 1/2 the Shapiro step becomes smaller in the rigid limit (i.e., small ) as expected for the XY model, and tends to the limit value of the single junctions for the decoupled case (i.e., large ). Received 9 November 1998 and Received in final form 6 April 1999     

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.     

Generation of macroscopic entangled coherent states with large Josephson junctions

We propose a simple and experimental architecture to generate macroscopic entanglement in a solid system which consists of two large Josephson junctions and a flux qubit. Through quantum measuring of flux qubit, entangled coherent states of two large Josephson junctions are obtained. The concurrence of entangled coherent states can be accommodated by adjusted systematic parameters. We also give a brief discussion on the experimental feasibility of this proposal.     

Computer simulations of the anisotropic Josephson junction arrays

Using complementary methods, we numerically investigate the anisotropic Josephson junction arrays (AJJAs). For various anisotropic strengths (λ$\lambda$), the Monte Carlo simulation gives a precise measurement of specific heat, magnetization, and magnetic susceptibility; while the resistively shunted-junction dynamical simulation produces the current–voltage characteristics. The critical temperatures obtained from the two approaches are well consistent with each other. We find that, except for the anisotropic limit (λ=0)$(\lambda =0)$, the quasi-long-range order is always established at a finite temperature. Further, the algebraically decaying spin–spin correlations in the low-temperature region are analyzed in detail. Finally, the full phase diagram of the AJJAs, which sheds some lights to the crossover of the XY model from one dimension to two, is constructed. These predictions are to be confronted with future experiments.     

Numerical analysis of the smart DROS

A digital superconducting quantum interference device (SQUID) has the potential for a very large dynamic range and a very high slew rate. Our concept of the digital SQUID consists of a double relaxation oscillation SQUID (DROS) with the complete flux locked loop (FLL) electronics on one single chip. The key element of the FLL circuitry is a superconducting up-down counter, which supplies the feedback flux to the DROS. In this paper we will concentrate on the numerical simulations of our new 100 MHz smart DROS. In this new design, the quantization unit of the feedback flux, δΦ_fb=52 mΦ₀, was optimized with respect to the flux noise of the DROS. By doing so, the flux slew rate was maximized without compromising the sensitivity. The optimization resulted in a maximum flux slew rate of δΦ_sig/δt=5×10⁶Φ₀/s.     

嵌入Fabry-Perot谐振腔的高温超导双晶约瑟夫森结的毫米波辐照特性研究

采用嵌入Fabry-Perot谐振腔的方式,研究了Tl2Ba2CaCu2O8(Tl-2212)高温超导薄膜双晶约瑟夫森结的毫米波辐照特性.重点研究了双晶约瑟夫森结与Fabry-Perot谐振腔的耦合特性,发现放置在谐振腔中的结的位置、角度、结的图形以及Fabry-Perot谐振腔中两镜面间的距离等对耦合都有很大的影响.通过精细调节这些参数,可使双晶约瑟夫森结与外加毫米波达到最佳耦合.在最佳耦合情况下,能观察到9级明显的夏皮罗台阶.利用Fabry-Perot谐振腔技术,解决了约瑟夫森结与毫米波的耦合问题,为高温超导约瑟夫森结的毫米波及太赫兹波的辐射和检测研究奠定了基础.     

Ac Josephson effect in Corbino-geometry Josephson junctions constructed on Bi2Te3 surface

Recently, a Corbino-geometry type of Josephson junction constructed on the surface of topological insulators has been proposed for hosting and braiding Majorana zero modes. As a first step to test this proposal, we successfully fabricated Corbino-geometry Josephson junctions (JJs) on the surface of Bi₂Te₃ flakes. Ac Josephson effect with fractional Shapiro steps was observed in the Corbino-geometry JJs while the flux in the junction area was quantized. By analyzing the experimental data using the resistively shunted Josephson junction model, we found that the Corbino-geometry JJs exhibit a skewed current—phase relation due to its high transparency. The results suggest that Corbino-geometry JJs constructed on the surface of topological insulators may provide a promising platform for studying Majorana-related physics.     

BCS quasi-particle tunnelling current in Josephson tunnel junctions

Summary The recent improvements in the fabrication technology have succeeded in obtaining high-quality Josephson tunnel junctions. TheI–V characteristics of these junctions exhibit now lesser and lesser differences from the theoretical predictions. The various figures of merit, so far introduced to qualify the junctions, appear now focused on too limited aspects and a direct comparison with the detailed prediction of the theory is in order. For this awaken interest in the detailed predictions of the BCS theory, we have revisited the relevant formulae for the quasi-particle tunnelling current. A detailed discussion of the analytical transformation necessary for a simple numerical evaluation of this current is reported. SeveralI–V curves are obtained using the parameter values corresponding to the case of Nb-based junctions, which is the actual running technology. Peculiar interesting aspects are outlined.     

高温超导约瑟夫森结阵列的相位锁定

根据交流约瑟夫森效应,研究了嵌入Fabry-Perot谐振腔里的约瑟夫森结阵列在微波辐照下的相位锁定问题。结阵列是由生长在双晶钇稳定氧化锆(YSZ)基片上的YB2Cu3O7(YBCO)超导薄膜光刻成微桥得到的。通过优化设计,在温度为79.2K辐照频率为77.465GHz的条件下,包含620个串联约瑟夫森双晶结的结阵列在外加微波辐照下实现了相位锁定,得到了陡峭的夏皮罗台阶。其第一级夏皮罗台阶的电压约为0.1V,台阶高度约为0.17mA。试验结果表明,这种结阵列结构在电压基准的应用上有极大的优势,而且这种准光学耦合方法在太赫兹信号发生和检测方面有很好的应用前景。     

Multifluxon dynamics in driven Josephson junctions

The dynamics of fluxons in a long Josephson junction driven by time-varying nonuniform bias currents are described by a generalization of the sine-Gordon equation. This equation has solitary wave solutions which correspond to current vortices or quantized packets of magnetic flux in the junction. As with the sine-Gordon equation, multifluxon solutions may be demonstrated for the long Josephson junction. Our numerical calculations show that several fluxons may be launched or annihilated at the end of a junction. We also show multiple steady state conditions which correspond to one or more flux quanta trapped in the junction.     

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.     

Synchronization of chaos in resistive-capacitive-inductive shunted Josephson junctions

We present a scheme for chaotic synchronization in two resistive- capacitive-inductive shunted Josephson junctions （RCLSJJs） by using another chaotic RCLSJJ as a driving system. Numerical simulations show that whether the two RCLSJJs are chaotic or not before being driven, they can realize chaotic synchronization with a suitable driving intensity, under which the maximum condition Lyapunov exponent （MCLE） is negative. On the other hand, if the driving system is in different periodic states or chaotic states, the two driven RCLSJJs can be controlled into the periodic states with different period numbers or chaotic states but still maintain the synchronization.     

超导量子器件片上皮法电容的制备及测量

片上集成电容是超导量子芯片上的核心器件，其数值一般在百飞法(fF)至皮法(pF)范围.采用常规微纳加工技术在蓝宝石基片上制备了铌-氧化硅-铝(Nb/SiO₂/Al)平行板电容.利用刻蚀工艺制备了平行板电容器的下极板Nb,利用剥离工艺制备平行板电容器的上极板Al和介电层SiO₂.室温下利用锁相放大原理和桥式电路原理测定电容大小，两种方法测定电容值基本一致，表明锁相放大原理测试pF级电容的可靠性.利用该电容与铝基约瑟夫森结组成谐振器，制备了中心频率位于4.35 GHz的约瑟夫森参量放大器.在稀释制冷机中10 mK温度下测定直流偏置谐振器的磁通-频率相位图，拟合数据获得的电容值与室温测定电容值接近，表明在mK、GHz条件下工作的片上集成电容可在室温、kHz条件下测定其数值大小.     

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.     

External electric field control in the charge qubits including three Josephson junctions

Based on the standard canonical quantization principle, this paper gives the quantization scheme for the charge qubits mesoscopic circuit including three Josephson junctions coupled capacitively. By virtue of the Heisenberg equation, the time evolution of the phase difference operators across the polar plates and the number operators of the Cooper-pairs on the island are investigated and the modification of the Josephson equation is discussed. The time evolution of the phase difference operators is analysed when the Josephson junctions are irradiated by the external electrical field, which is referred to as also the obtainable controlling parameter.     

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.