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。     

Chaotic behavior of a stack of intrinsic Josephson junctions at the transition to branching for overcritical currents

Phase dynamics of a stack of coupled intrinsic Josephson junctions was investigated in the framework of capacitively coupled Josephson junctions with diffusion current model. We study the transition from the current-voltage characteristic specific to Josephson junctions arrays with small dissipation and weak coupling between the junctions to the arrays with strong coupling between the junctions and high dissipation. Low dissipative arrays of Josephson junctions are characterized by the absence of branching for overcritical currents which appears for highly dissipative arrays. Described branching appears due to charging on the superconducting layers and charge traveling waves generation. Arrays of Josephson junctions with intermediate values of coupling and dissipation parameters are characterized by the chaotic behavior, confirmed by positive Lyapunov exponent, and branching on the current voltage characteristic for both sub- and overcritical currents.     

Quantum phase transition and Coulomb blockade with one-dimensional SQUID arrays

We report on experiments with one-dimensional (1D) arrays of small-capacitance superconducting quantum interference devices (SQUIDs), where an external magnetic field can be used to tune in situ the Josephson coupling between neighboring superconducting electrodes. We have studied the superconductor–insulator transition in such arrays, and have also used these arrays to bias a single Josephson junction. In the later experiment, we have observed a clear Coulomb blockade of Cooper-pair tunnelling (CBCPT) in the single junction.     

Josephson-junction networks and roughening problems

We discuss the phase diagram of regular networks of quantum mechanical Josephson junctions in one and two dimensions for different choices of the Coulomb interaction between pairs. In a particular case this is equivalent to a quantum interface with lateral tunneling along the boundary. Using a functional integral approach the partition function is transformed into that of classical roughening or Coulomb gas problems. It is shown, in particular, that the structure of the phase diagram depends crucially on the form of the Coulomb interaction and that with dissipative interactions both globally and locally superconducting phases are possible. The relation of our results to recent experiments on granular superconducting films and ideal Josephson junction arrays is discussed briefly.Dedicated to Professor W. Brenig on the occasion of his 60th birthday     

Symmetric behavior of vortex states of superconducting networks in a magnetic field

We present magnetic field dependence of phase transition temperature and vortex configuration of superconducting networks based on theoretical study. The applied magnetic field is called “filling field” that is defined by applied magnetic flux (in unit of the flux quantum) per unit loop of the superconducting network. If a superconducting network is composed of very thin wires whose thicknesses are less than coherence length, the de Gennes–Alexander (dGA) theory is applicable. We have already shown that field dependences of transition temperature curves have symmetric behavior about the filling field of 1/2 by solving the dGA equation numerically in square lattices, honeycomb lattices, cubic lattices and those with randomly lack of wires networks. Many experimental studies also show the symmetric behavior. In this paper, we make an explicit theoretical explanation of symmetric behaviors of superconducting network respect to the applied field.     

Josephson Currents and Gap Enhancement in Graph Arrays of Superconductive Islands

Evidence is reported that topological effects in graph-shaped arrays of superconducting islands can condition superconducting energy gap and transition temperature. The carriers giving rise to the new phase are couples of electrons (Cooper pairs) which, in the superconducting state, behave as predicted for bosons in our structures. The presented results have been obtained both on star and double comb-shaped arrays and the coupling between the islands is provided by Josephson junctions whose potential can be tuned by external magnetic field or temperature. Our peculiar technique for probing distribution on the islands is such that the hopping of bosons between the different islands occurs because their thermal energy is of the same order of the Josephson coupling energy between the islands. Both for star and double comb graph topologies the results are in qualitative and quantitative agreement with theoretical predictions.     

Peculiarity of charge dynamics in High-Tc cuprates

Discussion is focused on the peculiarity of the out-of-plane and the in-plane charge dynamics related to the two-dimensionality in high-T_c cuprates. Recent observations of a double Josephson plasmon and a intra-bilayer Josephson effect remind us that each CuO₂-plane is in fact an independent superconducting layer, suggesting that the superconducting coherence length in the c-direction is shorter than the interlayer distance. The origin of this extremely short c-axis coherence length as well as the long c-axis penetration depth is discussed in relation with the incoherent c-axis transport in the normal state. Another peculiarity is a strong itinerant nature of charges within the planes. As an example, it is demonstrated that a static charge order is inhibited even in the “stripe” phase in the cuprates.     

Novel magnetoinductance effects in Josephson junction arrays: A single-plaquette approximation

Using a single-plaquette approximation, novel magnetoinductance effects in Josephson junction arrays (JJAs) are predicted, including the appearance of steps in the temperature behavior of magnetic susceptibility. The number of steps (as well as their size) is controlled by the kinetic inductance of the plaquette whose field dependence is governed by the Abrikosov vortices penetrating superconducting regions of the array. The experimental conditions under which the predicted effects should manifest themselves in artificially prepared JJAs are discussed.     

Experimental evidence for anisotropic response of a driven vortex lattice

We present kinetic inductance measurements in current driven Josephson junction arrays. Measurements performed with circular coils indicate that this technique is very sensitive to the vortex mobility. Results obtained with anisotropic detection coils provide experimental evidence for the anisotropic response of a driven vortex lattice. Anisotropic behavior is obtained when rising the temperature or the mean vortex velocity as indicated by the loss of the superconducting shielding capability, first in the direction of vortex motion and then in the perpendicular direction.     

Quantum phase transitions and vortex dynamics in superconducting networks

Josephson-junction arrays are ideal model systems to study a variety of phenomena such as phase transitions, frustration effects, vortex dynamics and chaos. In this review, we focus on the quantum dynamical properties of low-capacitance Josephson-junction arrays. The two characteristic energy scales in these systems are the Josephson energy, associated with the tunneling of Cooper pairs between neighboring islands, and the charging energy, which is the energy needed to add an extra electron charge to a neutral island. The phenomena described in this review stem from the competition between single-electron effects with the Josephson effect. They give rise to (quantum) superconductor–insulator phase transitions that occur when the ratio between the coupling constants is varied or when the external fields are varied. We describe the dependence of the various control parameters on the phase diagram and the transport properties close to the quantum critical points. On the superconducting side of the transition, vortices are the topological excitations. In low-capacitance junction arrays these vortices behave as massive particles that exhibit quantum behavior. We review the various quantum–vortex experiments and theoretical treatments of their quantum dynamics.     

Theory of phase dynamics in intrinsic Josephson junctions with multigap superconducting layers

We construct a theory of dynamical behavior in intrinsic Josephson junction stacks with multigap superconducting layers. The theory predicts the existence of two kinds of phase modes, one of which is the Josephson-plasma mode and other of which is the Leggett’s mode. We discuss a cooperative phenomena induced by inter-band Josephson coupling in addition to capacitive and inductive couplings between the superconducting layers.     

Josephson effect between superconducting nanograins with discrete energy levels

We investigate the Josephson effect between two coupled superconductors, coupled by the tunneling of pairs of electrons, in the regime that their energy level spacing is comparable to the bulk superconducting gap, but neglecting any charging effects. In this regime, BCS theory is not valid, and the notion of a superconducting order parameter with a well-defined phase is inapplicable. Using the density matrix renormalization group, we calculate the ground state of the two coupled superconductors and extract the Josephson energy. The Josephson energy is found to display a reentrant behavior (decrease followed by increase) as a function of increasing level spacing. For weak Josephson coupling, a tight-binding approximation is introduced, which illustrates the physical mechanism underlying this reentrance in a transparent way. The DMRG method is also applied to two strongly coupled superconductors and allows a detailed examination of the limits of validity of the tight-binding model.Received: 8 September 2003, Published online: 28 May 2004PACS: 74.20.-z Theories and models of superconducting state - 74.78.-w Superconducting films and low-dimensional structures - 74.50. + r Tunneling phenomena; point contacts, weak links, Josephson effects     

Finite Josephson junction arrays with open boundaries in magnetic field: Ground state energy and first critical field

We have investigated the size dependence of the ground state energy as a function of the magnetic field in Josephson junction arrays with open boundaries. We present a simple rings model that reproduces with great confidence the size and field dependence of the energy of the system obtained by numerical simulation of the Hamiltonian. From these results we obtained the size dependence of the first penetration field, where the one-vortex state becomes favorable compared to the zero-vortex state.Received: 15 December 2003, Published online: 13 July 2004PACS: 74.81.Fa Josephson junction arrays and wire networks     

New model for systems of mesoscopic Josephson junctions

Quantum fluctuations of the phases of the order parameter in two-dimensional arrays of mesoscopic Josephson junctions and their effect on the destruction of superconductivity in the system are investigated by means of a quantum-cosine model that is free of the incorrect application of the phase operator. The proposed model employs trigonometric phase operators and makes it possible to study arrays of small superconducting granules, pores containing superfluid helium, or Josephson junctions in which the average number of particles n ₀ (effective bosons, He atoms, and so on) is small, and the standard approach employing the phase operator and the particle number operator as conjugate operators is inapplicable. There is a large difference in the phase diagrams between arrays of macroscopic and mesoscopic objects for n ₀<5 and U<J (U is the characteristic interaction energy of the particles per granule and J is the Josephson coupling constant). Re-entrant superconductivity phenomena are discussed. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 10, 649–654 (25 November 1997)     

Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture

Superconducting quantum circuits based on Josephson junctions have made rapid progress in demonstrating quantum behavior and scalability. However, the future prospects ultimately depend upon the intrinsic coherence of Josephson junctions, and whether superconducting qubits can be adequately isolated from their environment. We introduce a new architecture for superconducting quantum circuits employing a three-dimensional resonator that suppresses qubit decoherence while maintaining sufficient coupling to the control signal. With the new architecture, we demonstrate that Josephson junction qubits are highly coherent, with T2 ～ 10 to 20 μs without the use of spin echo, and highly stable, showing no evidence for 1/f critical current noise. These results suggest that the overall quality of Josephson junctions in these qubits will allow error rates of a few 10(-4), approaching the error correction threshold.     

Dissipative currents in superfluid 3He weak links

We calculate the current-pressure relation for pinholes connecting two volumes of bulk superfluid 3He-B. The theory of multiple Andreev reflections, adapted from superconducting weak links, leads to a nonlinear dependence of the dc current on pressure bias. In arrays of pinholes one has to take into account oscillations of the texture at the Josephson frequency. The associated radiation of spin waves from the junction leads to an additional dissipative current at small biases, in agreement with measurements.     

Observation of quantum oscillations between a Josephson phase qubit and a microscopic resonator using fast readout

We have detected coherent quantum oscillations between Josephson phase qubits and critical-current fluctuators by implementing a new state readout technique that is an order of magnitude faster than previous methods. These results reveal a new aspect of the quantum behavior of Josephson junctions, and they demonstrate the means to measure two-qubit interactions in the time domain. The junction-fluctuator interaction also points to a possible mechanism for decoherence and reduced fidelity in superconducting qubits.     

Magnetic properties of two-dimensional SNS-type Josephson junction arrays

JETP Letters - The field dependence of the magnetic moment of square (100×100) SNS-type Josephson junction arrays was studied by a SQUID magnetometer. A considerable difference in the behavior...     

本征约瑟夫森结阵列的PSpice模型及混沌行为研究

建立了电容耦合本征约瑟夫森结阵列在电路仿真软件PSpice中的模型，利用这个模型对恒定电流驱动下的本征约瑟夫森结阵列进行了仿真研究.通过与不存在电容耦合的本征约瑟夫森结的时域波形、频谱、分维和相图等结果的对比，发现了本征约瑟夫森结阵列中的混沌行为.这一发现对于本征约瑟夫森结的理论和应用研究有重要的意义.