Asymmetrical solutions and role of thermal fluctuations in dc current driven extended Josephson junction

Extended Josephson junction driven by dc bias current is studied numerically. Two types of solutions, symmetrical and asymmetrical, are found. The current–voltage characteristic (IVC) is calculated. The symmetrical solutions form main hysteretic IVC and asymmetrical ones create an additional branch. Depending on the bias current value periodic, quasiperiodic and chaotic modes of the junction motion was observed. Dynamics of the junction affected by thermal fluctuations was analyzed. Stability of different states of the junction is discussed.     

Direct observation of dynamical bifurcation between two driven oscillation states of a Josephson junction

We performed a novel phase-sensitive microwave reflection experiment which directly probes the dynamics of the Josephson plasma resonance in both the linear and the nonlinear regime. When the junction was driven below the plasma frequency into the nonlinear regime, we observed for the first time the transition between two different dynamical states predicted for nonlinear systems. In our experiment, this transition appears as an abrupt change in the reflected signal phase at a critical excitation power. This controlled dynamical switching can form the basis of a sensitive amplifier, in particular, for the readout of superconducting qubits.     

Tangential bifurcation and critical indices in a Josephson junction

The scaling properties of the “laminar time” of intermittently chaotic systems are used to investigate the critical behavior and the noise voltage of a Josephson junction.     

Interior crises and symmetries in a driven Josephson junction

The dynamics of a harmonically driven and nonlinearly damped pendulum is related to a current-fed Josephson junction. Through an extensive numerical simulation we show that the symmetry properties of the equation of motion are closely related with the development of chaotic solutions. Two different interior crises are discussed, both of them involve two broken-symmetric chaotic attractors.     

Mode selection in a neuron driven by Josephson junction current in presence of magnetic field

Josephson junction is an active electric component and its channel current can be adjusted by external magnetic field, which can trigger additive phase error along the junction. From physical viewpoint, the Josephson junction can capture and release field energy when it is exposed to a magnetic field, and this time-varying current can be used to excite neural circuit for generating target firing patterns. In this paper, a Josephson junction is connected to a simple neural circuit, which is made of a capacitor, induction coil, a nonlinear resistor, two linear resistors and one constant voltage source in the branch, and the improved neural circuit is adjusted to percept external magnetic field and estimate the potential application of Josephson junction in nonlinear circuits. Bifurcation analysis is applied to explore the mode selection and dynamics dependence on parameters setting in the biophysical neural circuits. Furthermore, the neural circuit is exposed to external magnetic field and its physical effect is estimated by applying scale transformation on the variables and parameters in the neural circuit. It is confirmed that the neural circuit can be controlled and the neural activity shows distinct mode transition by taming the intensity (or angular frequency in periodic field) of external magnetic field. This kind of neural circuit can be further used as smart sensor for detecting weak magnetic field.     

约瑟夫森结中周期解及其稳定性的解析分析

针对交流激励下电阻-电容分路的约瑟夫森结,采用增量谐波平衡法推导了系统中周期解的解析表达式,并运用Floquet理论分析了周期解的稳定性.发现系统处于稳定周期状态的同时,还存在着丰富的不稳定周期解.通过计算Floquet乘数,得到了系统稳定周期解失稳时的临界参数值,并确定了系统发生的分岔类型,从理论上证明了系统随激励电流幅值的增加由倍周期分岔通向混沌.解析分析与数值计算结果具有很好的一致性. 关键词： 约瑟夫森结 增量谐波平衡法 周期解 分岔     

Direct observation of dynamical bifurcation in a superfluid Josephson junction

We report a direct observation of dynamical bifurcation between two plasma oscillation states of a superfluid Josephson junction. We excite the superfluid plasma resonance into a nonlinear regime by driving below the natural plasma frequency and observe a clear transition between two dynamical states. We also demonstrate bifurcation by changing the potential well with temperature variations.     

Coherent motion of vortices driven by both dc and ac current in a Josephson junction ratchet array

We have studied the vortex dynamics in a ratchet array of Josephson junctions in the presence of magnetic field of 1/5 flux quantum per plaquette. The ratchet potential consists of both alternate critical currents for all the vertical junctions and alternate shunt capacitances for all the horizontal junctions. The vortices driven by an ac current in some parameters are found to show the directional motion as well as the asymmetric current-voltage characteristics. We use the time-dependent vorticity and the time-dependent vorticity-vorticity correlation function to analyze the motion of vortices on a few fractional Shapiro steps. We have found that vortices on a fractional Shapiro n/5-step move coherently through n plaquettes during a single ac cycle. The asymmetric features of the ratchet array gradually disappear as finite temperature increases.     

Josephson junction circuit model and its global bifurcation diagram

In order to understand the meaning of a typical Josephson junction, we introduce a circuit model which can be used to describe the dynamical behavior of the junction under the exciting of radio-frequency current. The global bifurcation diagram of the Josephson junction is demonstrated with a computer simulation. Through the diagram we observe the complex and rich dynamics of the junction, e.g. bifurcation, phase-locking, and chaos. The relation between motion and symmetry breaking is also discussed.     

Josephson current in a clean superconductor normal-metal superconductor junction

Based on a simple matrix method, we investigate the effects of Fermi vector mismatch and elastic barrier on the dc Josephoson current through a ballistic, normal, one-dimensional quantum channel in contact with two superconducting electrodes. Our results are able to account for the recent experimental results.     

Josephson current in a clean superconductor normal-metal superconductor junction

Based on a simple matrix method, we investigate the effects of Fermi vector mismatch and elastic barrier on the dc Josephoson current through a ballistic, normal, one-dimensional quantum channel in contact with two superconducting electrodes. Our results are able to account for the recent experimental results.     

Phase dynamics of a Josephson junction ladder driven by modulated currents

Phase dynamics of disordered Josephson junction ladders (JJLs) driven by external currents which are spatially and temporally modulated is studied using a numerical simulation based on a random field XY model. This model is considered theoretically as an effective model of JJLs with structural disorder in a magnetic field. The spatiotemporal modulation of external currents causes peculiar dynamical effects of phases in the system under certain conditions, such as the directed motion of phases and the mode-locking in the absence of dc currents. We clarify the details of effects of the spatiotemporal modulation on the phase dynamics.     

Spin Josephson current in a ferromagnet/noncentrosymmetric superconductor junction

We investigate the equilibrium spin transport in a ferromagnet/noncentrosymmetric superconductor (FM/NCS) junction where the NCS has a dominant triplet order parameter and helical edge state. Based on the symmetry analysis and numerical calculation, we demonstrate that there is a nonzero spin supercurrent flowing in the junction, which stems from the exchange coupling between the FM magnetization and triplet Cooper-pair spin. It is also found that a transverse spin current other than the helical edge spin current is flowing along the interface of the junction, and its polarization is related to the longitudinal spin supercurrent. Besides, an equilibrium Hall current is also shown to flow along the junction’s interface due to the broken time-reversal symmetry from the FM.     

线性延时反馈Josephson结的Hopf分岔和混沌化

考虑线性延时反馈控制下电阻-电容分路的Josephson结,运用非线性动力学理论分析了受控系统平凡解的稳定性.理论分析表明,随着控制参数的改变,系统的稳定平凡解将会通过Hopf分岔失稳,并推导了发生Hopf分岔的临界参数条件.对不同参数条件下受控系统的动力学进行了数值分析.结果显示,系统由Hopf分岔产生的稳定周期解,将进一步通过对称破缺分岔和倍周期分岔通向混沌. 关键词： 约瑟夫森结 线性延时反馈 Hopf分岔 混沌     

Josephson current in an irradiated Weyl semimetal junction

The influence of the off-resonant circularly polarized light on the Josephson current in the time-reversal broken superconducting Weyl semimetal junctions is investigated by using the Bogoliubov–de Gennes equation and the transfer matrix approach. Both the zero momentum BCS pairing states and the finite momentum Fulde–Ferrell–Larkin–Ovchinnikov(FFLO) pairing states are considered for the Weyl superconductors. When a circularly polarized light is applied, it is shown that the current phase relation remains unchanged for the BCS pairing with the increasing of incident radiation intensity A_0. For FFLO pairing, the Josephson current exhibits the 0–π transition and periodic oscillation as a function of A_0. The dependence of free energy and critical current on A_0 are also investigated.     

Closed form solutions for the self-resonances in a short Josephson junction

We present a closed form solution for the self-resonances in a short Josephson tunnel junction. This solution is alternative to the well-known textbook result (Barone and Paternó (1982) and Kulik (1965)) [1] and [2] based on a series expansion. Results are derived for the up-to-date case of a 0-π junction.     

Side-gate modulation of critical current in mesoscopic Josephson junction

We study the normal state conductance and the Josephson current in a superconductor–2DEG–superconductor structure where the size/shape of the 2DEG-region can be modified by an additional side-gate electrode. The considered transport properties follow from the retarded Green function which we compute by employing a tight-binding-like representation of the Hamiltonian in the 2DEG region. Our model studies offer a qualitative demonstration of the recently observed effects caused by side-gate modulation.     

Magnetic field dependence of the maximum Josephson current in a double-barrier junction

The influence of a constant magnetic field on the maximum Josephson current of a double-barrier junction is studied. Owing to the peculiarity of the current–phase relation of this composite device, the resulting Fraunhofer-like pattern shows an overall enhancement of the maximum Josephson current with respect to the usual single-junction curves for very small difference in the coupling energies of the two pairs of adjacent layers in the system.     

Inelastic tunnelling and the pair-quasiparticle interference current in Josephson junctions

The contribution to the quasiparticle current and pair—quasiparticle interference current of inelastic tunnelling due to the excitation of a boson mode in the tunnelling barrier is evaluated.