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.     

Quasiperiodically driven Josephson junctions: strange nonchaotic attractors, symmetries and transport

We consider the dynamics of the overdamped Josephson junction under the influence of an external quasiperiodic driving field. In dependence on parameter values either a quasiperiodic motion or a strange nochaotic attractor (SNA) can be observed. The latter corresponds to a resistive state in the current-voltage characteristics while for quasiperiodic motion a finite superconducting current exists for zero voltage. It is shown that in the case of SNA a nonzero mean voltage across the junction can appear due to symmetry breakings. Based on this observation a detailed symmetry consideration of the generalized equation of motion is performed and symmetry conditions ensuring zero mean voltage across the junction are found. Received 16 August 2001 and Received in final form 22 January 2002     

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.     

Directed transport and complex dynamics of vortices in a Josephson junction network driven by modulated currents

Directed transport of vortices in a Josephson junction network (JJN) with structural disorder is studied using a numerical simulation. Using spatiotemporal modulation of driving currents, the directed transport of vortices occurs even in the presence of disorder under certain conditions. From the analyses of the current–voltage and local voltage characteristics, it is found that the collective motion of vortices has an importance for the occurrence of directed transport.     

Quantitative calculation and bifurcation analysis of periodic solutions in a driven Josephson junction including interference current

The calculation scheme for periodic solutions in an rf-driven Josephson junction including interference current is derived by using the incremental harmonic balance method. The approximate analytical expressions of stable and unstable periodic orbits are obtained. The stability and bifurcation of the periodic solutions are analyzed based on Floquet theory. The results show that, with the increase of the driving amplitude, one of the periodic solutions undergoes symmetry-breaking and period-doubling bifurcation, which leads to chaos eventually. However, the other periodic solution of the system disappears via a saddle-node bifurcation.     

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.     

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.     

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.     

Quantum coherence in a superfluid Josephson junction

We report a new kind of experiment in which we take an array of nanoscale apertures that form a superfluid (4)He Josephson junction and apply quantum phase gradients directly along the array. We observe collective coherent behaviors from aperture elements, leading to quantum interference. Connections to superconducting and Bose-Einstein condensate Josephson junctions as well as phase coherence among the superfluid aperture array are discussed.     

Josephson effect in a Coulomb-blockaded SINIS junction

The problem of a Josephson current through a Coulomb-blocked nanoscale superconductor-normal-superconductor structure with tunnel contacts is reconsidered. Two different contributions to the phase-biased supercurrent I(?) are identified, which are dominant in the limits of weak and strong Coulomb interaction. Full expression for the free energy valid at arbitrary Coulomb strength is found. The current derived from this free energy interpolates between known results for weak and strong Coulomb interaction as the phase bias changes from 0 to π. In the broad range of Coulomb strength, the current-phase relation is substantially nonsinusoidal and qualitatively different from the case of semiballistic SNS junctions. The Coulomb interaction leads to the appearance of a local minimum in the current at some intermediate value of the phase difference applied to the junction.     

Novel spin dynamics in a Josephson junction

We address the dynamics of a single spin embedded in the tunneling barrier between two superconductors. As a consequence of pair correlations in the superconducting state, the spin displays a rich and unusual dynamics. To properly describe the time evolution of the spin we find the generalized Wess-Zumino-Witten-Novikov term in the effective action for the spin on the Keldysh contour. The superconducting correlations lead to an effective spin action which is nonlocal in time leading to unconventional precessions. Our predictions might be directly tested for macroscopic spin clusters.     

Fluxon interaction in a long Josephson junction

Fluxon interaction in a long Josephson junction with bias current and losses is investigated by means of a perturbational approach. A simple analytical theory of the congelation (bunching) of unipolar fluxons is presented. Asymptotic results are confirmed by numerical solutions. It is shown that a system of congealed fluxons reflects from an open end of the junction without being destroyed.     

Rabi-type oscillations in a classical Josephson junction

We study analytically and numerically the phase-modulation properties of a classical Josephson tunnel junction biased in the zero-voltage state and phase locked to an external ac field. We show that the phase-locked state is being modulated in the transients, or in response to perturbations, and the modulation frequency is calculated as a function of relevant system parameters, such as microwave field amplitude. Our analysis demonstrates that the modulation of a phase-locked state in an entirely classical Josephson junction produces oscillations analogous to quantum mechanical Rabi oscillations, expected to be observed under the same conditions.     

Curved Josephson junction

The constant curvature one and quasi-one dimensional Josephson junction is considered. On the base of Maxwell equations, the sine–Gordon equation that describes an influence of curvature on the kink motion was obtained. It is showed that the method of geometrical reduction of the sine–Gordon model from three to lower dimensional manifold leads to an identical form of the sine–Gordon equation.     

Current noises in a topological Josephson junction

We study the transport properties of a superconductor-quantum spin Hall insulator-superconductor Josephson junction both in the absence and in the presence of a DC bias voltage. As the system is predicted to host Majorana fermions at its interfaces,the Andreev bond states are supposed to exhibit a distinct 4π periodicity in the superconducting phase difference, namely the fractional Josephson effect. Using the non-equilibrium Green's function method, we calculate the current and the related current noise based on a tight-binding Hamiltonian. Our direct results show that the fractional Josephson effect can not be seen in equilibrium junctions. While in non-equilibrium junctions, this effect can be confirmed by the multiple Andreev reflections induced peaks of the non-equilibrium noise, which appear at discrete frequencies ω = ne V with n being an integer number.     

Vibrating superconducting island in a Josephson junction

We consider a combined nanomechanical-supercondcuting device that allows the Cooper pair tunneling to interfere with the mechanical motion of the middle superconducting island. Coupling of mechanical oscillations of a superconducting island between two superconducting leads to the electronic tunneling generates a supercurrent that is modulated by the oscillatory motion of the island. This coupling produces alternating finite and vanishing supercurrent as function of the superconducting phases. Current peaks are sensitive to the superconducting phase shifts relative to each other. The proposed device may be used to study the nanoelectromechanical coupling in case of superconducting electronics.     

Relaxation dynamics in a stochastic bosonic Josephson junction

We consider a bosonic Josephson junction in the Bose-Hubbard two-mode approximation where some of the parameters are corrupted by physically meaningful noise processes and study the corresponding relaxation dynamics towards its equilibrium state. We show with numerical simulations that this model can essentially capture all the important features observed in a recent experiment regarding the relaxation dynamics in one-dimensional bosonic Josephson junctions, namely the damped oscillations of the population imbalance and the relative phase, as well as the large final coherence factor. We expect that this work will further motivate research about the origin of relaxation mechanism in these systems.     

Electromagnetic waves in a randomly inhomogeneous Josephson junction

Spectrum modification and damping of Josephson plasma waves induced by random inhomogeneities of the critical current through the superconductor contact and the averaged Green function of such excitations are analyzed. In the self-consistent approximation that makes it possible to take into account multiple wave scattering on the inhomogeneities, the frequency and damping of averaged waves, as well as position ν _m and peak width Δν of the Fourier transform imaginary part of the averaged Green function, are determined as functions of wavevector k. The evolution of such functions with the variation of the correlation radius and the relative r.m.s. fluctuations of inhomogeneities is studied. The inhomogeneity-induced wave frequency decrease observed in the long wavelength spectral region qualitatively agrees with the ν _m behavior. It is established that in the case of “long-range” inhomogeneities, the linear dependence of damping on k changes to the inversely proportional one, and damping tends to zero as k → 0, while Δν at small k attains its maximal values due to nonuniform broadening. In the presence of “short-range” inhomogeneities, the wave damping and Δν are found to be similar functions of k. The results are compared to the numerical calculation data.     

Quantum fluctuations in a distributed Josephson junction and the spectral properties of Josephson oscillators

Within the framework of a tunneling Hamiltonian, we obtain an equation for the reduced density matrix to describe quasiclassical dynamics and fluctuation effects in distributed Josephson junctions for voltages comparable with the superconducting gap. For quasiclassical dynamics, we derive the Langevin equation describing in a self-consistent way the resistive state and fluctuations due to both the tunneling current and the electromagnetic field. Current-voltage characteristics of a Josephson oscillator are calculated in the high magnetic field approximation. The intensity and shape of the spectral line of radiation due to vortices moving in a distributed Josephson junction are found.