Josephson Junction Ladders Research Articles

Incommensurate dynamics of resonant breathers in Josephson junction ladders

We present theoretical and experimental studies of resonant localized resistive states in a Josephson junction ladder. These complex breather states are obtained by tuning the breather frequency into the upper band of linear electromagnetic oscillations of the ladder. Their prominent feature is the appearance of resonant steps in the current-voltage (I-V) characteristics. We have found the resonant breather-like states displaying incommensurate dynamics. Numerical simulations show that these incommensurate resonant breathers persist for very low values of damping. Qualitatively similar incommensurate breather states are observed in experiments performed with Nb-based Josephson ladders. We explain the appearance of these states with the help of resonance-induced hysteresis features in the I-V dependence.

Plastic depinning and nonlinear dynamics of vortices in disordered Josephson junction arrays

Pinning and plastic flow of superconducting phases of current-driven Josephson junction lattices in magnetic fields are studied using numerical simulations. We consider two kinds of lattice geometry: a two-dimensional array (Josephson junction array, JJA) and a ladder (Josephson junction ladder, JJL), and introduce positional disorder to the systems. In these systems in the presence of driving dc currents, the plastic deformation of a vortex lattice or the nucleation of vortex–antivortex pairs causes pinned, plastic flow and elastic flow states. We focus on two threshold currents that characterize the boundaries of these regimes. We analyse the threshold currents on the basis of the scaling theory of pinning due to random potentials. It is found that, for both JJL and JJA, the threshold currents show scaling behaviours characterized by certain scaling exponents. We discuss the relationship between the threshold currents and the parameters of the junctions. We also discuss the nonlinear dynamics of plastic flow and the transition from plastic to elastic flow of the present systems in comparison with other related models.

Interactions between Josephson vortices and breathers

We study vortex-breather collisions in a Josephson-junction ladder array. We have computed parameters values of the system for which both types of structures coexist in the ladder. In order of increasing bias current, we have found different possible scenarios for vortex-breather collisions. (i) At low bias current, the breather acts as a pinning center for a single vortex. (ii) Increasing the current, the vortex excites multisite breathers in its wake and is finally pinned by the breather. (iii) At still higher current, a whirling mode front is excited by the vortex. However, the breather still acts as a pinning center, but now for the front. (iv) At higher values of the bias, the front is able to destroy the breather. For scenario (i), we have also studied thermal activation properties associated with the presence of the vortex-breather pair in the array.

Observation of breather resonances in Josephson ladders.

We report experimental observation of resonances excited by nonlinear localized states (rotobreathers) in Josephson junction ladders. The rotobreathers are found to persist in a frequency range that allows for their resonant interaction with linear electromagnetic modes in the ladders. This interaction leads to nearly constant voltage steps on the current-voltage characteristics. We also present numerical simulations that agree well with experimental data and confirm the resonant interaction between breathers and linear waves. Resonances occur at the base frequency as well as higher harmonics of the linear modes. The observed substructures on the resonances are attributed to the cavity modes for the ladders. Both experimental and simulated current-voltage characteristics show good quantitative agreement with an analytically calculated dispersion relation for linear electromagnetic modes.

Breathers in Josephson junction ladders: resonances and electromagnetic wave spectroscopy.

We present a theoretical study of the resonant interaction between dynamical localized states (discrete breathers) and linear electromagnetic excitations (EE's) in Josephson junction ladders. By making use of direct numerical simulations we find that such an interaction manifests itself by resonant steps and various sharp switchings (voltage jumps) in the current-voltage characteristics. Moreover, the power of ac oscillations away from the breather center (the breather tail) displays singularities as the externally applied dc bias decreases. All these features may be mapped to the spectrum of EE's that has been derived analytically and numerically. Using an improved analysis of the breather tail, a spectroscopy of the EE's is developed. The nature of breather instability driven by localized EE's is established.

Penetration of dynamic localized states in dc-driven Josephson junction ladders by discrete jumps.

We give a theoretical study of unusual resistive (dynamic) localized states in anisotropic Josephson junction ladders, driven by a dc current at one edge. These states comprise nonlinearly coupled rotating Josephson phases in adjacent cells, and with increasing current they are found to expand into neighboring cells by a sequence of sudden jumps. We argue that the jumps arise from instabilities in the ladder's superconducting part, and our analytic expressions for the peculiar voltage (rotational frequency) ratios and I-V curves are in very good agreement with direct numerical simulations.

Discrete breathers in Josephson ladders

We present a study of nonlinear localized excitations called discrete breathers in a superconducting array. These localized solutions were recently observed in Josephson-junction ladder arrays by two different experimental groups [Phys. Rev. Lett. 84 (2000) 741; Phys. Rev. Lett. 84 (2000) 745; Phys. Rev. E 62 (2000) 2858]. We review the experiments made by Trı́as et al. [Phys. Rev. Lett. 84 (2000) 741]. We report the detection of different single-site and multi-site breather states and study the dynamics when changing the array bias current. By changing the temperature we can control the value of the damping (the Stewart–McCumber parameter) in the array, thus allowing an experimental study at different array parameters. We propose a simple DC circuit model to understand most of the features of the detected states. We have also compared this model and the experiments with simulations of the dynamics of the array. We show that the study of the resonances in the ladder and the use of harmonic balance techniques allow for understanding of most of the numerical results. We have computed existence diagrams of breather solutions in our arrays, found resonant localized solutions and described the localized states in terms of vortex and antivortex motion.

Phase shifting in a Josephson junction active antenna array

We present a design for an active antenna array employing triangular Josephson junction (JJ) sub-arrays as rf oscillator sources. The sub-arrays are kept in sync by coupling to a closed serpentine discrete JJ ladder. Phase shifts are introduced by adding external magnetic flux into the JJ ladders between sub-arrays. Phase shifting distortions are minimized by allowing only two contiguous sub-arrays on any row segment.

Spatiotemporal stochastic resonance in fully frustrated Josephson ladders

We consider a Josephson-junction ladder in an external magnetic field with half flux quantum per plaquette. When driven by external currents, periodic in time and staggered in space, such a fully frustrated system is found to display spatiotemporal stochastic resonance under the influence of thermal noise. Such resonance behavior is investigated both numerically and analytically, which reveals significant effects of anisotropy and yields rich physics.

Experimental critical current patterns in Josephson junction ladders

We present an experimental and theoretical study of the magnetic field dependence of the critical current of Josephson junction ladders. At variance with the well-known case of a one-dimensional (1D) parallel array of Josephson junctions the magnetic field patterns display a single minimum even for very low values of the self-inductance parameter $\beta_{\rm L}$. Experiments performed changing both the geometrical value of the inductance and the critical current of the junctions show a good agreement with numerical simulations. We argue that the observed magnetic field patterns are due to a peculiar mapping between the isotropic Josephson ladder and the 1D parallel array with the self-inductance parameter $\beta_{\rm L}^{\rm eff}=\beta_{\rm L}+2$.

Diversity of discrete breathers observed in a josephson ladder

We generate and observe discrete rotobreathers in Josephson junction ladders with open boundaries. Rotobreathers are localized excitations that persist under the action of a spatially uniform force. We find a rich variety of stable dynamic states including pure symmetric, pure asymmetric, and mixed states. The parameter range where the discrete breathers are observed in our experiment is limited by retrapping due to dissipation.

Finite-size-scaling analyses of the chiral ordert in the Josephson-junction ladder with half a flux quantum per plaquette

Chiral order of the Josephson-junction ladder with half a flux quantum per plaquette is studied by means of the exact diagonalization method. We consider an extreme quantum limit where each superconductor grain (order parameter) is represented by S=1/2 spin. So far, the semi-classical S -> \infty case, where each spin reduces to a plane rotator, has been considered extensively. We found that in the case of S=1/2, owing to the strong quantum fluctuations, the chiral (vortex lattice) order becomes dissolved except in a region, where attractive intrachain and, to our surprise, repulsive interchain interactions both exist. On the contrary, for considerably wide range of parameters, the superconductor (XY) order is kept critical. The present results are regarded as a demonstration of the critical phase accompanying chiral-symmetry breaking predicted for frustrated XXZ chain field-theoretically.

Resonant Steps in the Discrete sine-Gordon Chain**The project supported in part by the Research Grant Council RGC, the Hong Kong Baptist University Faculty Research Grant FRG, and National Natural Science Foundation of China

Low-velocity dynamics of a dc-driven discrete sine-Gordon chain is studied in the damped case. It is shown that resonant steps of the average velocity emerge due to the resonant phase locking between the kink motion and its radiated linear modes in its wake. A mean-field description is given, which can predict precisely the numerical results. The mechanism and formula proposed in this paper can be directly applied to the discussion of fluxon dynamics of one-dimensional Josephson junction arrays and Josephson junction ladders.

Observation of breathers in Josephson ladders.

We report on the observation of spatially localized excitations in a ladder of small Josephson junctions. The excitations are whirling states which persist under a spatially homogeneous force due to the bias current. These states of the ladder are visualized using a low temperature scanning laser microscopy. We also compute breather solutions with high accuracy in corresponding model equations. The stability analysis of these solutions is used to interpret the measured patterns in the I-V characteristics.

Cavity resonances in Josephson ladders

Electromagnetic waves which propagate along a Josephson junction ladder are shown to manifest themselves by resonant steps in the current-voltage characteristics. We report on experimental observation of resonances in ladders of different geometries. The step voltages are mapped on the wave dispersion relation which we derive analytically for the general case of a ladder of arbitrary anisotropy. Using the developed model, current amplitudes of the resonances are also calculated and their dependence on magnetic field is found to be in good accord with experiment.

Rotobreather dynamics in underdamped Josephson junction ladders

We study rotobreather properties in Josephson ladders with external dc currents and nonzero island-island capacitances. These solutions are localized in space, with tails characterized by exponential localization and a wave length which both vary smoothly upon varying the external bias. We demonstrate the existence of resonances for underdamped systems which are related to the plane wave spectrum of the nonresistive system. We propose experimental observations of these resonances.

Floquet stability of discrete breathers in anisotropic josephson junction ladders

We report on preliminary numerical results on linear stability (Floquet) analysis of discrete breather solutions of the resistively and capacitively shunted junction (RCSJ) dynamics of an anisotropic ladder of Josephson junctions biased by time periodic, uniform currents, Different types of bifurcations, driven by exponentially localized eigenvectors of the monodromy matrix, are shown to destabilize the intrinsic localized modes, when parameters such as Josephson coupling, resistive coupling or external currents intensity are varied. We show some two-dimensional sections of the computed sector of the stability phase diagram in the corresponding parameter space.

Rigorous analytical results on phase locking in Josephson junction ladder arrays

Based on a previously developed analytical procedure combining ideas from the first harmonic approximation with those from the slowly varying phase we obtain some rigorous analytical results on the dynamics of two-dimensional Josephson-junction ladder arrays composed of an arbitrary number of cells. We are able to derive a general analytic expression for the reduced equations governing phase locking of the cells. While solving these reduced equations seems not to be possible in general, we were able to evaluate them up to the end for three experimentally relevant cases: (i) arrays composed of strongly damped junctions and small ring inductances without an external shunt, (ii) arrays composed of strongly damped junctions and small ring inductances with an external shunt, and (iii) arrays composed of strongly damped junctions and large ring inductances without an external shunt.

Josephson-junction ladder: A benchmark for nonlinear concepts

The theoretical analysis of the ground state properties and dissipative dynamics of an anisotropic ladder of Josephson junctions has revealed interesting features associated to the nonlinear character of the Josephson effect, combined with the inherent discreteness of the system and the peculiarities of the ladder geometry. We analyse some aspects of its underdamped dynamics when spatially homogeneous time-periodic currents are injected into the islands, and predict the existence of attracting time-periodic spatially localised modes, for some ranges of junction characteristic parameters. These elementary dynamical excitations are of two different types, associated to oscillatory and rotating motion of a few superconducting island phases, respectively, revealing a dynamical mechanism of creation of vortex-antivortex pairs. These results are physical applications of recent advances in the theory of nonlinear dynamics of discrete macroscopic systems. Their experimental confirmation would probe the physical relevance of localisation in superconducting devices.

How to achieve in-phase locking in small-inductance Josephson junction ladder arrays

We present the results of an analytical study of phase locking in externally loaded two-dimensional Josephson junction ladder arrays with small, but non-vanishing ring inductances. A Lyapunov stability based condition is found controlling realization of the radiating in-phase oscillation regime.