Experimental and numerical study of dynamic regimes in a discrete sine-Gordon lattice

Experimental Study of Spectral Properties of a Frenkel-Kontorova System

We report on microwave emission from linear parallel arrays of underdamped Josephson junctions, which are described by the Frenkel-Kontorova (FK) model. Electromagnetic radiation is detected from the arrays when biased on current singularities (steps) appearing at voltages V(n)=Φ(0)(nc̅/L), where Φ(0)=2.07×10(-15)  Wb is the magnetic flux quantum, and c̅, L, and n are, respectively, the speed of light in the transmission line embedding the array, L its physical length, and n an integer. The radiation, detected at fundamental frequency c̅/2L when biased on different singularities, indicates shuttling of bunched 2π kinks (magnetic flux quanta). Resonance of flux-quanta motion with the small-amplitude oscillations induced in the arrays gives rise to fine structures in the radiation spectrum, which are interpreted on the basis of the FK model describing the resonance. The impact of our results on design and performances of new digital circuit families is discussed.

Fluxon mobility in an array of asymmetric superconducting quantum interference devices

Fluxon dynamics in the dc-biased array of asymmetric three-junction superconducting quantum interference devices (SQUIDs) is investigated. The array of SQUIDs is described by the discrete double sine-Gordon equation. It appears that this equation possesses a finite set of velocities at which the fluxon propagates with the constant shape and without radiation. The signatures of these velocities appear on the respective current-voltage characteristics of the array as inaccessible voltage intervals (gaps). The critical depinning current has a clear minimum as a function of the asymmetry parameter (the ratio of the critical currents of the left and right junctions of the SQUID), which coincides with the minimum of the Peierls-Nabarro potential.

Characterization of anomalous pair currents in Josephson junction networks

Measurements performed on superconductive networks shaped in the form of planar graphs display anomalously large currents when specific branches are biased. The temperature dependences of these currents evidence that their origin is due to Cooper pair hopping through the Josephson junctions connecting the superconductive islands of the array. The experimental data are discussed in terms of theoretical models which predict, for the system under consideration, an inhomogeneous Cooper pair distribution on the superconductive islands of the network as a consequence of a Bose-Einstein condensation phenomenon.

Effect of Cherenkov radiation on the jitter of solitons in the driven underdamped Frenkel-Kontorova model

The effect of complex dynamics of solitons on the output noise of the system (thermal jitter) is studied in the frame of the driven underdamped Frenkel-Kontorova model. In contrast to the continuous case, we have observed a dramatic splash of the jitter. It is demonstrated that this jitter increase is related to the joining of an initial soliton with the one generated by large amplitude oscillations of the Cherenkov radiation tail, which results in the establishment of a unified soliton structure.

Energy flow of moving dissipative topological solitons

We study the energy flow due to the motion of topological solitons in nonlinear extended systems in the presence of damping and driving. The total field momentum contribution to the energy flux, which reduces the soliton motion to that of a point particle, is insufficient. We identify an additional exchange energy flux channel mediated by the spatial and temporal inhomogeneity of the system state. In the well-known case of a dc external force the corresponding exchange current is shown to be small but nonzero. For the case of ac driving forces, which lead to a soliton ratchet, the exchange energy flux mediates the complete energy flow of the system. We also consider the case of combination of ac and dc external forces, as well as spatial discretization effects.

Observation of soliton fusion in a Josephson array

The behavior of topological solitons in a parallel array of a Josephson junction is studied experimentally. We observe the fusion of two relativistic solitons of the same polarity into a single soliton. The soliton carries two quanta of magnetic flux and, most strikingly, travels 18% faster than an ordinary soliton under the same driving force. We also find a variety of bunched states composed of solitons of the same polarity, moving with fixed separation.

Collective topological dynamics in the frenkel-kontorova chains

Topological dynamics of an array of harmonically coupled damped dc-driven nonlinear oscillators are studied by introducing a dynamical contraction factor and a deviation factor. Different dynamical transitions are identified, and topological changes for these transitions are studied. A bifurcation from the kink state to the kink-antikink-pair state is found, which relates the topological change to the spatiotemporal dynamics of the system. The presence of antikinks leads to the extension of the localized kink, and collisions of kinks and antikinks induce strong oscillations of the topology of the array.

Floquet exponents of underdamped josephson ladders: A comparison with predictions of the discrete sine-gordon equation

We calculate Floquet exponents for phase-locked solutions in ladder arrays of Josephson junctions in zero external field. We assume a resistively and capacitively shunted junction (RCSJ) model, and we allow for critical current anisotropy between the horizontal and vertical junctions. The ladders range in size from 5 to 30 plaquettes and are biased along the rungs with uniform dc bias currents. The Floquet exponents quantify the stability of the solutions and are calculated numerically for the RCSJ model as a function of junction capacitance (beta(c)) as well as critical current anisotropy (Lambda). We also model the array with the discrete sine-Gordon (DSG) equation, and we are able to calculate the exponents analytically in that case. We find the analytic results from the DSG equation agree quantitatively with the numerical results from the RCSJ model over a wide range of beta(c) and Lambda values and even agree qualitatively for beta(c)-->1 and Lambda-->0. Based on the analytic result we argue that perturbations in the array are damped by the small-angle phase oscillations of the underlying lattice (the "phonons" of the lattice), and like a classical harmonic oscillator with damping, each phonon mode has a crossover (as a function of decreasing beta(c) or Lambda) from underdamped to overdamped dynamics. Such crossover behavior is clearly visible in the results for the Floquet exponents and is manifested as a maximum in the Floquet exponent as a function of the junction capacitance. This intriguing result speaks to the opportunity, in principle, of tuning the capacitance such as to optimize the stability of the phase-locked solutions.