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.The present decade has been marked by an intense theoretical research on dynamical localization phenomena in spatially discrete systems, namely on discrete breathers (DB). These exact solutions of the underlying equations of motion are characterized by periodicity in time and localization in space. Away from the DB center the system approaches a stable (typically static) equilibrium. (For reviews see [1], [2]). These solutions are robust to changes of the equations of motion, exist in translationally invariant systems and any lattice dimension. Discrete breathers have been discussed in connection with a variety of physical systems such as large molecules, molecular crystals [3], spin lattices [4,5], to name just a few.For a localized excitation such as a DB, the excitation of plane waves which might carry the energy away from the DB does not occur due to the spatial discreteness of the system. The discreteness provides a cutoff for the wave length of plane waves and thus allows to avoid resonances of all temporal DB harmonics with the plane waves. The nonlinearity of the equations of motion is needed to allow for the tuning of the DB frequency [1].Though the DB concept was initially developed for conservative systems, it can be easily extended to dissipative systems [6]. There discrete breathers become timeperiodic spatially localized attractors, competing with other (perhaps nonlocal) attractors in phase space. The characteristic property of DBs in dissipative systems is that these localized excitations are predicted to persist under the influence of a spatially homogeneous driving force. This is due to the fact, that the driving force compensates the dissipative losses of the DB.So far research in this field was predominantly theoretical. Identifying and analyzing of experimental systems for the direct observation of DBs thus becomes a very actual and challenging problem. Experiments on localization of light propagating in weakly coupled optical waveguides [7], low-dimensional crystals [8] and antiferromagnetic materials [9] have been recently reported. In this work we realize the theoretical proposal [10] to observe DB-like localized excitations in arrays of coupled Josephson junctions. A Josephson junction is formed between two superconducting islands. Each island is characterized by a macroscopic wave function Ψ ∼ e iθ of the superconducting state. The dynamics of the junction is described by the time evolution of the gauge-invariant phase difference ϕ = θ 2 − θ 1 − 2π Φ0A · ds between adjacent islands. H...

Electrical transport in semiconductor superlattices is studied within a fully self-consistent quantum transport model based on nonequilibrium Green functions, including phonon and impurity scattering. We compute both the drift velocity-field relation and the momentum distribution function covering the whole field range from linear response to negative differential conductivity. The quantum results are compared with the respective results obtained from a Monte Carlo solution of the Boltzmann equation. Our analysis thus sets the limits of validity for the semiclassical theory in a nonlinear transport situation in the presence of inelastic scattering.

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. 63.20.Ry, 74.50.+r Nonlinearity and lattice discreteness lead to a generic class of excitations that are spatially localized on the scale comparable to the lattice constant. These excitations, also known as discrete breathers, have recently attracted a lot of interest in theory of nonlinear lattices 1,2 . It is believed that discrete breathers might play an important role in the dynamics of various physical systems consisting of coupled nonlinear oscillators. It has been even said that that for discrete nonlinear systems breathers might be as important as solitons are for the continuous nonlinear media.There have been several recent experiments that reported on generation and detection of discrete breathers in diverse systems. These are low-dimensional crystals 3 , anti-ferromagnetic materials 4 , coupled optical waveguides 5 , and Josephson junction arrays 6,7 . By using the method of low temperature scanning laser microscopy, we have recently reported the first direct visualization of discrete breathers 7 .In this paper we present new measurements of localized modes in Josephson ladders. Using the same method as in our first experiment, we study an even more tightly coupled lattice of Josephson junctions and observe a rich diversity of localized excitations that persist under the action of a spatially uniform force.A biased Josephson junction behaves very similar to its mechanical analog that is a forced and damped pendulum. An electric bias current flowing across the junction is analogous to a torque applied to the pendulum. The maximum torque that the pendulum can sustain and remain static corresponds to the critical current I c of the junction. For low damping and bias below I c , the junction allows for two states: the superconducting (static) state and the resistive (rotating) state. The phase difference ϕ of the macroscopic wave functions of the superconducting islands on both sides of the junction plays the role of an angle coordinate of the pendulum. According to the Josephson relation, a junction in a rotating state generates dc voltage V = 1 2π Φ 0 dϕ dt , where ... is the time average. By connecting many Josephson junctions by superconducting leads one gets an array of coupled nonlinear oscillators.We perform experiments with a particular type of

The dc current in strongly coupled superlattices can either be described in a semiclassical picture in terms of miniband transport or in a quantum mechanical theory based on hopping transitions between the localized wave functions of the Wannier-Stark ladder. We demonstrate the equivalence of both models in the field regime of Bloch-oscillating electrons. Combining these two pictures we calculate the superlattice drift velocity resulting from microscopic phonon scattering between the Wannier-Stark levels. Our results show that previous discussions of the temperature dependence of the drift velocity have to be revised drastically. ͓S0163-1829͑99͒05011-0͔Electronic transport in man-made semiconductor superlattices offers a wide range of new high-field phenomena that cannot be observed in conventional bulk semiconductors: Due to the large superlattice constant d and the small width of the resulting minibands, electric fields F at which the potential drop per superlattice period eFd is comparable to or even larger than the miniband width can be easily obtained. Furthermore, scattering in these structures can be strongly reduced compared to bulk material by designing the miniband width ⌬ to be smaller than the optical-phonon energy. If the resulting scattering rate 1/ becomes lower than the Bloch frequency B ϭeFd/ប, the electrons perform Bloch oscillations in the mini-Brillouin zone.As Bloch-oscillating electrons do not contribute to a net current through the superlattice structure, negative differential conductivity ͑NDC͒ can be observed at moderately high fields. While this was explained as early as 1970 by Esaki and Tsu 1 within a semiclassical miniband model, Tsu and Döhler 2 soon afterwards proposed a quantum-mechanical explanation of this phenomenon, which is based on the fieldinduced localization of the superlattice wave functions. In analyzing their experimental results, 3,4 most of the authors came to the conclusion that the semiclassical momentum space picture ͑the Esaki-Tsu model or more sophisticated approaches 5,6 ͒ provides the correct description for wide minibands, whereas the quantum-mechanical real-space picture was assumed to be correct for narrow minibands only. Based on our recent detailed study of the hopping transport, 7 we claim that the applicability of this picture depends rather on the field range than on the miniband width.Our goal in this paper is to provide a consistent scheme for a quantitative description of transport in strongly coupled superlattices for the whole range of fields and temperatures, combining the semiclassical momentum space ͑or Boltz-mann͒ picture with the quantum-mechanical hopping picture. Taking advantage of the correspondence between the hopping picture and the semiclassical description in terms of electrons performing Bloch oscillations at moderately high fields, we are able to establish a link between the high-field hopping drift velocity and two fundamental quantities describing miniband transport, i.e., the momentum-relaxation time M and the energy-relaxation ti...

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.