Resonances between fluxons and plasma waves in underdamped Josephson transmission lines of stripline geometry

Abstract

We present experiments and theoretical studies on the propagation of Josephson fluxons and electromagnetic waves in parallel arrays of Josephson junctions in the limit of small discreteness. Locking between the fluxon rotation frequency and the frequency of the radiated electromagnetic waves leads to a series of resonances, which we observe on the dc-current-voltage characteristics of the arrays. The arrays consist of small Josephson junctions embedded in an annular superconducting stripline. The experimental data are analyzed using the discrete sine-Gordon model and an extension by including a capacitive interaction between neighboring Josephson junctions. We compare experimental data with both analysis and numerical simulations and find an excellent quantitative agreement.

Experimental Study of Spectral Properties of a Frenkel-Kontorova System

“…Here we show evidence that, for this type of array in the strong coupling regime, stable single and multiple flux-quanta propagation exists over broad bias current ranges. Our experiments also confirm predictions of the theoretical modeling of the complex dynamics of 2π kinks in the Frenkel-Kontorova model [9,[12][13][14][15][16][17]. Figure 1(a) displays a photo of a portion of the real device showing the open-ended [13] parallel array of small junctions.…”

“…2 we observed in most of the cases switching from the lowest part of the Josephson current as shown by the horizontal arrows in the IVs: these indicate that static flux quanta trapped in the JTL start moving at a threshold current and generate a voltage. Thus, the Lorentz force needs a threshold current to overcome the potential barrier pinning flux quanta in their locations [5,12,13,17]. From the current-voltage characteristics of the test junction we also estimated the McCumber parameter [2] The evaluation of the inductance l 0 of a single section of the array (given the speed of light in the transmission line and the specific capacitance of the junctions) enables us to evaluate the discreteness parameter a ¼ ð2πl 0 I c =Φ 0 Þ 1=2 [5,11,12], where Φ 0 ¼2.07×10 −15 Wb is the magnetic flux quantum.…”

“…Measurements of radiation emission from the 1st and 2nd ZFS of this sample are shown in Figs. 3(a) and 3(b): the observed fine structure of the fluxon steps (in the case of periodic boundary conditions [12,16,17]) and ZFS modes (in the case of open boundary conditions [13]) is due to resonant locking of the fluxon oscillations to the frequency of Josephson plasma waves in the fluxon's tail, which propagate with a phase velocity equal to the fluxon velocity. Note that most of the emission from the 2nd ZFS is measured at double frequency, meaning that both two-bunch fluxon oscillations [ Fig.…”

Inhomogeneous parallel arrays of Josephson junctions

“…c o m / l o c a t e / p h y s c results. For arrays of equidistant junctions, a recent study by Pfeiffer et al [13] analyzed the fine features of the first resonant step in terms of Cerenkov radiation between a sine-Gordon discrete kink (fluxon) and a cavity mode. For one junction placed arbitrarily in the strip, our theoretical study [14] revealed that all the linear modes are excited with different amplitudes.…”

Frequency divider by underdamped Josephson transmission line

“…One can quote the perturbation analysis [6] and modulation instability studies [7] of a e-mail: khomeriki@hotmail.com the process, theoretical [8,9] and experimental [10,11] investigations of the resonances between fluxons and linear plasma oscillations, fluxon dynamics studies in case of coupled JTL-s [12,13], fluxon induced directed transport under homogeneous ac driving with broken time symmetry [14] and many other interesting phenomena. At the same time, much less studies have been devoted to the dynamics of nonlinear excitations under the local (boundary) driving: In this connection one should mention the investigation of hysteretic regimes appearing due to the phase locking effect between the boundary driving and breather type localizations [15][16][17] (where the breathing frequency coincides with the driver frequency [18][19][20]) or, on the other hand, boundary driving can maintain stationary motion of the fluxon which creates a new frequency in the system being an odd fraction of the driving frequency [21][22][23].…”