Fluxon Oscillations Research Articles

Use of a spoof plasmon to optimize the coupling of infrared radiation to Josephson-junction fluxon oscillations

We show that Infrared radiation impinging onto a 1-d array of grooves drilled in the superconductor electrode of a long overlap junction can improve matching between fluxon oscillations at THz frequencies and a spoof plasmon of comparable wavelength. This example proves that metamaterials can be very helpful in integrating superconductive and subwavelength optical circuits with optimized matching bridging the gap between infrared and microwave radiation.

Oscillations in Josephson transmission line stimulated by load in the presence of noise

The joint action of the matching to a common RC-load and thermal noise on the spectral properties of parallel Josephson junction array is studied. It is demonstrated that proper matching suppresses the chaotic dynamics of the system. The efficiency of radiation is found to be highest within a limited frequency band, which corresponds to transformation of the shuttle soliton oscillating regime into the linear wave resonance synchronization mode. In this frequency band the spectral linewidth agrees well with a double of the linewidth for a shuttle fluxon oscillator, divided by a number of the oscillators in the array. When the oscillations demonstrate strong amplitude modulation, the linewidth increases roughly by a factor of five compared with theoretical linewidth formula.

Fluxon readout of a superconducting qubit.

An experiment demonstrating a link between classical single-flux quantum digital logic and a superconducting quantum circuit is reported. We implement coupling between a moving Josephson vortex (fluxon) and a flux qubit by reading out of a state of the flux qubit through a frequency shift of the fluxon oscillations in an annular Josephson junction. The energy spectrum of the flux qubit is measured using this technique. The implemented hybrid scheme opens an opportunity to readout quantum states of superconducting qubits with the classical fluxon logic circuits.

Josephson vortex coupled to a flux qubit

Experiments towards realizing a readout of superconducting qubits by using ballistic Josephson vortices are reported. We measured the microwave radiation induced by a fluxon moving in an annular Josephson junction. By coupling a flux qubit as a current dipole to the annular junction, we detect periodic variations of the fluxon's oscillation frequency versus magnetic flux through the qubit. We found that the scattering of a fluxon on a current dipole can lead to the acceleration of a fluxon regardless of a dipole polarity. We use the perturbation theory and numerical simulations of the perturbed sine-Gordon equation to analyze our results.

Synchronization of intrinsic Josephson junctions to a cavity

In the utilization of intrinsic Josephson junctions of the highly anisotropic BSCCO type for microwave generation the in-phase motion of fluxons in the different layers is highly desirable but difficult to obtain. We propose to couple each stack junction––which constitutes an underdamped fluxon oscillator––to an external high-Q resonator. We have numerically investigated the possibility for in-phase fluxon synchronization using the external cavity.

Phase-locking Josephson junctions arrays

We demonstrate that a large area Josephson junction oscillating in the fluxon oscillator mode can be synchronized to other large junctions and simultaneously pump, by emitted radiation, a small area junction. We study the synchronization of the oscillations of the long junctions as a function of relevant experimental parameters such as bias current and stripline coupling characteristics. Experimental results obtained on coupled series arrays of Josephson junctions designed on the basis of our calculations are presented. We have fabricated coupled arrays containing each up to 1500 junctions in order to estimate the usefulness of our calculations for voltage standard devices.

A survey of phase-locking in the dc and ac-driven Josephson transmission line

We present a review of the dynamical states of the long Josephson junction when dc and ac currents are considered as bias terms. When only the dc terms are present, depending on the value of the external magnetic field, the excitations consists of fluxon oscillations, cavity modes and travelling waves interactions with the Josephson effect. These three different modes generate well identified singularities in the current-voltage characteristics. We also report on the effect that ac current terms applied to the transmission line can have on these current singularities. In this case a theoretical analysis, based on the nature of dc excitations, has provided predictions for the ranges of locking of the external signal to junction’s oscillations. These predictions are in good agreement with experimental and numerical data that have been reported in the literature.

Conversion efficiency in a resonant Josephson effect mixer

The RCSJ (resistor - capacitor shunted junction) model provides us with an analytical formula for the conversion efficiency for a resonant Josephson effect mixer. An external rf signal is applied to a long Josephson junction operating in the fluxon oscillating regime. The sine - Gordon equation is used to investigate the dynamics of the phase-locking of the fluxon oscillations and the external signal. We establish that it is possible to have conversion efficiency greater than unity.

Fluxon dynamics in discrete Josephson transmission lines with stacked junctions

The experimental and numerical study of parallel one-dimensional arrays consisting of double-layer stacked small Josephson tunnel junctions is reported. In addition to several features already known for classic single-layer arrays, we find a new resonant state which corresponds to the locking of the fluxon oscillations to a frequency of small-amplitude oscillations of the superconducting phase in middle islands of small stacks. Numerical simulations of a simplified circuit agree well with experiments and confirm the suggested qualitative mechanism. In these experiments we find no indication for the so-called multiple-fluxon propagation in double-junction arrays.

High-frequency pumping of Josephson soliton oscillators.

We study the phase locking of a long Josephson junction operating in a fluxon oscillator regime to external rf signals whose frequency is an even harmonic of the oscillator frequency. The phenomenon is investigated for different values of the dc bias current in the junction, and around each value the current intervals that allow phase locking are evaluated. These intervals can be well identified even when the drive frequency is sixteen times the fluxon oscillator frequency. The explanation of the numerical data that we obtain is given in terms of analytical approximations for a long Josephson junction model. An equation containing relevant experimental parameters is derived for the current-locking ranges generated by the different harmonics. This equation establishes that the amplitude of these intervals decreases exponentially with the harmonic number and we show how this result can be related to a property of the Fourier spectrum of fluxon oscillations. In all the cases that we analyze very good agreement is found between the numerical evidence and theoretical analysis.

Long Josephson junctions with uniform dc and rf driving currents: General results for the phase-locked regimes

We investigate the dynamics of a long overlap Josephson junction in the presence of constant and sinusoidally time-varying currents on a finite-length spatial interval imposing open circuit boundary conditions at the ends. We scan the behavior of the system in parameter plane regions where the phase locking between the fluxon oscillations in the junction and the external time-varying field is possible. This scanning is performed for different values of the dc driving term and for lengths of the spatial interval ranging from 3.8 up to 15 and dissipation parameters ranging from 0.025 to 0.25. In spite of the complexity of the system and of the broad range of parameters investigated we find that the response to the rf excitation presents general features that can be well understood in terms of current-voltage characteristics of the junctions (and related experimental parameters). The results are compared with a recent theoretical model based on a perturbation approach of the sine-Gordon Hamiltonian.

IV curves of Josephson Fluxon oscillators coupled to a cavity

IV curves of Josephson Fluxon oscillators coupled to a cavity

Soliton bunching in annular Josephson junction

Numerical simulations have been performed for an annular Josephson junction with a normalized length equal to 6, using the perturbed sine-Gordon equation. The calculated current-voltage characteristics reveal a small jump on the steps 3 and 4 in accordance with experimental observations. The computer simulations show that the jumps are caused by a transition from a non-bunched to a bunched fluxon oscillation state as the bias current is increased.

Radiation detection from Fiske steps in Josephson junctions above 200 GHz

We have measured the Josephson radiation emitted at millimeter-wave frequencies by a long Josephson junction dc-current biased on Fiske steps of the current-voltage characteristic. Our measurements demonstrate that differences between dynamic excitation generating Fiske steps and fluxon oscillations giving rise to zero-field steps in long junctions may exist. The radiation, whose maximum measured frequency is 240 GHz, is generated by an in-line junction and detected on a chip by a small planar tunnel junction. From measurements of Shapiro steps amplitude and photon-assisted tunneling steps we find that the coupled radiation has a power tunability of 350 nW and the maximum coupled power is 20 nW in a 30-Ω normal-state resistance tunnel junction.

Kink excitations and fluxon oscillators in coupled long Josephson junctions

The properties of a system of N=3 maximally coupled Josephson junctions for which symmetry is broken by having the physical parameters of one junction (the shunt junction) different from those of the other two are examined. It is found that the family of integer fluxon excitations of the symmetric case becomes distorted in a way that is best described in terms of two independent fractional fluxon subkinks theta and psi . The subkinks retain some of the qualities of quarks in that they may not be liberated from the integer-valued fluxons in which they reside, but may be created and destroyed in subkink-antisubkink pairs and exchanged in collisions. The authors have investigated forming resonant fluxon oscillators in shunt coupled Josephson-junction (JJ) systems using both bound K-K ( theta - theta ) pairs of fluxons accelerated by parallel forcing currents and bound K-K pairs ( psi - psi ) of fluxons accelerated by series forcing currents. These systems are able to accommodate larger pair breaking forces induced by forcing currents than those of similar coupled JJ systems where the pairs are bound only by mutual inductance coupling.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

SUSAN (Superconducting Systems Analysis) by Low Temperature Scanning Electron Microscopy (LTSEM)

Low-temperature scanning electron microscopy was used for spatially resolved investigations of both Josephson junctions and superconducting integrated circuits during their operation with a spatial resolution of about 1 mu m. Using single Josephson tunnel junctions of various geometries, the authors studied different dynamic states such as fluxon oscillations or unidirectional flux flow. With an integrated circuit consisting of a two-dimensional array of tunnel junctions and an RF detection circuit they investigated the RF properties of the coupling circuit and confirmed the existence of an impedance mismatch and a geometrical standing wave in the blocking capacitor. The studies of the dynamics of single Josephson tunnel junctions of various geometries showed a linear behavior (excitation of single cavity modes) if the boundary conditions dominate, and otherwise a nonlinear behavior (excitation of solutions).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Model studies of long Josephson junction arrays coupled to a high-Q resonator

Series-biased arrays of long Josephson junction fluxon oscillators can be phase locked by mutual coupling to a high-Q, linear distributed resonator. A simplified model of such a device, consisting of junctions described by the particle-map perturbation theory approach which are capacitively coupled to a lumped, linear tank circuit, reproduce the essential experimental observations at a very low computational cost. A more sophisticated model, consisting of partial differential equation descriptions of the junctions, again mutually coupled to a linear tank, substantially confirm the predictions of the simplified model. In the particle-map model, the locking range in junction bias current increases linearly with the coupling capacitance; in the partial differential equation (p.d.e.) model, this holds up to a certain maximum value of the capacitance, after which a saturation of the locking range is observed. In both models, for a given spread of junction lengths, the existence of a minimum value of the capacitance for locking to a tank with a given resonant frequency is evidenced.

Coherence of Josephson soliton oscillators in the millimeter-wave range

We report on the observation of phase-locking and radiation enhancement from two dc series-biased Josephson fluxon oscillators ac-coupled by a thin film-integrated capacitor. The radiation is detected by a small area Josephson junction displaying, under the effect of the radiation, critical current suppression and Shapiro steps at a voltage of 220μV. The phenomena that we observe are the higher frequency counterpart of the superradiant effects measured by means of X-band room temperature receivers detecting the radiation emitted by series arrays of long Josephson junctions.

Effect of thermal noise on the phase locking of a Josephson fluxon oscillator.

The influence of thermal noise on fluxon motion in a long Josephson junction is investigated when the motion is phase locked to an external microwave signal. It is demonstrated that the thermal noise can be treated theoretically within the context of a two-dimensional map that models the dynamics of a single fluxon.

Experiments on the interaction between long Josephson junctions and a coplanar strip resonator

Experiments are reported on a new geometry designed to couple long Josephson junction fluxon oscillators to a resonant cavity. The junctions were made with a niobium-aluminum oxide-niobium trilayer process with a critical-current density of around 1000 A/cm2. Various numbers of such junctions were incorporated directly as part of a coplanar strip half-wave resonator, with fundamental mode of about 34 GHz. Both the current density and oscillation frequency are higher than in previous experiments. Evidence for phase locking of multiple junctions is presented.