Dynamics of point Josephson junctions in a microstrip line

Caputo, Jean-Guy; Loukitch, L.

doi:10.1016/j.physc.2005.06.005

Cited by 11 publications

(13 citation statements)

References 30 publications

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“…From remark (8), φ is a polynomial by parts. We define P i+1 (x) the second degree polynomial such that P i+1 (x) = φ(x) for a i ≤ x ≤ a i+1 .…”

Section: Piece-wise Polynomialmentioning

confidence: 96%

Designing arrays of Josephson junctions for specific static responses

Caputo¹,

Loukitch²

2008

Inverse Problems

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We consider the inverse problem of designing an array of superconducting Josephson junctions that has a given maximum static current pattern as function of the applied magnetic field. Such devices are used for magnetometry and as Terahertz oscillators. The model is a 2D semilinear elliptic operator with Neuman boundary conditions so the direct problem is difficult to solve because of the multiplicity of solutions. For an array of small junctions in a passive region, the model can be reduced to a 1D linear partial differential equation with Dirac distribution sine nonlinearities. For small junctions and a symmetric device, the maximum current is the absolute value of a cosine Fourier series whose coefficients (resp. frequencies) are proportional to the areas (resp. the positions) of the junctions. The inverse problem is solved by inverse cosine Fourier transform after choosing the area of the central junction. We show several examples using combinations of simple three junction circuits. These new devices could then be tailored to meet specific applications.

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“…From remark (8), φ is a polynomial by parts. We define P i+1 (x) the second degree polynomial such that P i+1 (x) = φ(x) for a i ≤ x ≤ a i+1 .…”

Section: Piece-wise Polynomialmentioning

confidence: 96%

Designing arrays of Josephson junctions for specific static responses

Caputo¹,

Loukitch²

2008

Inverse Problems

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“…The electrodes forming the array of junctions are part of the central conductor of a coplanar waveguide allowing radiation detection. The junctions were windowlike fabricated using the standard Nb-AlO x -Nb trilayer technology [18,19] and had a current density of 110 A=cm 2 . The measurements herein presented are part of an investigation performed on arrays which were made of 50, 30, and 25 junctions in parallel; all the measurements were performed at 4.2 K. In Fig.…”

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confidence: 99%

Experimental Study of Spectral Properties of a Frenkel-Kontorova System

et al. 2015

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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 ¼ Φ 0 ðnc=LÞ, where Φ 0 ¼ 2.07 × 10 −15 Wb is the magnetic flux quantum, andc, 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 frequencyc=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. The physics of single flux quanta, or fluxons, (corresponding to 2π kinks of the superconducting phase difference φ) in spatially extended Josephson junctions structures has attracted the attention of the scientific community since the early stages of the research on weak superconductivity [1,2]. Fluxon dynamics served as a relevant experimental test bench for soliton perturbation theory and nonlinear physics [3]. The features of topological kinks in the discrete, nonintegrable, FrenkelKontorova model [4,5], implemented by a chain of pointlike Josephson junctions connected by inductors to form a one-dimensional (1D) array, has also attracted attention due to the interest for the dynamics of solitons in condensed matter physics [6]. On the practical side, the storage and manipulation of flux quanta in Josephson transmission lines (JTLs) [7] is the physical phenomenon underlying the principles of a successful logic family operating at unprecedented clock frequencies [8].Recently, new low-dissipative logic families, still relying on Josephson flux quanta as carriers of bits of information [9][10][11], have been proposed. One of the new logic families [9] relies on moving flux quanta along 1D underdamped arrays in which the Josephson junctions are strongly coupled by inductors along the flux-quanta propagation direction. 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. The electrodes forming the array of junctions are part of the central conductor of a coplanar waveguide allowing radiation detection. The junctions were windowlike fabricated using the standard Nb-AlO x -Nb trilayer technology [18,19] and had a current density of 110 A=cm 2 . The measurements ...

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“…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. In particular the junction can stop waves across the strip or enhance them throughout.…”

Section: Contents Lists Available At Sciencedirectmentioning

confidence: 88%

“…We choose a device with l = p, a 1 = l/3, d 1 = 1 and take three limiting cases j = 0 j = 1 and j = 30. When there is no capacity miss-match (j = 0) we showed in [14] that the resonances of the I-V curve are positioned at V = kp/l with k integer and are bounded by Table 2 together with the coupling coefficient / n (a 1 ). The eigenvalues are clearly not harmonic.…”

Section: Eigenvalues and I-v Curvesmentioning

confidence: 95%