Experimental Study of Spectral Properties of a Frenkel-Kontorova System

Abstract

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 ...

Engineering quantum interference

“…The voltage spacing between the resonances is 40 lV: relating this value to frequency f by the Josephson ac relation, given the resonance condition f ¼ c/2W (W ¼ 240 lm), a speed of light along the onedimensional structure c ¼ 0.03c is calculated . This result agrees with previous data 15,19 confirming that resonances develop over the whole length W and that makes even dynamical sense to consider the arrays like a single junction.…”

Frequency spectrum of a superconducting metadevice

“…The We look, similarly to what we did in the previous section, for solutions of eqs. ( 14) and (15) in the forms…”

“…We are interested again in solutions of eqs. ( 14) and (15) in the form of small oscillations around equilibrium angles ϕ ea and ϕ eb . Inserting eqs.…”

Anodization-based process for the fabrication of all niobium nitride Josephson junction structures

“…Niobium (Nb) is the most commonly used material in superconducting electronics [1–3], but several groups have been investigating the properties of metals and alloys that could represent an alternative to it. Niobium nitride (NbN), in particular, is a promising material in this respect given its relatively high critical temperature and energy gap of the order, respectively, of 16 K and 2.5 mV [4–8].…”