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arXiv:2201.11453 · Physical Review Applied

Nonlocal Long-Range Synchronization of Planar Josephson-Junction Arrays

Sergey Grebenchuk, Roger Cattaneo, V. M. Krasnov

Published Jun 16, 2022• 17 citations
arXivHTMLPDF

Abstract

We study arrays of planar $\mathrm{Nb}$ Josephson junctions with contacts to intermediate electrodes, which allow measurements of individual junctions and, thus, provide an insight into intricate array dynamics. We observe strong indications for array phase locking, despite a significant interjunction separation. Several unusual phenomena are reported, such as a bistable critical current with reentrant superconductivity upon switching of nearby junctions; and ``incorrect'' Shapiro steps, occurring at mixing frequencies between the external rf radiation and the internal Josephson frequency in nearby junctions. Our results reveal a surprisingly strong and long-range interjunction interaction, which is attributed to nonlocality of planar-junction electrodynamics, caused by the long-range spreading of stray electromagnetic fields. The nonlocality greatly enhances the high-frequency interjunction coupling and enables large-scale synchronization. Therefore, we conclude that planar geometry is advantageous for the realization of coherent Josephson electronics.

DOI
10.1103/physrevapplied.17.064032

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We analyze experimentally and theoretically mutual phase locking and electromagnetic interaction between two linear arrays with a large number of Josephson junctions. Arrays with different separation, either on the same chip or on two separate substrates are studied. We observe a large coherent gain, up to a factor of three, of emitted power from two simultaneously biased arrays, compared to the sum of powers from two individually biased arrays. The phenomenon is attributed to the phase locking of junctions in different arrays via a common electromagnetic field. Remarkably, the gain can exceed the factor of two expected for a simple constructive interference of two oscillators. The larger gain is explained by an additional consequence of mutual interaction between two large arrays. Mutual phase locking of large arrays does not only result in constructive interference outside the arrays, but also improved synchronization of junctions inside each array. Our conclusion is supported by numerical modelling.
Mutual locking due to the internal coupling in two-dimensional arrays of Josephson junctions was investigated. The appearance of Shapiro steps in the current versus voltage curve of a coupled on-chip detector junction is used to indicate coherent oscillations in the array. A highly coherent state is observed for some range of the array bias current. By scanning the array with a low-power electron beam, mutually locked junctions remain locked while the unlocked junctions generate a beam-induced additional voltage drop at the array. This imaging technique allows the detection of the nonlocked or weakly locked Josephson junctions in a (partially) locked array state.
Arrays of phase locked Josephson junctions are attractive for use as sub-mm wavelength voltage controlled oscillators for heterodyne mixers and free space radiators. We have performed phase locking experiments on 40 junction, parallel biased arrays of Josephson junctions coupled through transmission lines of varying delays. The longest junction to junction delay implemented was 5.4 ps for a design frequency of 90 GHz, while the shortest was 1.45 ps, for a design frequency of 345 GHz. The resonant frequency f/sub 0/ of the arrays was found to be almost independent of the transmission line delay with f/sub 0/, scaling with the plasma frequency for arrays fabricated at critical current densities of 10/sup 3/ and 4.5/spl times/10/sup 3/A/cm/sup 2/. The data indicate that at the resonant frequency, strong phase locking is present among the junctions for junction separations significantly less than one half wavelength even in arrays many wavelengths long.>
The authors report on measurements performed on integrated superconducting devices based on arrays of long Josephson tunnel junctions operating in the resonant fluxon oscillation regime (i.e. biased on the zero field steps). The electromagnetic coupling among the junctions causes a mutual phase-locking of the fluxon oscillations with a corresponding increase of the emitted power and a decrease of the signal linewidth. This phase-locked state can be controlled by means of an external DC bias current and magnetic field. The effect of the generated microwave signal has been observed on a small Josephson tunnel junction coupled to the array via a microstrip transmission line. The feasibility of the reported devices as local oscillators in an integrated microwave Josephson receiver is discussed.>
Measurements indicating that planar networks of superconductive islands connected by Josephson junctions display long-range quantum coherence are reported. The networks consist of superconducting islands connected by Josephson junctions and have a tree-like topological structure containing no loops. Enhancements of superconductive gaps over specific branches of the networks and sharp increases in pair currents are the main signatures of the coherent states. In order to unambiguously attribute the observed effects to branches being embedded in the networks, comparisons with geometrically equivalent-but isolated-counterparts are reported. Tuning the Josephson coupling energy by an external magnetic field generates increases in the Josephson currents, along the above-mentioned specific branches, which follow a functional dependence typical of phase transitions. Results are presented for double comb and star geometry networks, and in both cases, the observed effects provide positive quantitative evidence of the predictions of existing theoretical models.
Mutual phase locking of Josephson oscillations in a two-junction cell and multijunction arrays is analysed. The locking is due to ac currents of Josephson frequency ω, which flow through some special coupling circuit. For the most important case of almost identical junctions, the locking frequency range is shown to be proportional to the imaginary part of the complex conductivity Y(ω) of the coupling circuit. The power and linewidth of coherent oscillations, as well as the coherence stability with respect to the junction intrinsic noise and parameter spread, have been calculated. The maximum locking range and, hence, the maximum parameter tolerances are shown to take place in the closed-loop-type (ring) structures with long-range junction interactions.