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IEEE Transactions on Magnetics

Mutual phase locking in multijunction Josephson arrays

K. K. Likharev, L. S. Kuzmin, G. A. Ovsyannikov

Published Jan 1, 1981• 22 citations
Publisher

Abstract

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.

DOI
10.1109/tmag.1981.1061150

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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.
We have demonstrated mutual phase locking of two YBa2Cu3O7 Josephson junction oscillators in the frequency range from 0.2 to 1 THz. A maximum power of 0.2 μW was delivered to a distributed 8 Ω load at 0.7 THz. The corresponding dc locking current, ‖IL‖, was 43 μA. A maximum locking current of 75 μA at 0.44 THz or 7% of the critical current agrees well with a calculated maximum value of 6% for this circuit. The excellent high frequency operation is due to the use of a lumped microstrip circuit and a high characteristic voltage of the grain boundary junctions (1.7 mV at 4 K). This circuit was continuously tunable for all frequencies and was operated from 4 to 60 K.
The results of numerical simulations of phase-locked 1D and 2D Josephson-junction arrays are reported. It is shown that the multi-junction structures with non-local junction interaction provide phase-locked oscillation state within wide critical current margins /spl Delta/I/sub c/ up to 40...50%. The effective non-local interaction in 2D structure based on 4-junction interferometer cell can be provided by the regular single flux quantum array flow across it. The wide tolerable spread in /spl Delta/I/sub c/ allows one to realize both (i) phase-locked 2D high-T/sub c/ Josephson-junction array with the oscillation frequency F close to characteristic value F/sub c/ and (ii) based on Nb tunnel Josephson-junction technology 1D array with the voltage-controlled phase-locked oscillation frequency within wide frequency band from 0.4 F/sub c/ to 1.2 F/sub c/.
We have studied a new type of Josephson junction amplifier which is based on a two-junction array; the junctions are mutually phase locked at the Josephson self-oscillation frequency. With this frequency at 82 GHz, the voltages of the junctions remain equal (locked) for a bias current range as large as 60% of the critical current. Over a much smaller bias range, with an applied signal frequency of 1 kHz, a small-signal power gain of 19 dB was measured, accompanied by a negative resistance input impedance. This performance is consistent with a quasistatic theory of the amplifier.
A high temperature superconducting YBa2Cu3Oy array of five Josephson junctions designed with additional coupling lines has been developed to demonstrate the effects of frequency locking and impedance matching for applications such as oscillators, mixers, and detectors. The Josephson self-radiation power was directly detected by a superheterodyne receiver, and Shapiro steps were also measured. The Josephson self-radiation properties reveal good quality of phase locking and microwave coupling with external circuits. The maximum self-radiation power of our array is about 50 pW which is several ten times higher than that of a single Josephson junction, and its peak point exactly satisfies the Josephson current-voltage relation. The Shapiro-step measurements show that the behavior of current-voltage curve depends on the effective inductance of coupling lines which affects the total impedance of Josephson junction array and microwave coupling. The Josephson oscillation frequency was obtained up to about 880 GHz which is 73% of the maximum available frequency calculated from the characteristic voltage of the Josephson junctions. Experimental results show that this type of Josephson junction array can improve the Josephson self-radiation power and increase the maximum detectable frequency.
Mutual phase locking has been demonstrated in series arrays of two and four Josephson junctions at millimeter-wave frequencies. Experimental observations are in good agreement with theory reported earlier. This technique increases the output power available from a Josephson junction source. Available output power is expected to be proportional to the square of the number of junctions until the array impedance approaches the load impedance. The output frequency is voltage tunable over as much as an octave. Theory indicates that the technique can be extended to even larger arrays.
Strong mutual phase locking of Josephson oscillations in unshunted tunnel junctions in-coporated into a special common millimeter-wave resonance structure has been observed and studied. The observed locking range was especially wide (up to ±10%) when the both junctions were dc biased at the current steps corresponding to the common resonance modes (frequencies from 25 to 200 GHz). Main features of the junction interaction have been found to be in a qualitative agreement with our earlier theory developed for lumped junctions. For larger junctions (S = 30×30 μm2), quantitative deviations from the theoretical predictions have been observed and identified as resulting from interaction of the (external) common resonance mode with the (internal) Fiske modes of the junctions.