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Physical review. B, Condensed matter

Phase locking of Josephson junctions in a two-dimensional array

S. G. Lachenmann, T. Doderer, R. P. Huebener

Published Jun 1, 1996• 9 citations
Publisher

Abstract

We studied the behavior of Josephson junctions in a two-dimensional array under the influence of micro-wave irradiation. We are able to distinguish between junctions that are phase locked to the external microwave and unlocked junctions by means of spatially resolving measurements. The degree of coherence in the array can be influenced by tuning the external rf power. Analogies to the coherent behavior of atoms in a laser are pointed out.

DOI
10.1103/physrevb.53.14541

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We studied the behavior of Josephson junctions in a two-dimensional array under the influence of micro-wave irradiation. We are able to distinguish between junctions that are phase locked to the external microwave and unlocked junctions by means of spatially resolving measurements. The degree of coherence in the array can be influenced by tuning the external rf power. Analogies to the coherent behavior of atoms in a laser are pointed out.
We discuss the dynamics of two-dimensional arrays of Josephson junctions in the overdamped regime. Our discussion is restricted to “classical” arrays, where the Josephson coupling energy is much larger than the charging energy. Such arrays represent a highly controllable system to study the dynamics of vortices. Furthermore, they are promising for applications like, e.g., a coherent microwave source. The experiments have been performed with arrays of Nb/AlOx/Nb-tunnel junctions allowing a high degree of junction uniformity across the array. The typical array size is 10×10 junctions. We show spatially resolved measurement results obtained by low-temperature scanning electron microscopy, and demonstrate the merit of these investigations for the clarification of complex regimes of vortex dynamics as well as for the optimization of coherent microwave sources. In the case of external microwave irradiation with increasing power, a continuous transition from a non-locked to a completely locked oscillation state is presented. In addition, we report on the quantitative measurement of the emitted microwave power from the arrays.
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.
Two-dimensional arrays of Josephson junctions have been shown to operate in a state in which the microwave oscillations of the junctions are phase-coherent. However, the performance of an array is strongly dependent on both the details of the load-coupling circuit and the characteristic parameters of the junctions. We have measured two-dimensional arrays of resistively shunted Josephson tunnel junctions which are capacitively coupled to a nearby detector junction. Changing the critical current of the junctions in our arrays, while keeping the junction parasitics and array coupling roughly the same, results in an unexpected change in device operation. We have also investigated variations of the coupling circuit. Numerical simulations of the detection circuit enable us to estimate the power output from the array and to optimize the parameters of the system.
We have studied via computer simulations the dynamical properties of a circuit consisting of two arrays of Josephson junctions closed into a superconducting loop. Due to an internal circuit resonance the phase locking of Josephson junctions is enhanced, which makes possible the application of such a circuit as a source of coherent microwave radiation. The optimal circuit parameters and the influence of thermal noise are discussed. It is shown that the critical spread in junction parameters is about twice that of linear Josephson junction arrays. The possibility of tuning such a device is demonstrated.