Stable phase locking in a two-cell ladder array of Josephson junctions

Abstract

The stability of the periodic solution of the two-cell ladder array has been numerically investigated in order to explore intrinsic phase-locking mechanisms relevant to arrays and stacked junction oscillators. In zero magnetic field the periodic in-phase solution of the system is neutrally stable. However, this solution is stable over a finite voltage range when an applied control current exceeds a critical value. The dependence upon system parameters of the boundaries of the stable range and the critical control current is investigated. Finally, the influence of the control current on the microwave power in a typical range of stability is calculated.

Millimetre and sub-mm wavelength radiation sources based on discrete Josephson junction arrays

“…As well as the experimental efforts to study phase locking in 2D arrays, there is a growing field of theoretical studies [31,32,36,113,[122][123][124][125][126][127]. The subject of mutual phase locking in arrays is an example of self-organized non-linear and dissipative dynamics, often in the presence of disorder.…”

Disorder-induced desynchronization in a2×2circular Josephson junction array

“…Some involve linking the array in an external fashion ͑e.g., coupling the array to an external load, applying a highfrequency external signal, etc.͒, while others rely on various spatially distributed array designs that demand a somewhat more sophisticated analysis to properly model ͑since the standard ''lump circuit'' analysis fails͒. [6][7][8] Though these approaches can at times be effective, a basic underlying question remains largely unanswered: To what extent does the lattice geometry of an array determine its intrinsic robustness against disorder? In particular, are certain array geometries naturally more conducive to maintaining coherence in the presence of disorder than others?…”

Two-dimensional arrays of Josephson junctions in a magnetic field: A stability analysis of synchronized states

“…[1][2][3][4][5][6][7][8] Theoretical studies have begun to determine under what conditions and for what ranges of circuit parameters coherent emission should be possible from such arrays. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] These arrays are also of interest as paradigms of nonlinear dynamical systems with many degrees of freedom. [24][25][26][27] Of particular interest have been the so-called phaselocked states of such arrays.…”