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IEEE Transactions on Magnetics

Dynamic stabilization of a microwave-driven Josephson tunnel junction against a period-doubling bifurcation

Jørn Bindslev Hansen, G.F. Eriksen, Mogens R. Samuelsen, Henrik Svensmark

Published Mar 1, 1989• 0 citations
Publisher

Abstract

The authors present theoretical and experimental results on the effect of periodic perturbations on microwave-driven Josephson tunnel junctions close to a period-doubling bifurcation. The theory, which is quite general, describes how a periodic near-resonant perturbation changes the stability of the system. The phenomenon was investigated experimentally in small Nb-NbO/sub x/-Pb tunnel junctions, and experimental findings were found to be in agreement with the theory. The effect has importance for the performance of parametric amplifiers based on Josephson tunnel junctions.>

DOI
10.1109/20.92559

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The authors present theoretical and experimental results on the effect of periodic perturbations on microwave-driven Josephson tunnel junctions close to a period-doubling bifurcation. The theory, which is quite general, describes how a periodic near-resonant perturbation changes the stability of the system. The phenomenon was investigated experimentally in small Nb-NbO/sub x/-Pb tunnel junctions, and experimental findings were found to be in agreement with the theory. The effect has importance for the performance of parametric amplifiers based on Josephson tunnel junctions.>
A Josephson tunnel junction which is rf driven near a dynamical bifurcation point can amplify quantum signals. However, the bifurcation point will exist robustly only if the electrodynamic environment of the junction meets certain criteria. We develop a general formalism for dealing with the nonlinear dynamics of a Josephson junction embedded in an arbitrary microwave circuit. We find sufficient conditions for the existence of the bifurcation regime: (a) the embedding impedance of the junction needs to present a resonance at a particular frequency ${\ensuremath{\omega}}_{R}$, with the quality factor QQQ of the resonance and the participation ratio ppp of the junction satisfying Qp⪢1Qp⪢1Qp⪢1, and (b) the drive frequency should be low frequency detuned away from ${\ensuremath{\omega}}_{R}$ by more than $\sqrt{3}{\ensuremath{\omega}}_{R}∕(2Q)$.
We have observed the dynamical bistability of a microwave superconducting Fabry-Perot cavity incorporating a non-linear element in the form of Josephson tunnel junction. The effect, which is the analog of optical bistability, manifests itself in the transmission and reflection characteristics of the cavity and is governed by a competition between the wave amplitude dependence of the resonant frequency and the finite residence time of the field energy inside the cavity. This finite residence time is solely due to extraction of radiation from the cavity by the measurement process. The tight quantitative agreement with a simple model based on the Duffing oscillator equation shows that the nonlinearity, and hence the bifurcation phenomenon, is solely dispersive.
The electric coupling and the magnetic coupling between the Josephson tunnel junction and applied microwaves have been studied separately. The theoretical analysis (based on the forced vibration model) and experimental results indicate that for a half-wavelength junction only even microwave-induced steps can be obtained under magnetic coupling, but for the electric coupling, odd steps appear simultaneously, and that for an integral wavelength junction only even steps can be observed under the two couplings. The efficiency of the electric coupling, according to the theory and the experimental results, is found to be better than that of the magnetic coupling for the Nb-NbO/sub x/-Pb junction.