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Physical Review E

Reexamination of Josephson junctions coupled to transmission lines

Anedio Ranfagni, Paolo Moretti, Ilaria Cacciari, Maria Angela Vitali

Published May 13, 2008• 2 citations
Publisher

Abstract

The effect of dissipation when due to the load of a transmission line coupled to a Josephson junction is reconsidered and evaluated by means of a simple direct procedure that supplies analytical expressions. The results are in good agreement with the ones previously reported in the literature. A simple criterion for testing experimental results is introduced.

DOI
10.1103/physreve.77.057601

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The effect of dissipation when due to the load of a transmission line coupled to a Josephson junction is reconsidered and evaluated by means of a simple direct procedure that supplies analytical expressions. The results are in good agreement with the ones previously reported in the literature. A simple criterion for testing experimental results is introduced.
The problem of evaluating dissipative effects in macroscopic quantum tunneling is re-examined for the case of Josephson junctions, with the adoption of an alternative way with respect to several previously proposed and, in some cases, contradictory approaches. The system, which consists of a junction coupled to a transmission line, is analyzed both analytically and numerically. A test of the theoretical model, as compared to the experimental results available, is performed in accordance with a criterion based on a shortening of the traversal time.
The various ways of evaluating dissipative effects in macroscopic quantum tunneling are re-examined. The results obtained by using functional integration, while confirming those of previously given treatments, enable a comparison with available experimental results relative to Josephson junctions. A criterion based on the shortening of the semiclassical traversal time $\ensuremath{\tau}$ of the barrier with regard to dissipation can be established, according to which $\ensuremath{\Delta}\ensuremath{\tau}/\ensuremath{\tau}\ensuremath{\gtrsim}N/Q$, where QQQ is the quality factor of the junction and NNN is a numerical constant of order unity. The best agreement with the experiments is obtained for N=1.11N=1.11N=1.11, as it results from a semiempirical analysis based on an increase in the potential barrier caused by dissipative effects.