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Physica Scripta

Traversal Time as Deduced from Decay Time Measurements in Josephson Junctions

Anedio Ranfagni, Pasquale Fabeni, Daniela Mugnai, Gian Paolo Pazzi, Lawrence S. Schulman, G. Ventura, Roberto Cristiano, Luigi Frunzio

Published Nov 1, 1998• 11 citations
Publisher

Abstract

The macroscopic quantum tunneling rate out of the metastable state of a Josephson junction has been measured in a range of temperature where the quantum contribution is comparable with the thermal escape. From such measurements the traversal time of the barrier has been deduced and compared with the theoretical predictions of a semiclassical model.

DOI
10.1088/0031-8949/58/5/020

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The macroscopic quantum tunneling rate out of the metastable state of a Josephson junction has been measured in a range of temperature where the quantum contribution is comparable with the thermal escape. From such measurements the traversal time of the barrier has been deduced and compared with the theoretical predictions of a semiclassical model.
The results relative to macroscopic quantum tunneling rate, out of the metastable state of Josephson junctions, are examined in view of determining the effect of dissipation. We adopt a simple criterion in accordance to which the effect of dissipation can be evaluated by analyzing the shortening of the semiclassical traversal time of the barrier. In almost all the considered cases, especially those with relatively large capacitance values, the relative time shortening turns out to be about 20% and with a corresponding quality factor Q ≃ 5.5. However, beyond the specific cases here considered, still in the regime of moderate dissipation, the method is applicable also to different situations with different values of the quality factor. The method allows, within the error limits, for a reliable determination of the load resistance RL, the less accessible quantity in the framework of the resistively and capacitively shunted junction model, provided that the characteristics of the junction (intrinsic capacitance, critical current, and the ratio of the bias current to the critical one) are known with sufficient accuracy.
High-resolution (sub-microsecond to nanosecond) time-resolved measurements of the dynamics of superconducting electronic devices, such as Josephson tunnel junctions and SQUIDs, are indispensable for fundamental physics research, such as quantum mechanics of macroscopic variables. We describe the development of a time-resolved measurement technique that enables direct measurements, in the time domain, of the temporal evolution of Josephson junctions with a nanosecond resolution. The technique was applied to study escape dynamics of Josephson junctions, as macroscopic quantum systems, in the quantum tunnelling regime. The measured probability of junctions remaining in the initial metastable state—the survival probability—as a function of time decayed exponentially, agrees very well with the theoretical prediction of the incoherent tunnelling process.
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.
Experiments to investigate the quantum behavior of a macroscopic degree of freedom, namely the phase difference across a Josephson tunnel junction, are described. The experiments involve measurements of the escape rate of the junction from its zero voltage state. Low temperature measurements of the escape rate for junctions that are either nearly undamped or moderately damped agree very closely with predictions for macroscopic quantum tunneling, with no adjustable parameters. Microwave spectroscopy reveals quantized energy levels in the potential well of the junction in excellent agreement with quantum-mechanical calculations. The system can be regarded as a "macroscopic nucleus with wires."
We present an interpretation of traversal time results in Josephson junctions, based on a stochastic model of tunneling processes which include dissipative effects. With the use of semiclassical analysis, the experiments performed up until now have supplied a time duration of the order of 102ps{10}^{2}\mathrm{ps}102ps (a remarkably long time, even considering the macroscopic nature of the systems under examination). According to our interpretation, this duration is only the imaginary part of a complex quantity, the real part of which (presumably the true physical duration) lies in the range of a few picoseconds.