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Physical Review B

Dissipation and traversal time in Josephson junctions

Ilaria Cacciari, Paolo Moretti, Anedio Ranfagni

Published May 28, 2010• 5 citations
Publisher

Abstract

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 $Q$ is the quality factor of the junction and $N$ is a numerical constant of order unity. The best agreement with the experiments is obtained for $N=1.11$, as it results from a semiempirical analysis based on an increase in the potential barrier caused by dissipative effects.

DOI
10.1103/physrevb.81.172506

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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 \ensuremathτ\ensuremath{\tau}\ensuremathτ of the barrier with regard to dissipation can be established, according to which \ensuremathΔ\ensuremathτ/\ensuremathτ\ensuremath≳N/Q\ensuremath{\Delta}\ensuremath{\tau}/\ensuremath{\tau}\ensuremath{\gtrsim}N/Q\ensuremathΔ\ensuremathτ/\ensuremathτ\ensuremath≳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.
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.
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.
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.
Measurements of macroscopic quantum tunnelling (MQT) in intrinsic Josephson junctions (IJJs) suggest that they may be suitable as qubits. An advantage of using IJJs over trilayers is the absence of any artificial barrier and hence the possible absence of decohering two-level fluctuators. A disadvantage is that it is difficult to fabricate single IJJs. Hence all IJJ MQT experiments have been carried out on arrays of many IJJs in series. Since MQT is suppressed by dissipation, it is important (a) to understand the role of dissipation on the dynamics of IJJs and (b) to consider how the dissipation and the dynamics change as a function of the number of junctions in the array which are in the voltage state. We have measured distributions of the nth-order switching current in TlBaCaCuO IJJ arrays, where n indicates switching from n to n+1 junctions being in the voltage state. The junctions show conventional underdamped behaviour at temperatures below some temperature T*, with a suppression of the width of the distribution above T*. We find that T* depends upon n. For n = 0 (i.e. switching from the supercurrent branch), T* is less than 4.2 K. For n > 0, we measured T* values between 20 K and 40 K. Calculations and simulations show that a change in T* results from a change in Q. Analysis suggests that the Q of the IJJs is determined by the environmental impedance when all junctions in the array are in the zero-voltage state, whereas having one junction or more in the voltage state isolates the array from the environment leading to a higher Q. We discuss our data in the context of possible qubit applications.