Characteristic Times of Tunneling Processes in Josephson Junctions

In cases of macroscopic quantum tunneling with Josephson junctions, we have to consider different times, such as the decay time of the superconductive metastable state, the semiclassical traversal time of the barrier, and the "true" tunneling time. As for the decay time the only one accessible for direct measurements and which crucially depends on the load "seen" by the junction, some important effects can be envisaged when the load is constituted by a real transmission line. In general, the tunneling time must to be considered as a complex quantity, the real part of which, i.e. the true duration of the process, is not directly accessible. What is usually deduced from measurements of the decay time is the semiclassical traversal time of the barrier which, as is well known, is an imaginary quantity. By starting from a knowledge of this latter quantity, it is possible to perform an evaluation of the real-time duration of the process. According to path-integral analysis, relations can indeed be established between real and imaginary parts of the tunneling duration. In typical cases of moderate dissipation, the real part is found to be (much) smaller than the imaginary one, while the situation is different, in cases of stronger dissipation. This can be made evident by applying the above procedure to several cases of available experimental results.