The role of quantized energy levels in the macroscopic quantum behavior of Josephson junctions

The effects of the presence of quantized levels in the problem of the (V = 0)-state decay ill Josephson junctions have been investigated. In considering the dynamics of the junction in the quantum picture, a preliminary study of the classical thermal fluctuation is necessary especially for the determination of the relevant junction parameters to be used in the quantum limit. Measurements of the lifetime of the zero-voltage state in a single hysteretic Josephson junction show clear evidence of two different damping regimes. Results are obtained for a wide range of damping within the underdamped region because the damping resistance depends exponentially on Inverse temperature as does the junction quasiparticle resistance. This latter aspect is relevant because or allows to obtain a damping level that decreases with temperature, and hence, at low temperature we are able to study an extremely underdamped system. Many new interesting aspects related to the quantum behavior of the junction can be observed with such a low damping level. It is shown that a fast sweep of a Josephson tunnel junction call reveal the presence of quantum energy levels in the associated washboard potential. Peculiar effects, which can be observed on P(I) and Gamma(I), are obtained by numerical integration of the entire time dependent master equation describing the dynamics of the statistical population of each quantum level. The curves obtained predict the results of possible new experiments. Finally, we discuss, within the well-established quantum picture of the junction, the idea of a resonant macroscopic quantum tunneling between levels with the same energy ill neighboring wells of the potential shape describing the junction. This process produces small voltage spikes in the current-voltage characteristics, as well as peculiar peaks In the current switching distributions at given current values, which call be measured in junctions and SQUIDs with suitable parameters.