Resonant Phenomena in an rf-SQUID: moderate underdamped and extreme underdamped limit

We study the resonant quantum behaviour of a macroscopic superconducting system interacting with an external field. First we consider the resonant tunneling assisted by microwave frequency in the moderate underdamped quantum regime. Then we consider the resonant process in the extreme underdamped limit. In both regimes we have investigated a small frequency range, where resonant phenomena take place. The transition probability W from the left to the right potential well has been numerically calculated for an rf-SQUID as function of the external flux ? x for both regimes. Results indicate that, in a proper frequency and ? x range, the transition probability W can present two or three resonant peaks, depending on the damping regime.