Resonance phenomena in Macroscopic Quantum Tunneling: the small   viscosity limit
  We present a new theoretical approach to describe the quantum behavior of a macroscopic system interacting with an external irradiation field, close to the resonant condition. Here we consider the extremely underdamped regime for a system described by a double well potential. The theory includes both: transitions from one well to the other and relaxation processes. We simulate resonant phenomena in a rf-SQUID, whose parameters lie in the range typically used in the experiments. The dependence of the transition probability W on the external drive of the system $\phi_x$ shows three resonance peaks. One peak is connected with the resonant tunneling and the two others with the resonant pumping. The relative position of the two peaks correlated to the resonant pumping depends on the pumping frequency $\nu$ and on the system parameters. The preliminary measurements on our devices show a low dissipation level and assure that they are good candidates in order to realize new experiments on the resonant phenomena in the presence of an external microwave irradiation of proper frequency. 
Yu.N.Ovchinnikov, S.Rombetto, B.Ruggiero, V.Corato, P.Silvestrini