Superconducting single-charge transistor in a tunable dissipative environment.

We study a superconducting single-charge transistor, where the coherence of Cooper pair tunneling is destroyed by the coupling to a tunable dissipative environment. Sequential tunneling and cotunneling processes are analyzed to construct the shape of the conductance peaks and their dependence on the dissipation and temperature. Unexpected features are found due to a crossover between two distinct regimes, one "environment assisted" the other "environment dominated." Several of the predictions have been confirmed by recent experiments. The model and results apply also to the dynamics of Josephson junction quantum bits on a conducting ground plane, thus explaining the influence of dissipation on the coherence.