Single Cooper-pair tunnelling induced by non-classical microwaves

A mesoscopic Josephson junction interacting with a mode of non-classical microwaves with frequency ω is considered. Squeezing of the electromagnetic field drastically affects the dynamics of Cooper tunnelling. In particular, Bloch steps can be observed even when the microwaves are in the squeezed vacuum state with zero average amplitude of the field E(t) = 0. The interval between these steps is double in size in comparison to the conventional Bloch steps.