Single Cooper pair tunneling induced by non-classical microwaves

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