  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.
