  Two mesoscopic SQUID rings which are far from each other, are considered. A
source of two-mode nonclassical microwaves irradiates the two rings with
correlated photons. The Josephson currents are in this case quantum mechanical
operators, and their expectation values with respect to the density matrix of
the microwaves, yield the experimentally observed currents. Classically
correlated (separable) and quantum mechanically correlated (entangled)
microwaves are considered, and their effect on the Josephson currents is
quantified. Results for two different examples that involve microwaves in
number states and coherent states are derived. It is shown that the quantum
statistics of the tunnelling electron pairs through the Josephson junctions in
the two rings, are correlated.
