  The interaction of mesoscopic interference devices with nonclassical
electromagnetic fields is studied. The external quantum fields induce a phase
factor on the electric charges. This phase factor, which is a generalization of
the standard Aharonov-Bohm phase factor, is in the case of nonclassical
electromagnetic fields a quantum mechanical operator. Its expectation value
depends on the density matrix describing the nonclassical photons and
determines the interference. Several examples are discussed, which show that
the quantum noise of the nonclassical photons destroys slightly the electron
interference fringes. An interesting application arises in the context of
distant electron interference devices, irradiated with entangled photons. In
this case the interfering electrons in the two devices become entangled. The
same ideas are applied in the context of SQUID rings irradiated with
nonclassical electromagnetic fields. It is shown that the statistics of the
Cooper pairs tunneling through the Josephson junction depend on the statistics
of the photons.
