  Based on a microscopic model, we study the interplay between
superconductivity and antiferromagnetism in a multi-layered system, where two
superconductors are separated by an antiferromagnetic region. Within a
self-consistent mean-field theory, this system is solved numerically. We find
that the antiferromagnetism in the middle layers profoundly affects the
supercurrent flowing across the junction, while the phase difference across the
junction influences the development of antiferromagnetism in the middle layers.
This study may not only shed new light on the mechanism for high-$T_{c}$
superconductors, but also bring important insights to building
Josephson-junction-based quantum devices, such as SQUID and superconducting
qubit.
