  In the Josephson effect, coherent Cooper pair tunneling is driven by the
phase difference between the superconducting order parameters on opposite sides
of the junction. By analogy, differences in order parameters across a junction
should lead to coherent tunneling of the condensed objects that exist in the
broken symmetry state. To exhibit the generality of this phenomenon and make
predictions from a realistic model, we study the case of a tunnel junction
between two itinerant antiferromagnets. At the mean-field level, we find an
equilibrium current of the staggered magnetization through the junction that is
proportional the normal state conductance and to $\mathbf{S}_{L}\times
\mathbf{S}_{R}$ where $\mathbf{S}_{L}$ and $\mathbf{S}_{R}$ are the staggered
magnetizations on either sides. Microscopically, this effect comes from
coherent tunneling of spin-one charge-zero particle-hole pairs that have a net
wave vector equal to the antiferromagnetic one. We explain similarities and
differences with the standard DC and AC Josephson effects.
