  We have developed a theory of a Josephson junction formed by two
tunnel-coupled Bose-Einstein condensates in a double-well potential in the
regime of strong atom-atom interaction for an arbitrary total number $N$ of
bosons in the condensates. The tunnel resonances in the junction are shown to
be periodically spaced by the interaction energy, forming a single-atom
staircase sensitive to the parity of $N$ even for large $N$. One of the
manifestations of the staircase structure is the periodic modulation with the
bias energy of the visibility of the interference pattern in lattices of
junctions.

Mesoscale and Nanoscale Physics