The single-atom box: bosonic staircase and effects of parity

We have developed [1] 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. A different, e.g. fermionic, additional particle in the junction leads to non-trivial modifications of the staircase, that can be experimentally observed in the visibility of the interference pattern. [1] D.V. Averin, T. Bergeman, P.R. Hosur, and C. Bruder, Phys. Rev. A {\bf 78}, 031601(R) (2008).