Two atoms in a double well: Exact solution with a Bethe ansatz

We propose to experimentally realize an odd-parity eigenstate vertical bar b > of two atoms in a double well. The occupation probability of this state shows evident dependence on the interaction, distinct from the result of two-mode model adopted in the Heidelberg experiment. The tunneling dynamics of two atoms starting from the NOON state with infinite barrier height can be derived from the exactly solved model of a delta-barrier split double well based on a Bethe ansatz type hypothesis of the wave functions. We find that the single-particle tunneling shifts between the probability of double occupancy in the same well and that of single occupancy in different wells.