Occupation Statistics of a BEC for a Driven Landau-Zener Crossing

We consider an atomic Bose-Einstein condensate (BEC) loaded in a biased double-well trap with tunneling rate $K$ and inter-atomic interaction $U$. The BEC is prepared such that all $N$ atoms are in the left well. We drive the system by sweeping the potential difference $ϵ$ between the two wells. Depending on the interaction $u=NU\mathrm{/}K$, and the sweep rate $\dot{ϵ}$, we distinguish three dynamical regimes: adiabatic, diabatic, and sudden, and consider the occupation statistics of the final state. The analysis goes beyond mean-field theory and is complemented by a semiclassical picture.