Tunnelling and Superposition in a Non-orthogonal Two-State Model

The two-state model has demonstrated great success in describing a variety of phenomena in Bose Einstein condensates, including Josephson oscillations, self trapping and collapse and revival. We extend this model to allow the many-body states to be constructed from non-orthogonal single-particle orbitals. This allows us to consider more intuitive single-particle orbitals. The use of the intuitive single-particle orbitals uncovers hidden structure in the revivals. In addition, the possibility of using non-orthogonal orbitals to construct many-body wave-functions allows us to numerically consider a two-state model with orbitals that adapt to their occupation number. We use this possibility to study superposition of a BEC bubble immersed in a bath condensate.