  Inspired by the increasing possibility of experimental control in ultracold
atomic physics, we introduce a new Lax operator and use it to construct and
solve models with two wells and two on-well states together with its
generalization for n on-well states. The models are solved by the algebraic
Bethe ansatz method and can be viewed as describing two Bose-Einstein
condensates allowing for an exchange interaction through Josephson tunnelling.
