Ground-state and Josephson dynamics of double-well condensates interacting with trap oscillations

In the present paper, it is shown that the interaction between classical anharmonic oscillations of a trapped condensate and excited Josephson states corresponding to a large enough initial imbalance of particle number generates their equilibrium bound state. The dynamics of the system are determined by the self-consistent oscillations of the initial imbalance of the particle number and condensate shape. The existence of the bound state implies that the Josephson states can be detected by observing the change of the condensate shape.