Ground state and Josephson dynamics of the 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 disbalance of the particle number generates their equilibrium bound state. The dynamics of the system is determined by the self-consistent oscillations of the initial disbalance of the particle number and condensate shape. The existense of the bound state implies that the Josephson states can be detected by observing the change of the condensate shape.