  In a system of ac-driven condensed bosons we study a new type of Josephson
effect occurring between states sharing the same region of space and the same
internal atom structure. We first develop a technique to calculate the long
time dynamics of a driven interacting many-body system. For resonant
frequencies, this dynamics can be shown to derive from an effective
time-independent Hamiltonian which is expressed in terms of standard creation
and annihilation operators. Within the subspace of resonant states, and if the
undriven states are plane waves, a locally repulsive interaction between bosons
translates into an effective attraction. We apply the method to study the
effect of interactions on the coherent ratchet current of an asymmetrically
driven boson system. We find a wealth of dynamical regimes which includes Rabi
oscillations, self-trapping, and chaotic behavior. In the latter case, a full
many-body calculation deviates from the mean-field results by predicting large
quantum fluctuations of the relative particle number.
