  We explore the interplay between tunneling and interatomic interactions in
the dynamics of a bosonic Josephson junction. We tune the scattering length of
an atomic $^{39}$K Bose-Einstein condensate confined in a double-well trap to
investigate regimes inaccessible to other superconducting or superfluid
systems. In the limit of small-amplitude oscillations, we study the transition
from Rabi to plasma oscillations by crossing over from attractive to repulsive
interatomic interactions. We observe a critical slowing down in the oscillation
frequency by increasing the strength of an attractive interaction up to the
point of a quantum phase transition. With sufficiently large initial
oscillation amplitude and repulsive interactions the system enters the
macroscopic quantum self-trapping regime, where we observe coherent undamped
oscillations with a self-sustained average imbalance of the relative well
population. The exquisite agreement between theory and experiments enables the
observation of a broad range of many body coherent dynamical regimes driven by
tunable tunneling energy, interactions and external forces, with applications
spanning from atomtronics to quantum metrology.
