  We explore the tunneling dynamics of strongly correlated bosonic mixtures in
a one-dimensional double-well. The role of the inter- and intra-species
interactions and their interplay is investigated using the numerically exact
Multi-Configuration Time dependent Hartree (MCTDH) method. The dynamics is
studied for three initial configurations: complete and partial population
imbalance and a phase separated state. Increasing the inter-species interaction
leads to a strong increase of the tunneling time period analogous to the
quantum self-trapping for condensates. The intra-species repulsion can suppress
or enhance the tunneling period depending on the strength of the inter-species
correlations as well as the initial configuration. Completely correlated
tunneling between the two species and within the same species as well as
mechanisms of species separation and counterflow are revealed. These effects
are explained by studying the many-body energy spectra as well as the
properties of the contributing stationary states.
