  We unravel the correlated tunneling dynamics of a mass imbalanced few-body
fermi-fermi mixture upon quenching the tilt of a double-well. The
non-equilibrium dynamics of both species changes from Rabi-oscillations close
to the non-interacting limit to a delayed tunneling dynamics for moderate
interspecies repulsions. Considering strong interspecies interactions the
lighter species experiences quantum self-trapping due to the heavier species
which acts as an effective material barrier, while performing almost perfect
Rabi-oscillations. The degree of entanglement, inherent in the system, is
analyzed and found to be significant both at moderate and strong repulsions. To
relate our findings with possible experimental realizations we simulate in-situ
single-shot measurements and discuss how a sampling of such images dictates the
observed dynamics. Finally, the dependence of the tunneling behavior on the
mass ratio, the particle number in each species and the height of the barrier
of the double-well is showcased.
