  We consider the tunneling properties of a single fermionic impurity immersed
in a Bose-Einstein condensate in a double-well potential. For strong
boson-fermion interaction, we show the existence of a tunnel resonance where a
large number of bosons and the fermion tunnel simultaneously. We give
analytical expressions for the lineshape of the resonance using degenerate
Brillouin-Wigner theory. We finally compute the time-dependent dynamics of the
mixture. Using the fermionic tunnel resonances as beam splitter for
wave-functions, we construct a Mach-Zehnder interferometer that allows complete
population transfer from one well to the other by tilting the double-well
potential and only taking into account the fermion's tunnel properties.
