Effects of a single fermion in a Bose Josephson junction

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 line shape of the resonance using degenerate Brillouin-Wigner theory. We finally compute the time-dependent dynamics of the mixture. Using the fermionic tunnel resonances as a 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.