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The time evolution of probability density, the ground-state fidelity and theentanglement of a Bose-Fermi mixture in a 1D double well potential, are studiedthrough the two mode approximation. We found that the behaviour of the quantumreturn probability shows three distinct regions. The first region ischaracterized by a complete miscibility, and correlated tunneling of bosons andfermion. The second region is characterized by correlated sequential tunnelingand in the last region we found an increase in the tunneling frequency of thetwo species.  We found through the Von Neumann entropy, that the boson-fermion couplingallows a maximum entanglement of quantum correlations of bosons and fermions inthe same value. Finally we calculated the fidelity in the$\lambda_{FF}-\lambda_{BF}$ and $\lambda_{BB}-\lambda_{BF}$ planes and we foundthat the drop of the two fidelities becomes deeper and deeper as theboson-fermion interaction decreases.

Density probabilities and quantum critical phenomena of a Bose-Fermi Mixture in 1D Double well potential