Densities probabilities of a Bose-Fermi Mixture in 1D Double well potential

We use the two mode approximation for a interacting one-dimensional spinless soft core bosons and one half spin fermions in a double-well potential with a large central barrier. We include all the on-site boson-boson, fermion-fermion and boson-fermion repulsive contact potential represented by delta-function and considered bosonic and fermionic isotopes of ytterbium(Yb) $^{170}Yb$ and $^{171}Yb$ respectively. By means of the approximation, we find that in the regime $U_{BF}>U_{BB}$ give rise to a immiscible phase and in the regime $U_{BB}\geq U_{BF}$ give rise to a miscible phase, that is characterized by a temporal overlap of the bosonic and fermionic probability densities. We also report that due to the Bose-Fermi interaction, the system presents an apparent destruction of the collapse-revival oscillation of boson density probability at least in the ranges investigated.