In this paper, we study the interaction-modulated tunneling dynamics of a Bose-Fermi superfluid mixture, where a BEC with weak repulsive interaction are confined in a symmetric deep double-well potential and an equally populated two-component Fermi gas in a harmonic potential symmetrically positioned at the center of the double-well potential. The tunneling between the two wells is modulated by fermions trapped in a harmonic potential. When the temperature is adequately low and the bosonic particle number is adequately large, we can employ the mean-field theories to describe the evolution of the BEC in the double-well potential with the time-dependent Gross–Pitaevskii equation. For the Fermi gas in the harmonic potential trap, we consider the case where the inter-fermion interaction is tuned on the deep Bose-Einstein condensate of the inter-fermion Feshbach resonance, where two fermions of spin-up and spin-down form a two-body bound state. Within the regime, the Fermi gas is well described by a condensate of these fermionic dimers, hence can be simulated as well by a Gross–Pitaevskii equation of dimers. The inter-species interactions couple the dynamics of the two species, which result in interesting features in the tunneling oscillations. The dynamic equations of the BEC in the double-well potential is described by a two-mode approximation. Coupling it with time-dependent Gross-Pitaevskii equation of the harmonically potential trapped molecular BEC, we numerically investigate the dynamical evolution of the Boson-Fermi hybrid system under different initial conditions. It is found that the interaction of fermions in a harmonic potential leads to strong non-linearity in the oscillations of the bosons in the double-well potential and enriches the tunneling dynamics of the bosons. Especially, it strengthens macroscopic quantum self-trapping. And the macroscopic quantum self-trapping can be manifested in three forms: the phase tends to be negative and monotonously decrease with time, the phase evolves bounded with time, and the phase tends to be positive and monotonously increase with time. This means that it is possible the tunneling dynamics of the BEC in double-well potential is adjustable. Our results can be verified experimentally in Bose–Fermi superfluid mixture by varying different interactions parameters via Feshbach resonance and confinement-induced resonance.
