  We study the interaction-modulated tunneling dynamics of a Bose-Einstein
condensate (BEC) in a deep double-well potential, where the tunneling between
the two wells is modulated by another BEC trapped in a harmonic potential
symmetrically positioned at the center of the double-well potential. The
inter-species interactions couple the dynamics of the two BECs, which give rise
to interesting features in the tunneling oscillations. Adopting a two-mode
approximation for the BEC in the double-well potential and coupling it with the
Gross-Pitaevskii equation of the harmonically trapped BEC, we numerically
investigate the coupled dynamics of the BEC mixture, and map out the phase
diagram of the tunneling dynamics. We show that the dynamical back action of
the BEC in the harmonic trap leads to strong non-linearity in the oscillations
of the BEC in the double-well potential, which enriches the system dynamics,
and enhances macroscopic self trapping. The transition between the Josephson
oscillation and the self-trapping dynamics can be identified by monitoring the
oscillation frequency of the double-well BEC. Our results suggest the
possibility of tuning the tunneling dynamics of BECs in double-well potentials.
