  We study the mean-field dynamics of a Bose Josephson junction which is
dispersively coupled to a single mode of a high-finesse optical cavity. An
effective classical Hamiltonian for the Bose Josephson junction is derived and
its dynamics is studied in the perspective of phase portrait. It is shown that
the strong condensate-field coupling does alter the dynamics of the Bose
Josephson junction drastically. The possibility of coherent manipulating and
\textsl{in situ} observation of the dynamics of the Bose Josephson junction is
discussed.

Quantum Physics;Statistical Mechanics