  We investigate the interplay dynamics of a cavity qed system, where the
two-level atoms are trapped in a double-well potential, and the cavity mode,
with a frequency largely detuned to the atomic level splitting, is driven by a
probe laser. The interaction between the center-of-mass motion of the atoms and
the cavity mode is induced by the position dependent atom-field coupling. The
dynamics of the system is characterized by two distinct time scales, the
inverse of the atomic interwell tunneling rate and the inverse of the cavity
loss rate. The system shows drastically different (quasi) steady behaviors in
the short-time and long-time intervals.
