  We investigate the dynamics of a population-imbalanced two-species fermionic
system trapped in an optical lattice. The paired fermions here can form bosonic
molecules via Feshbach coupling in the presence of an external magnetic field.
It is shown that the natural fluctuations of the condensate fraction are
periodic beyond a threshold Feshbach detuning; and below this threshold value,
the condensate fraction shows no oscillation at all. The oscillation frequency
vs. detuning curve is linear in nature. The slope and intercept of this line
are shown to carry important information about the amount of imbalance present
in the system, and the momentum space structure of the exotic phases.
