  We investigate a population-imbalanced two-species fermionic system where the
resonantly-paired fermions combine to form bosonic molecules via Feshbach
interaction. We study the dynamics of the intrinsic quantum fluctuations of the
system. It is shown that the natural fluctuations of the condensate fraction
consists of a fixed number of periodic components : indicating that these
oscillations do not die out, and are sustained in the mean field dynamics of
the system. These frequency components bear distinct signatures of the nature
of pairing present in the system. We describe how a time dependent external
magnetic field can be used to locate these oscillation frequencies, and thus to
explore the momentum space structure of the population imbalanced system. We
propose that this method can be used as an indirect experimental probe for
detecting exotic phases like the breached pair state, FFLO state, and a
phase-separated state comprising of BCS and normal regions.
