  We describe and justify a simple model for the dynamics associated with rapid
sweeps across a Feshbach resonance, from the atomic to the molecular side, in
an ultra cold Fermi system. The model allows us to relate the observed molecule
momentum distribution, including its dependence on the sweep rate, to
equilibrium properties of the initial state. For initial state near resonance,
we find that phase fluctuations sharply reduce the observed condensate
fraction. Moreover, for very fast sweeps and low temperatures, we predict a
surprising nonmonotonic dependence of the molecule condensate fraction on
detuning, that is a direct signature of quantum phase fluctuations. The
dependence of the total molecule number on sweep rate is found to be a
sensitive probe of pairing in the initial state, whether condensed or not.
Hence it can be utilized to establish the presence of a phase fluctuation
induced `psuedogap' phase in these systems.
