Dynamical projection of atoms to Feshbach molecules at strong coupling

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The dynamical atom/molecule projection, recently used to probe fermion pairing, is fast compared to collective fermion times, but slow on the Feshbach resonance width scale. Theory of detuning-induced dynamics of molecules coupled to resonantly associating atom pairs, employing a time-dependent many-body Green's function approach, is presented. An exact solution is found, predicting a 1/3 power law for molecule production efficiency at fast sweep. The results for s- and p-wave resonances are obtained and compared. The predicted production efficiency agrees with experimental observations for both condensed and incoherent molecules away from saturation.