Fast Sweeping into Feshbach Molecules as a Probe of Fermionic Condensates

Fast sweep projection onto Feshbach molecules has been widely used as a probe to explore the properties of fermionic condensates, in particular the condensate fraction. By determining the exact dynamics of a pair of atoms in time varying magnetic fields across a Feshbach resonance, we calculate the number of condensed and noncondensed molecules created after fast magnetic field sweeps from the BCS to the BEC side of the resonance. We analyse the dependence of the molecular conversion efficiency for condensed and noncondensed molecules on the sweep rate, and on the initial and final magnetic fields, for $^{40}$K and $^{6}$Li resonances; and discuss the relation between the initial fermionic condensate fraction and the molecular condensate fraction measured after the sweep.