  A debated issue in the physics of the BCS-BEC crossover with trapped Fermi
atoms is to identify characteristic properties of the superfluid phase.
Recently, a condensate fraction was measured on the BCS side of the crossover
by sweeping the system in a fast (nonadiabatic) way from the BCS to the BEC
sides, thus ``projecting'' the initial many-body state onto a molecular
condensate. We analyze here the theoretical implications of these projection
experiments, by identifying the appropriate quantum-mechanical operator
associated with the measured quantities and relating them to the many-body
correlations occurring in the BCS-BEC crossover. Calculations are presented
over wide temperature and coupling ranges, by including pairing fluctuations on
top of mean field.
