Adiabatic phase diagram of a degenerate fermi gas with a feshbach resonance

We determine the adiabatic phase diagram of a resonantly-coupled system of Fermi atoms and Bose molecules confined in a harmonic trap by using the local density approximation. The key idea of our work is conservation of entropy through the adiabatic process. We also calculate the molecular conversion efficiency as a function of the initial temperature. Our work helps to understand recent experiments on the BCS-BEC crossover, in terms of the initial temperature measured before a sweep of the magnetic field.