Evolution of the Normal State of a Strongly Interacting Fermi Gas from a Pseudogap Phase to a Molecular Bose Gas

Wave-vector resolved radio frequency spectroscopy data for an ultracold trapped Fermi gas are reported for several couplings at $T_c$, and extensively analyzed in terms of a pairing-fluctuation theory. We map the evolution of a strongly interacting Fermi gas from the pseudogap phase into a fully gapped molecular Bose gas as a function of the interaction strength, which is marked by a rapid disappearance of a remnant Fermi surface in the single-particle dispersion. We also show that our theory of a pseudogap phase is consistent with a recent experimental observation as well as with quantum Monte Carlo data of thermodynamic quantities of a unitary Fermi gas above $T_c$.