Isothermal compressibility and effects of multibody molecular interactions in a strongly interacting ultracold Fermi gas

We theoretically investigate the isothermal compressibility κT in the normal state of an ultracold Fermi gas. Including pairing fluctuations, as well as preformed-pair formations, within the framework of the self-consistent T-matrix approximation, we evaluate the temperature dependence of this thermodynamic quantity over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. While κT in the weak-coupling BCS regime is dominated by Fermi atoms near the Fermi surface, correlations between tightly bound Cooper-pair molecules are found to play crucial roles in the strong-coupling BEC regime. In the latter region, besides a two-body molecular interaction, a three-body one is shown to sizably affect κT near the superfluid phase-transition temperature. Our results indicate that the strong-coupling BEC regime of an ultracold Fermi gas would provide a unique opportunity to study multibody correlations between Cooper-pair molecules.