Isothermal compressibility and effects of multi-body molecular interactions in a strongly interacting ultracold Fermi gas

TL;DR

This paper theoretically studies the isothermal compressibility of an ultracold Fermi gas across the BCS-BEC crossover, highlighting the importance of multi-body molecular interactions in the strong-coupling regime.

Contribution

It introduces a comprehensive analysis of multi-body molecular interactions affecting thermodynamics in strongly interacting Fermi gases using the self-consistent T-matrix approximation.

Findings

Correlations between Cooper-pair molecules are crucial in the strong-coupling BEC regime.

Three-body molecular interactions significantly influence compressibility near the superfluid transition.

The BEC regime offers a platform to explore multi-body correlations in ultracold Fermi gases.

Abstract

We theoretically investigate the isothermal compressibility $\kappa_{T}$ 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 (SCTMA), we evaluate the temperature dependence of this thermodynamic quantity over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. While $\kappa_T$ 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 $\kappa_T$ 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 multi-body correlations between Cooper-pair molecules.