# Strong-coupling corrections to ground-state properties of a superfluid Fermi gas

## TL;DR

This paper introduces a simplified method to accurately determine ground-state properties of strongly interacting superfluid Fermi gases by focusing on quantum fluctuation corrections to the chemical potential and applying thermodynamic identities.

## Contribution

The authors propose an efficient approach that uses strong-coupling calculations only for quantum fluctuations, then derives other properties via thermodynamics, reducing computational complexity.

## Key findings

- Extended T-matrix approximation effectively models superfluid Fermi gases.
- Results align well with recent experimental measurements of chemical potential.
- Many-body effects are primarily due to superfluid fluctuations in the BCS-unitary regime.

## Abstract

We theoretically present an economical and convenient way to study ground-state properties of a strongly interacting superfluid Fermi gas. Our strategy is that complicated strong-coupling calculations are used only to evaluate quantum fluctuation corrections to the chemical potential $\mu$. Then, without any further strong-coupling calculations, we calculate the compressibility, sound velocity, internal energy, pressure, and Tan's contact, from the calculated $\mu$ without loss of accuracy, by using exact thermodynamic identities. Using a recent precise measurement of $\mu$ in a superfluid $^6$Li Fermi gas, we show that an extended $T$-matrix approximation (ETMA) is suitable for our purpose, especially in the BCS-unitary regime, where our results indicate that many-body corrections are dominated by superfluid fluctuations. Since precise determinations of physical quantities are not always easy in cold Fermi gas physics, our approach would greatly reduce experimental and theoretical efforts toward the understanding of ground-state properties of this strongly interacting Fermi system.