The ground-state energy of an attractive Fermi gas along the Bardeen–Cooper–Schrieffer-unitarity crossover

Abstract

The ratio f(x) of the ground-state energy of an attractive Fermi gas to that of the noninteracting Fermi gas is a smooth and continuous function of x = kFa in the Bardeen–Cooper–Schrieffer (BCS)-unitarity crossover regime −∞ < x ⩽ 0. Here kFℏ is the Fermi momentum, ℏ is the Planck constant and a is the s-wave scattering length. The respective coefficients of the perturbation expansions of f(x) in the BCS regime and in the unitary regime are expected to be related to each other. Unitary Fermi gases are expected to exhibit universal behaviors. So f(−∞) is universal and is only a function of the universal coefficients of the perturbation expansion of f(x) in the BCS regime. Using these facts, we extend the perturbation expansion of f(x) in the BCS regime to the BCS-unitarity crossover regime. f(−∞) is predicted to be 0.400 98(0.422 94) for the Bose (Fermi) function, which are in good agreement with the quantum Monte Carlo results and the experimental results.