Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

We investigate small equal-mass two-component Fermi gases under external spherically symmetric confinement in which atoms with opposite spins interact through a short-range two-body model potential. We employ a non-perturbative microscopic framework, the stochastic variational approach, and determine the system properties as functions of the interspecies s-wave scattering length a s , the orbital angular momentum L of the system, and the numbers N 1 and N 2 of spin-up and spin-down atoms (with N 1 − N 2 = 0 or 1 and N ⩽ 6 , where N = N 1 + N 2 ). At unitarity, we determine the energies of the five- and six-particle systems for various ranges r 0 of the underlying two-body model potential and extrapolate to the zero-range limit. These energies serve as benchmark results that can be used to validate and assess other numerical approaches. We also present structural properties such as the pair distribution function and the radial density. Furthermore, we analyze the one-body and two-body density matrices. A measure for the molecular condensate fraction is proposed and applied. Our calculations show explicitly that the natural orbitals and the momentum distributions of atomic Fermi gases approach those characteristic for a molecular Bose gas if the s-wave scattering length a s , a s > 0 , is sufficiently small.