Energetics and structural properties of trapped two-component Fermi gases

Using two different numerical methods, we study the behavior of two-component Fermi gases interacting through short-range $s$-wave interactions in a harmonic trap. A correlated Gaussian basis-set expansion technique is used to determine the energies and structural properties, i.e., the radial one-body densities and pair distribution functions, for small systems with either even or odd $N$, as functions of the $s$-wave scattering length and the mass ratio $\kappa$ of the two species. Particular emphasis is put on a discussion of the angular momentum of the system in the BEC-BCS crossover regime. At unitarity, the excitation spectrum of the four-particle system with total angular momentum $L=0$ is calculated as a function of the mass ratio $\kappa$. The results are analyzed from a hyperspherical perspective, which offers unique insight into the problem. Additionally, fixed-node diffusion Monte Carlo calculations are performed for equal-mass Fermi gases with up to $N=30$ atoms. We focus on the odd-even oscillations of the ground-state energy of the equal-mass unitary system having up to $N=30$ particles, which are related to the excitation gap of the system. Furthermore, we present a detailed analysis of the structural properties of these systems.