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 new insights 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.