Exact results of two-component Fermi gas in a hard wall trap

We investigate the ground state properties of a one-dimensional two-component ultra-cold Fermi gas in an infinite potential well. Exact Bethe ansatz solution is used to calculate the many-body wave function of the system. Then we evaluate the single-particle reduced density matrix and two-particle density density correlations of the system for different interaction strengths. We find that the momentum density distributions of the strongly interacting two-component Fermi gas is distinct from that of free spinless Fermi gas although their position density distributions are similar. This interacting system may be experimentally accessible using ultra-cold atoms.