Composite-fermionization of the mixture composed of Tonks gas and Fermi gas

This paper investigates the ground-state properties of the mixture composed of the strongly interacting Tonks-Girardeau gas and spin polarized Fermi gas confined in one-dimensional harmonic traps, where the interaction between the Bose atoms and Fermi atoms is tunable. With a generalized Bose-Fermi transformation the mixture is mapped into a two-component Fermi gas. The homogeneous Fermi gas is exactly solvable by the Bethe-ansatz method and the ground state energy density can be obtained. Combining the ground-state energy function of the homogeneous system with local density approximation it obtains the ground-state density distributions of inhomogeneous mixture. It is shown that with the increase in boson-fermion interaction, the system exhibits composite-fermionization crossover.