Ground-state properties of interacting two-component Bose gases in a hard-wall trap

We investigate ground-state properties of interacting two-component Bose gases in a hard-wall trap using both the Bethe ansatz and exact numerical diagonalization method. For equal intra-atomic and interatomic interaction, the system is exactly solvable. Thus the exact ground-state wave-function and density distributions for the whole interacting regime can be obtained from the Bethe ansatz solutions. Since the ground state is a degenerate state with total spin S=N/2, the total density distributions are the same for each degenerate state. The total density distribution evolves from a Gauss-like Bose distribution to a Fermi-like one as the repulsive interaction increases. The distribution of each component is N-alpha/N of the total density distribution. This is approximately true even in the experimental situation. In addition the numerical results show that with the increase in interspecies interaction the distributions of two Tonks-Girardeau gases exhibit composite-fermionization crossover with each component developing N peaks in the strongly interacting regime.