Fermionization and fractional statistics in the strongly interacting one-dimensional Bose gas

We discuss recent results on the relation between the strongly interacting one-dimensional Bose gas and a gas of ideal particles obeying nonmutual generalized exclusion statistics (GES). The thermodynamic properties considered include the statistical profiles, the specific heat and local pair correlations. In the strong coupling limit γ → ∞, the Tonks-Girardeau gas, the equivalence is with Fermi statistics. The deviation from Fermi statistics during boson fermionization for finite but large interaction strength γ is described by the relation α, ≈ 1 - 2/γ, where α is a measure of the GES. This gives a quantitative description of the fermionization process. In this sense the recent experimental measurement of local pair correlations in a 1D Bose gas of ⁸⁷Rb atoms also provides a measure of the deviation of the GES parameter α away from the pure Fermi statistics value α = 1. Other thermodynamic properties, such as the distribution profiles and the specific heat, are also sensitive to the statistics. They also thus provide a way of exploring fractional statistics in the strongly interacting 1D Bose gas. A graph is presented. The total energy per particle in units of the free Fermi energy ^EF as a function of the effective temperature τ and the coupling strength γ.