Fermionization and fractional statistics in the stronglyinteracting one-dimensional Bose gas

Abstract

We discuss recent results on the relation between thestrongly interacting one-dimensional Bose gas and a gas of idealparticles obeying nonmutual generalized exclusion statistics(GES). The thermodynamic properties considered include thestatistical profiles, the specific heat and local paircorrelations. In the strong coupling limit γ → ∞,the Tonks-Girardeau gas, the equivalence is with Fermi statistics.The deviation from Fermi statistics during boson fermionizationfor finite but large interaction strength γ is described bythe relation α ≈ 1 - 2/γ, where α is ameasure of the GES. This gives a quantitative description of thefermionization process. In this sense the recent experimentalmeasurement of local pair correlations in a 1D Bose gas of87Rb atoms also provides a measure of the deviation of theGES parameter α away from the pure Fermi statistics valueα=1. Other thermodynamic properties, such as thedistribution profiles and the specific heat, are also sensitive tothe statistics. They also thus provide a way of exploringfractional statistics in the strongly interacting 1D Bose gas.