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

Abstract

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 $γ\to \infty$, 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 $α\approx 1 - 2/γ$, 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 $^{87}$Rb 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.