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

TL;DR

This paper explores how strongly interacting 1D Bose gases exhibit fractional statistics, transitioning from Bose to Fermi behavior, and provides a quantitative description of this fermionization process through generalized exclusion statistics.

Contribution

It introduces a quantitative relation between interaction strength and GES parameter, linking experimental observations with fractional statistics in 1D Bose gases.

Findings

Fermionization characterized by GES parameter pproaching 1 as ecomes large

Deviation from Fermi statistics quantified by pproximate 1 - 2/or finite nd ynamics

Thermodynamic properties sensitive to fractional statistics

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 $\gamma \to \infty$, the Tonks-Girardeau gas, the equivalence is with Fermi statistics. The deviation from Fermi statistics during boson fermionization for finite but large interaction strength $\gamma$ is described by the relation $\alpha \approx 1 - 2/\gamma$, where $\alpha$ 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 $\alpha$ away from the pure Fermi statistics value $\alpha=1$. 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.