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

• Published in: Laser physics letters Vol. 4; no. 1; pp. 77 - 83
• Main Authors: Batchelor, M. T., Guan, X.-W.
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01.01.2007; WILEY‐VCH Verlag
• Subjects: fermionization; fractional statistics; generalized exclusion statistics; one-dimensional Bose gas; Tonks-Girardeau gas
• ISSN: 1612-2011; 1612-202X
• DOI: 10.1002/lapl.200610068

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. (© 2006 by Astro, Ltd. Published exclusively by WILEY‐VCH Verlag GmbH & Co. KGaA)