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 $\gamma \to \infty$, 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.

7 pages, 4 figures

References in corpus (5)

• Bosonizing one-dimensional cold atomic gases
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Dynamics of a Tonks-Girardeau gas released from a hard-wall trap
• Decay by tunneling of Bosonic and Fermionic Tonks-Girardeau Gases
• The q-deformed Bose gas: Integrability and thermodynamics

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• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• Evidences for interaction-induced Haldane fractional exclusion statistics in one and higher dimensions
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Thermodynamics of Statistical Anyons
• Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas
• Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective
• Exotic critical states as fractional Fermi seas in the one-dimensional Bose gas