Many-body properties of quasi–one-dimensional boson gas across a narrow CIR

¹ Institute for Advanced Study, Tsinghua University - Beijing, 100084, China
² State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences - Wuhan 430071, China
³ Department of Theoretical Physics, Research School of Physics and Engineering, the Australian National University Canberra ACT 0200, Australia

Received: 21 November 2012
Accepted: 4 February 2013

Abstract

We study strong interaction effects in a one-dimensional (1D) boson gas across a narrow confinement-induced resonance (CIR). In contrast to the zero-range potential, the 1D two-body interaction in the narrow CIR can be written as a polynomial of derivative δ-function interaction on many-body level. Using the asymptotic Bethe ansatz, we find that the low-energy physics of this many-body problem is described by the Tomonaga-Luttinger liquid where the Luttinger parameters are essentially modified by an effective finite-range parameter v. This parameter drastically alters quantum criticality and universal thermodynamics of the gas. In particular, it drives the Tonks-Girardeau (TG) gas from non-mutual Fermi statistics to mutual statistics or to a more exclusive super-TG gas. This novel feature is further discussed in terms of the breathing mode which is experimentally measurable.