Finite temperature correlations and density profiles of an inhomogeneous interacting 1D Bose gas

K. V. Kheruntsyan ¹, D. M. Gangardt ^2, 3, P. D. Drummond ¹, G. V. Shlyapnikov ^2, 4

Physical Review A: Atomic, Molecular and Optical Physics 71 (2005) 053615

We calculate the density profiles and density correlation functions of the one-dimensional Bose gas in a harmonic trap, using the exact finite-temperature solutions for the uniform case, and applying a local density approximation. The results are valid for a trapping potential which is slowly varying relative to a correlation length. They allow a direct experimental test of the transition from the weak coupling Gross-Pitaevskii regime to the strong coupling, \’fermionic\’ Tonks-Girardeau regime. We also calculate the average two-particle correlation which characterizes the bulk properties of the sample, and find that it can be well approximated by the value of the local pair correlation in the trap center.

• 1. ARC Centre of Excellence for Quantum-Atom Optics, Department of Physics,
  University of Queensland
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
  CNRS : UMR8626 – Université Paris XI – Paris Sud
• 3. Laboratoire Kastler Brossel (LKB (Lhomond)),
  CNRS : UMR8552 – Université Paris VI – Pierre et Marie Curie – Ecole Normale Supérieure de Paris – ENS Paris
• 4. Van der Waals–Zeeman Institute,
  University of Amsterdam