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Phys. Rev. A 71, 053615 (2005) [17 pages]

Finite-temperature correlations and density profiles of an inhomogeneous interacting one-dimensional Bose gas

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K. V. Kheruntsyan1, D. M. Gangardt2,3, P. D. Drummond1, and G. V. Shlyapnikov2,4
1ARC Centre of Excellence for Quantum-Atom Optics, Department of Physics, University of Queensland, Brisbane, Queensland 4072, Australia
2Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris Sud, 91405 Orsay Cedex, France
3Laboratoire Kastler-Brossel, Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
4Van der Waals–Zeeman Institute, University of Amsterdam, Valckenierstraat 65/67, 1018 XE Amsterdam, The Netherlands

Received 18 February 2005; published 26 May 2005

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 that 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.


©2005 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevA.71.053615
DOI: 10.1103/PhysRevA.71.053615
PACS: 03.75.Hh, 05.30.Jp, 03.75.Pp

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