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

Karen V. Kheruntsyan, Dimitri M. Gangardt, P. D. Drummond, Gora V. Shlyapnikov

Published Jan 1, 2005• 1 citation

Abstract

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.

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