Low dimensional quantum gases

In 2005, we have made further progress in the studies of atom correlations in one-dimensional (1D) Bose gases [1]. We have calculated the density profiles and density correlation functions of a harmonically trapped (nonuniform) 1D Bose gas, 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 have also computed the average two-particle correlation g(2) which characterizes the bulk properties of the sample, and found that it can be well approximated by the more readily calculated local pair correlation in the trap center, g(2)(0, 0).