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Bulletin of the American Physical Society

Calculation of $g_2$ for a Finite Temperature Gas

A. Bezett, E. Toth, Blair Blakie

Published Jun 9, 2007• 0 citations
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Abstract

We present a finite temperature theoretical model for calculating correlations in degenerate Bose gas that systematically includes the effects of harmonic trap confinement, interactions between the particles and is valid in the critical regime. This model is based on the non-pertubative Projected Gross Pitaevskii (PGPE) formalism 6 , which includes the dynamics of the low lying modes of the thermal cloud, coupled to a semiclassical description of high the energy modes. We discuss progress on the application of this formalism to the experiment of Schellekens et al. 5 where a direct measurement of correlation length is made

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Calculation of g2g_2g2​ for a Finite Temperature Gas
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We develop a computationally tractable method for calculating correlation functions of the finite temperature trapped Bose gas that includes the effects of sss-wave interactions. Our approach uses a classical field method to model the low energy modes and treats the high energy modes using a Hartree-Fock description. We present results of first and second order correlation functions, in position and momentum space, for an experimentally realistic system in the temperature range of 0.6Tc0.6{T}_{c}0.6Tc​ to 1.0Tc1.0{T}_{c}1.0Tc​. We also characterize the spatial coherence length of the system. Our theory should be applicable in the critical region where experiments are now able to measure first and second order correlations.
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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.