Dynamic correlation functions in one-dimensional quasi-condensates

We calculate the static and dynamic single-particle correlation functions in one-dimensional (1D) trapped Bose gases and discuss experimental measurements that can directly probe such correlation functions. Using a quantized hydrodynamic theory for the low energy excitations, we calculate both the static and dynamic single-particle correlation functions for a 1D Bose gas that is a phase-fluctuating quasi-condensate. For the static (equal-time) correlation function, our approximations and results are equivalent to those of Petrov, Shlyapnikov and Walraven. The Fourier transform of the static single-particle correlation function gives the momentum distribution, which can be measured using Doppler-sensitive Bragg scattering experiments on a highly elongated Bose gas. We show how a two-photon Raman out-coupling experiment can measure the characteristic features of the dynamic or time-dependent single-particle correlation function of a 1D Bose quasi-condensate.Comment: 19 pages, 4 figures; submitted to Phys. Rev.

Finite-temperature correlations in the one-dimensional trapped and untrapped Bose gases

We calculate the dynamic single-particle and many-particle correlation functions at non-zero temperature in one-dimensional trapped repulsive Bose gases. The decay for increasing distance between the points of these correlation functions is governed by a scaling exponent that has a universal expression in terms of observed quantities. This expression is valid in the weak-interaction Gross-Pitaevskii as well as in the strong-interaction Girardeau-Tonks limit, but the observed quantities involved depend on the interaction strength. The confining trap introduces a weak center-of-mass dependence in the scaling exponent. We also conjecture results for the density-density correlation function.Comment: 18 pages, Latex, Revtex