Dynamic correlation functions in one-dimensional quasi-condensates

TL;DR

This paper computes static and dynamic single-particle correlation functions in 1D trapped Bose gases using hydrodynamic theory, linking theoretical predictions with experimental measurement techniques like Bragg scattering and Raman out-coupling.

Contribution

It provides a detailed calculation of correlation functions for 1D Bose gases and discusses how to experimentally measure these correlations, extending previous static results to dynamic cases.

Findings

Static correlation functions match previous theoretical results.

Momentum distribution can be obtained via Bragg scattering.

Dynamic correlations can be probed with Raman out-coupling experiments.

Abstract

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.