Tomography of correlation functions for ultracold atoms via time-of-flight images

TL;DR

This paper introduces a method to reconstruct single-particle correlation functions of ultracold atoms from time-of-flight images, enabling detailed analysis of quantum correlations in trapped atomic gases.

Contribution

It presents a novel technique to extract real- and momentum-space correlations from experimental images, advancing the quantitative study of quantum many-body systems.

Findings

Method successfully reconstructs correlation functions in simulations.

Feasibility demonstrated considering experimental resolution limits.

Applicable to quasi-one-dimensional ultracold atom systems.

Abstract

We propose to utilize density distributions from a series of time-of-flight images of an expanding cloud to reconstruct single-particle correlation functions of trapped ultra-cold atoms. In particular, we show how this technique can be used to detect off-diagonal correlations of atoms in a quasi-one-dimensional trap, where both real- and momentum- space correlations are extracted at a quantitative level. The feasibility of this method is analyzed with specific examples, taking into account finite temporal and spatial resolutions in experiments.