Testing quantum correlations in a confined atomic cloud by scattering fast atoms: Direct and time reversed processes

TL;DR

This paper proposes a method to measure quantum correlations in ultracold atomic clouds by analyzing the scattering patterns of fast atoms, revealing the density matrix through differential cross-sections.

Contribution

It introduces a novel scattering technique to directly access the one-particle density matrix of trapped atomic clouds, including condensates with vortices or phase differences.

Findings

Fourier transform of the density matrix can be obtained from scattering data

Scattering processes reveal quantum correlations in ultracold gases

Method applicable to various condensate configurations

Abstract

We suggest measuring the one-particle density matrix of a trapped ultracold atomic cloud by scattering fast atoms in a pure momentum state off the cloud. The lowest-order probability for the process, resulting in a pair of outcoming fast atoms for each incoming one, as well as of its time reversed counterpart, turns out to be given by the Fourier transform of the density matrix. Accordingly, important information about quantum correlations can be deduced directly from the differential scattering cross-section of these processes. Several most interesting cases of scattering - from a single condensate containing a vortex, and from a split condensate characterized by some phase difference - are discussed.