Testing quantum correlations in a confined atomic cloud by the scattering of fast atoms

We suggest measuring the one-particle density matrix of a trapped ultracold atomic cloud by the scattering of 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.