Detection and engineering of spatial mode entanglement with ultracold bosons

We outline an interferometric scheme for the detection of bimode and multimode spatial entanglement of finite-temperature interacting Bose gases. Whether entanglement is present in the gas depends on the existence of the single-particle reduced density matrix between different regions of space. We apply the scheme to the problem of a harmonically trapped repulsive boson pair and show that while entanglement is rapidly decreasing with temperature, a significant amount remains for all interaction strengths at zero temperature. Thus, by tuning the interaction parameter, the distribution of entanglement between many spatial modes can be modified