  Quantum simulation is a rapidly advancing tool to gain insight into complex
quantum states and their dynamics. Trapped ion systems have pioneered
deterministic state preparation and comprehensive state characterization,
operating on localized and thus distinguishable particles. With ultracold atom
experiments, one can prepare large samples of delocalized particles, but the
same level of characterization has not yet been achieved. Here, we present a
method to measure the positions and momenta of individual particles to obtain
correlations and coherences. We demonstrate this with deterministically
prepared samples of two interacting ultracold fermions in a coupled double
well. As a first application, we use our technique to certify and quantify
different types of entanglement.
