Experimental characterization of two-particle entanglement through position and momentum correlations

Quantum simulation is a rapidly advancing tool for gaining 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 particles1. With ultracold atom experiments, one can prepare large samples of delocalized particles, but the same level of characterization has not yet been achieved2. 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 well3. As a first application, we use our technique to certify and quantify different types of entanglement4,5,6