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

## Abstract

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.

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## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.

Journal peer review information: Nature Physics thanks Luca Pezzè and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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## Acknowledgements

The authors acknowledge insightful discussions with A. Daley, N. Defenu, A. Elben, M. Gärttner, P. Hauke and M. Piani. This work has been supported by ERC consolidator grant 725636, DFG grant JO970/1-1, the Heidelberg Center for Quantum Dynamics and is part of the DFG Collaborative Research Centre SFB 1225 (ISOQUANT). A.B. acknowledges funding from the International Max-Planck Research School (IMPRS-QD). P.M.P. acknowledges funding from the European Union’s Horizon 2020 programme under Marie Sklodowska-Curie grant agreement no. 706487 and from the Daimler and Benz Foundation.

## Author information

A.B., V.M.K., G.Z., S.J. and P.M.P. conceived the experiment. A.B., V.M.K., J.H.B., R.K. and P.M.P. performed the experiment and, together with L.P., performed data analysis, developed theory and wrote the manuscript. All authors contributed to discussions about the experiment and manuscript. S.J. and P.M.P. supervised the project.

### Competing interests

The authors declare no competing interests.

Correspondence to Philipp M. Preiss.

## Electronic supplementary material

1. ### Supplementary Information

Supplementary text, Supplementary Figures 1–5 and Supplementary references.