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Measuring entanglement entropy in a quantum many-body system

Nature volume 528, pages 77–83 (2015)Cite this article

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Abstract

Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.

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Figure 1: Bipartite entanglement and partial measurements.
Figure 2: Measurement of quantum purity with many-body bosonic interference of quantum twins.
Figure 3: Many-body interference to probe entanglement in optical lattices.
Figure 4: Entanglement in the ground state of the Bose–Hubbard model.
Figure 5: Rényi mutual information in the ground state.
Figure 6: Entanglement dynamics in a quench.

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Acknowledgements

We thank D. Abanin, J. I. Cirac, M. Cramer, A. Daley, A. DelMaestro, E. Demler, M. Endres, S. Gopalakrishnan, M. Headrick, A. Kaufman, M. Knap, T. Monz, A. Pal, H. Pichler, S. Sachdev, B. Swingle, P. Zoller, and M. Zwierlein for useful discussions. This work was supported by grants from the Gordon and Betty Moore Foundations EPiQS Initiative (grant GBMF3795), the NSF through the Center for Ultracold Atoms, the Army Research Office with funding from the DARPA OLE programme and a MURI programme, an Air Force Office of Scientific Research MURI programme, and an NSF Graduate Research Fellowship (to M.R.).

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Authors and Affiliations

  1. Department of Physics, Harvard University, Cambridge, 02138, Massachusetts, USA

    Rajibul Islam, Ruichao Ma, Philipp M. Preiss, M. Eric Tai, Alexander Lukin, Matthew Rispoli & Markus Greiner

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  1. Rajibul Islam
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All authors contributed to the construction and execution of the experiments, data analysis and the writing of the manuscript.

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Correspondence to Markus Greiner.

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Islam, R., Ma, R., Preiss, P. et al. Measuring entanglement entropy in a quantum many-body system. Nature 528, 77–83 (2015). https://doi.org/10.1038/nature15750

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