Machine-learning techniques such as artificial neural networks are currently revolutionizing many technological areas and have also proven successful in quantum physics applications1,2,3,4. Here, we employ an artificial neural network and deep-learning techniques to identify quantum phase transitions from single-shot experimental momentum-space density images of ultracold quantum gases and obtain results that were not feasible with conventional methods. We map out the complete two-dimensional topological phase diagram of the Haldane model5,6,7 and provide an improved characterization of the superfluid-to-Mott-insulator transition in an inhomogeneous Bose–Hubbard system8,9,10. Our work points the way to unravel complex phase diagrams of general experimental systems, where the Hamiltonian and the order parameters might not be known.
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We thank M. Lewenstein for stimulating our interest in machine learning of quantum phase transitions and A. Dauphin and J. Thywissen for useful discussions. The computational resources were provided by the PHYSnet-Rechenzentrum of Universität Hamburg and we thank B. Krause-Kyora and M. Stieben for technical support. We acknowledge financial support from the Deutsche Forschungsgemeinschaft via the Research Unit FOR 2414 and the Collaborative Research Center SFB 925. B.S.R. acknowledges financial support from the European Commission (Marie Skłodowska Curie Fellowship ISOTOP, grant number 652837).
The authors declare no competing interests.
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Rem, B.S., Käming, N., Tarnowski, M. et al. Identifying quantum phase transitions using artificial neural networks on experimental data. Nat. Phys. 15, 917–920 (2019). https://doi.org/10.1038/s41567-019-0554-0
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