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Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array

Nature volume 548, pages 7073 (03 August 2017) | Download Citation


Interacting fermions on a lattice can develop strong quantum correlations, which are the cause of the classical intractability of many exotic phases of matter1,2,3. Current efforts are directed towards the control of artificial quantum systems that can be made to emulate the underlying Fermi–Hubbard models4,5,6. Electrostatically confined conduction-band electrons define interacting quantum coherent spin and charge degrees of freedom that allow all-electrical initialization of low-entropy states and readily adhere to the Fermi–Hubbard Hamiltonian7,8,9,10,11,12,13,14,15,16,17. Until now, however, the substantial electrostatic disorder of the solid state has meant that only a few attempts at emulating Fermi–Hubbard physics on solid-state platforms have been made18,19. Here we show that for gate-defined quantum dots this disorder can be suppressed in a controlled manner. Using a semi-automated and scalable set of experimental tools, we homogeneously and independently set up the electron filling and nearest-neighbour tunnel coupling in a semiconductor quantum dot array so as to simulate a Fermi–Hubbard system. With this set-up, we realize a detailed characterization of the collective Coulomb blockade transition20, which is the finite-size analogue of the interaction-driven Mott metal-to-insulator transition1. As automation and device fabrication of semiconductor quantum dots continue to improve, the ideas presented here will enable the investigation of the physics of ever more complex many-body states using quantum dots.

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We acknowledge discussions with M. Veldhorst, A. F. Otte, R. Sensarma and the members of the Vandersypen group, sample fabrication by F. R. Braakman, set-up preparation by T. A. Baart and experimental assistance from M. Ammerlaan, J. Haanstra, R. Roeleveld, R. Schouten and R. Vermeulen. This work was supported by the Netherlands Organization of Scientific Research (NWO) VICI programme, the European Commission via the integrated project SIQS, the Japan Society for the Promotion of Science (JSPS) Postdoctoral Fellowship for Research Abroad, LPS-MPO-CMTC and the Swiss National Science Foundation.

Author information


  1. QuTech and Kavli Institute of Nanoscience, TU Delft, 2600 GA Delft, The Netherlands

    • T. Hensgens
    • , T. Fujita
    • , L. Janssen
    •  & L. M. K. Vandersypen
  2. Condensed Matter Theory Center and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA

    • Xiao Li
    •  & S. Das Sarma
  3. QuTech and Netherlands Organization for Applied Scientific Research (TNO), 2600 AD Delft, The Netherlands

    • C. J. Van Diepen
  4. Solid State Physics Laboratory, ETH Zürich, 8093 Zürich, Switzerland

    • C. Reichl
    •  & W. Wegscheider


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T.H., T.F., C.J.v.D. and L.J. performed the experiments and analysed the data, C.R. and W.W. grew the heterostructure, X.L. and S.D.S. performed the theoretical analyses with X.L. carrying out the numerical simulations, T.H., T.F., X.L., L.J., S.D.S. and L.M.K.V. contributed to the interpretation of the data, and T.H. wrote the manuscript (X.L. wrote part of the Methods), with comments from T.F., X.L., S.D.S. and L.M.K.V.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to L. M. K. Vandersypen.

Reviewer Information thanks S. Bose, S. Rogge, J. Salfi and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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