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Witnessing quantum correlations in a nuclear ensemble via an electron spin qubit

Nature Physics volume 17, pages 1247–1253 (2021)Cite this article

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Abstract

A coherent ensemble of spins interfaced with a proxy qubit is an attractive platform to create many-body coherences and probe the regime of collective excitations. An electron spin qubit in a semiconductor quantum dot can act as such an interface to the dense nuclear spin ensemble within the quantum dot consisting of multiple high-spin atomic species. Earlier work has shown that the electron can relay properties of its nuclear environment through the statistics of its mean-field interaction with the total nuclear polarization, namely its mean and variance. Here, we demonstrate a method to probe the spin state of a nuclear ensemble that exploits its response to collective spin excitations, enabling a species-selective reconstruction beyond the mean field. For the accessible range of optically prepared mean fields, the reconstructed populations indicate that the ensemble is in a non-thermal, correlated nuclear state. The sum over reconstructed species-resolved polarizations exceeds the classical prediction threefold. This stark deviation follows from a spin ensemble that contains inter-particle coherences, and serves as an entanglement witness that confirms the formation of a dark many-body state.

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Fig. 1: Proxy qubit interface to spin states of a nuclear ensemble.
Fig. 2: Magnon sideband asymmetry.
Fig. 3: From sideband asymmetry to species-resolved spin populations.
Fig. 4: Fingerprint of a nuclear dark state.

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Data availability

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

Code availability

All code that was used in the analysis of data shown in this paper is available from the corresponding authors on reasonable request.

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Acknowledgements

We thank N. R. Cooper and D. M. Kara for helpful discussions. We acknowledge support from the US Office of Naval Research Global (N62909-19-1-2115), ERC PHOENICS (617985), EPSRC NQIT (EP/M013243/1), EU H2020 FET-Open project QLUSTER (DLV-862035) and the Royal Society (EA/181068). Samples were grown in the EPSRC National Epitaxy Facility. D.A.G. acknowledges a St John’s College Fellowship and C.L.G. a Royal Society Dorothy Hodgkin Fellowship.

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Author notes

  1. These authors contributed equally: Dorian A. Gangloff, Leon Zaporski, Jonathan H. Bodey.

Authors and Affiliations

  1. Cavendish Laboratory, University of Cambridge, Cambridge, UK

    Dorian A. Gangloff, Leon Zaporski, Jonathan H. Bodey, Clara Bachorz, Daniel M. Jackson, Gabriel Éthier-Majcher, Constantin Lang, Claire Le Gall & Mete Atatüre

  2. EPSRC National Epitaxy Facility, University of Sheffield, Sheffield, UK

    Edmund Clarke

  3. Université Côte d’Azur, CNRS, CRHEA, Valbonne, France

    Maxime Hugues

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Contributions

D.A.G., C.L.G. and M.A. conceived the experiments. J.H.B., C.B., D.A.G., G.E.-M. and C.L. carried out the experiments. J.H.B., L.Z. and D.A.G. performed the data analysis. L.Z. performed the theory and simulations with guidance from C.L.G. and D.A.G. E.C. and M.H. grew the material. All authors contributed to the discussion of the analysis and the results. All authors participated in preparing the manuscript.

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Correspondence to Claire Le Gall or Mete Atatüre.

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Peer review information Nature Physics thanks Hendrik Bluhm, Alex Greilich and Gloria Platero for their contribution to the peer review of this work.

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Supplementary Figs. 1–15, Discussion and Tables 1–3.

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Gangloff, D.A., Zaporski, L., Bodey, J.H. et al. Witnessing quantum correlations in a nuclear ensemble via an electron spin qubit. Nat. Phys. 17, 1247–1253 (2021). https://doi.org/10.1038/s41567-021-01344-7

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