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Entanglement in a solid-state spin ensemble

Abstract

Entanglement is the quintessential quantum phenomenon. It is a necessary ingredient in most emerging quantum technologies, including quantum repeaters1, quantum information processing2 and the strongest forms of quantum cryptography3. Spin ensembles, such as those used in liquid-state nuclear magnetic resonance4,5, have been important for the development of quantum control methods. However, these demonstrations contain no entanglement and ultimately constitute classical simulations of quantum algorithms. Here we report the on-demand generation of entanglement between an ensemble of electron and nuclear spins in isotopically engineered, phosphorus-doped silicon. We combined high-field (3.4 T), low-temperature (2.9 K) electron spin resonance with hyperpolarization of the 31P nuclear spin to obtain an initial state of sufficient purity to create a non-classical, inseparable state. The state was verified using density matrix tomography based on geometric phase gates, and had a fidelity of 98% relative to the ideal state at this field and temperature. The entanglement operation was performed simultaneously, with high fidelity, on 1010 spin pairs; this fulfils one of the essential requirements for a silicon-based quantum information processor.

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Figure 1: Sequences for nuclear spin hyperpolarization and entanglement generation for this coupled S = 1/2, I = 1/2 spin system.
Figure 2: Electron and nuclear spin phase rotations reveal the off-diagonal elements of the density matrix.
Figure 3: Measuring an entangled density matrix.

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Acknowledgements

We thank J. Fitzsimons, S. Benjamin, A. Ardavan, A. Briggs and B. Lovett for discussions, and P. Höfer and Bruker BioSpin for support with instrumentation. Three-dimensional images were created using POV-RAY open-source software. We thank EPSRC for supporting work at Oxford through CAESR (EP/D048559/1) and the Oxford–Keio collaboration through the JST-EPSRC SIC programme (EP/H025952/1). Work at Keio has been supported by Grants-in-aid for Scientific Research by MEXT, FIRST by JSPS, Nanoquine and Keio GCOE. S.S. is supported by the Clarendon Fund, J.J.L.M. is supported by St John’s College, Oxford, and the Royal Society.

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S.S., R.M.B. and J.J.L.M. designed and performed the experiments and wrote the paper. H.R., N.V.A., P.B. and H.-J.P. grew the 28Si crystal. K.M.I and M.L.W.T. analysed and prepared the sample and discussed the experiments, results and manuscript.

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Correspondence to John J. L. Morton.

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The authors declare no competing financial interests.

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Simmons, S., Brown, R., Riemann, H. et al. Entanglement in a solid-state spin ensemble. Nature 470, 69–72 (2011). https://doi.org/10.1038/nature09696

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