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Spatially resolving valley quantum interference of a donor in silicon

Abstract

Electron and nuclear spins of donor ensembles in isotopically pure silicon experience a vacuum-like environment, giving them extraordinary coherence. However, in contrast to a real vacuum, electrons in silicon occupy quantum superpositions of valleys in momentum space. Addressable single-qubit and two-qubit operations in silicon require that qubits are placed near interfaces, modifying the valley degrees of freedom associated with these quantum superpositions and strongly influencing qubit relaxation and exchange processes. Yet to date, spectroscopic measurements have only probed wavefunctions indirectly, preventing direct experimental access to valley population, donor position and environment. Here we directly probe the probability density of single quantum states of individual subsurface donors, in real space and reciprocal space, using scanning tunnelling spectroscopy. We directly observe quantum mechanical valley interference patterns associated with linear superpositions of valleys in the donor ground state. The valley population is found to be within 5% of a bulk donor when 2.85 ± 0.45 nm from the interface, indicating that valley-perturbation-induced enhancement of spin relaxation will be negligible for depths greater than 3 nm. The observed valley interference will render two-qubit exchange gates sensitive to atomic-scale variations in positions of subsurface donors. Moreover, these results will also be of interest for emerging schemes proposing to encode information directly in valley polarization.

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Figure 1: Spatial measurement of single quantum states of a subsurface donor.
Figure 2: Valley interference of a single quantum state in reciprocal space.
Figure 3: Valley population.
Figure 4: Valley interference of a single quantum state in real space.

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Acknowledgements

The authors would like to thank J. Verduijn for helpful discussions. This work is supported by the European Commission Future and Emerging Technologies Proactive Project MULTI (317707) and the ARC Centre of Excellence for Quantum Computation and Communication Technology (CE110001027), and in part by the US Army Research Office (W911NF-08-1-0527). This work is part of the research program of the Foundation for Fundamental Research on Matter (FOM), which is part of the Netherlands Organization for Scientific Research (NWO). S.R. acknowledges a Future Fellowship (FT100100589). M.Y.S. acknowledges a Laureate Fellowship. The use of nanoHUB.org computational resources operated by the Network for Computational Nanotechnology funded by the US National Science Foundation under grant EEC-0228390 is gratefully acknowledged.

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J.S., J.A.M. and S.R. designed and conducted the experiments. R.R. performed the multi-million atom calculations. J.S., L.C.L.H. and S.R. made the key contributions to the Fourier analysis. All the authors contributed to analysis and writing the paper.

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Correspondence to S. Rogge.

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The authors declare no competing financial interests.

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Salfi, J., Mol, J., Rahman, R. et al. Spatially resolving valley quantum interference of a donor in silicon. Nature Mater 13, 605–610 (2014). https://doi.org/10.1038/nmat3941

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