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# Coherent electrical control of a single high-spin nucleus in silicon

## Abstract

Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, for example, in chemistry, medicine, materials science and mining. Nuclear spins also featured in early proposals for solid-state quantum computers1 and demonstrations of quantum search2 and factoring3 algorithms. Scaling up such concepts requires controlling individual nuclei, which can be detected when coupled to an electron4,5,6. However, the need to address the nuclei via oscillating magnetic fields complicates their integration in multi-spin nanoscale devices, because the field cannot be localized or screened. Control via electric fields would resolve this problem, but previous methods7,8,9 relied on transducing electric signals into magnetic fields via the electron–nuclear hyperfine interaction, which severely affects nuclear coherence. Here we demonstrate the coherent quantum control of a single 123Sb (spin-7/2) nucleus using localized electric fields produced within a silicon nanoelectronic device. The method exploits an idea proposed in 196110 but not previously realized experimentally with a single nucleus. Our results are quantitatively supported by a microscopic theoretical model that reveals how the purely electrical modulation of the nuclear electric quadrupole interaction results in coherent nuclear spin transitions that are uniquely addressable owing to lattice strain. The spin dephasing time, 0.1 seconds, is orders of magnitude longer than those obtained by methods that require a coupled electron spin to achieve electrical driving. These results show that high-spin quadrupolar nuclei could be deployed as chaotic models, strain sensors and hybrid spin-mechanical quantum systems using all-electrical controls. Integrating electrically controllable nuclei with quantum dots11,12 could pave the way to scalable, nuclear- and electron-spin-based quantum computers in silicon that operate without the need for oscillating magnetic fields.

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## Data availability

All data necessary to evaluate the claims of this paper are provided in the main manuscript and Supplementary Information. Raw data files, data analysis code and simulation code are available at https://doi.org/10.26190/5de9c295a8821.

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## Acknowledgements

We thank T. Botzem and J. T. Muhonen for discussions. The research was funded by the Australian Research Council Discovery Projects (grants DP150101863 and DP180100969) and the Australian Department of Industry, Innovation and Science (grant AUSMURI00002). V.M. acknowledges support from a Niels Stensen Fellowship. M.A.I.J. and H.R.F. acknowledge the support of Australian Government Research Training Program Scholarships. J.J.P. is supported by an Australian Research Council Discovery Early Career Research Award (DE190101397). A.M. was supported by a Weston Visiting Professorship at the Weizmann Institute of Science during part of the writing of this manuscript. We acknowledge support from the Australian National Fabrication Facility (ANFF), and from the laboratory of R. Elliman at the Australian National University for the ion implantation facilities. A.D.B. was supported by the Laboratory Directed Research and Development programme at Sandia National Laboratories, Project 213048. Sandia National Laboratories is a multi-missions laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the National Nuclear Security Administration of the US Department of Energy under contract DE-NA0003525. The views expressed in this manuscript do not necessarily represent the views of the US Department of Energy or the US Government. K.M.I. acknowledges support from Grant-in-Aid for Scientific Research by MEXT.

## Author information

Authors

### Contributions

S.A. and M.A.I.J. performed the measurements under the supervision of V.M., A.L. and A.M., with the assistance of V.S., M.T.M. and H.R.F.; S.A. and M.A.I.J. analysed the data under the supervision of V.M. and A.M., with the assistance of H.R.F., V.S., J.J.P. and A.L.; A.D.B., S.A., V.M., B.J. and A.M. developed a microscopic theory supported by finite-element modelling by B.J. and electronic structure calculations by A.D.B.; F.E.H. partially fabricated the device under the supervision of A.S.D., on isotopically enriched material supplied by K.M.I. and M.T.M. subsequently fabricated the aluminium gate structures under the supervision of V.M. and A.M.; J.C.M. designed and performed the 123Sb ion implantation; S.A., V.M., B.J., M.A.I.J., A.D.B., H.R.F. and A.M. wrote the manuscript and Supplementary Information, with input from all co-authors; A.M. initiated and supervised the research programme.

### Corresponding author

Correspondence to Andrea Morello.

## Ethics declarations

### Competing interests

S.A., V.M. and A.M. have submitted a patent application that describes the use of electrically controlled high-spin nuclei for quantum information processing (AU2018900665A).

## Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 ESR spectrum in a magnetic field of B0 = 1.496 T.

a, ESR frequencies for eight nuclear states. The average difference between successive ESR transition frequencies (black line) gives a hyperfine interaction of A = 96.5 MHz, substantially lower than the bulk value of 101.52 MHz. One possible cause for this deviation is strain, which is known to modify the hyperfine interaction39. b, ESR spectral lines. For each nuclear state, the nucleus was initialized at the start of each microwave sweep, and adiabatic ESR pulses with 1 MHz frequency deviation were applied to excite the electron.

### Extended Data Fig. 2 NER Rabi oscillations on resonance.

a, b, Nuclear Rabi oscillations measured with varying NER pulse duration, tNER, while the pulse amplitude was fixed at $${V}_{{\rm{gate}}}^{{\rm{RF}}}=20\,{\rm{mV}}$$ for ΔmI = ±1 transitions (a) and $${V}_{{\rm{gate}}}^{{\rm{RF}}}=40\,{\rm{mV}}$$ for ΔmI = ±2 transitions (b). Black lines are non-decaying sinusoidal fits to the data, and error bars show the 68% confidence level.

### Extended Data Fig. 3 NER spectral line shifts for varying d.c. gate voltage.

a, b, The spectral lines of all ΔmI = ±1 transitions (a) and ΔmI = ±2 (b) transitions are measured while the d.c. gate voltage bias $$\Delta {V}_{{\rm{DC}}}^{{\rm{gate}}}$$ is varied (columns) during the NER pulse. We note that this change in $${V}_{{\rm{DC}}}^{{\rm{gate}}}$$ is applied on top of large gate voltages, of the order of 0.5 V, which are necessary to electrostatically tune the device to enable its operation. The varying $$\Delta {V}_{{\rm{DC}}}^{{\rm{gate}}}$$ modifies the quadrupole interaction via the LQSE (see Supplementary Information section 7 for details), resulting in shifts of the resonance peaks. A single fit to the resonance frequency shifts of all ΔmI = ±1 and ΔmI = ±2 transitions (solid lines) gives an estimate of the gate-dependent quadrupole shift of $$\partial {f}_{{\rm{Q}}}/\partial {V}_{{\rm{DC}}}^{{\rm{gate}}}=9.9(3)\,{\rm{Hz}}\,{{\rm{mV}}}^{-1}$$. From the top to the bottom transition, the drive strengths $${V}_{{\rm{RF}}}^{{\rm{gate}}}$$ are 20 mV, 20 mV, 25 mV, 25 mV, 20 mV and 25 mV for ΔmI = ±1 (a) and 30 mV, 30 mV, 40 mV, 40 mV, 40 mV and 40 mV for ΔmI = ±2 (b). Error bars show the 68% confidence level.

### Extended Data Fig. 4 Position triangulation of the 123Sb donor.

The colour map shows the probability of finding the donor in a certain location. a, b, Probability density function found using a least-squares estimation comparing simulated gate-to-donor coupling strengths with the experimentally observed strengths (see Supplementary Information section 7A for details, including the locations of the donor gates DFR, DFL and DBR). To improve on the low resolving power of the triangulation method in the y direction, the triangulation probability density function is multiplied with the donor implantation probability density function (see Supplementary Information section 7A for details). This has little effect laterally, but greatly confines the likely depth range of the donor within the range expected on the basis of the donor implantation parameters. The most likely donor position, indicated by a cross, is at the lateral location (x, z) = (13 nm, 8 nm) at a depth of y = −5 nm. The probability density functions are normalized over the model volume and are integrated over the out-of-plane axis in both panels, specifically, P(xz) = ∫P(r)dy and P(yz) = ∫P(r)dx. The contour lines mark the 68% and 95% confidence regions.

## Supplementary information

### Supplementary Information

This file contains Supplementary Materials, Sections S1 – S8, which include Supplementary Figures S1 – S16, and 46 Supplementary References. It provides experimental and theoretical details on the electrical control of a nuclear spin in silicon.

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### Cite this article

Asaad, S., Mourik, V., Joecker, B. et al. Coherent electrical control of a single high-spin nucleus in silicon. Nature 579, 205–209 (2020). https://doi.org/10.1038/s41586-020-2057-7

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