Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Atomic clock transitions in silicon-based spin qubits

Subjects

A Corrigendum to this article was published on 07 November 2013

This article has been updated

Abstract

A major challenge in using spins in the solid state for quantum technologies is protecting them from sources of decoherence. This is particularly important in nanodevices where the proximity of material interfaces, and their associated defects, can play a limiting role. Spin decoherence can be addressed to varying degrees by improving material purity or isotopic composition1,2, for example, or active error correction methods such as dynamic decoupling3,4 (or even combinations of the two5,6). However, a powerful method applied to trapped ions in the context of atomic clocks7,8 is the use of particular spin transitions that are inherently robust to external perturbations. Here, we show that such ‘clock transitions’ can be observed for electron spins in the solid state, in particular using bismuth donors in silicon9,10. This leads to dramatic enhancements in the electron spin coherence time, exceeding seconds. We find that electron spin qubits based on clock transitions become less sensitive to the local magnetic environment, including the presence of 29Si nuclear spins as found in natural silicon. We expect the use of such clock transitions will be of additional significance for donor spins in nanodevices11, mitigating the effects of magnetic or electric field noise arising from nearby interfaces and gates.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: ESR-type clock transitions (CTs) of Si:Bi.
Figure 2: Decoherence mechanisms of Bi donors in Si and their dependence on df/dB.
Figure 3: Hahn echo decay at the clock transition.

Change history

  • 26 September 2013

    In the version of this Letter originally published, ref. 21 should have read: Morley. G. W. et al. Quantum control of hybrid nuclear-electronic qubits. Nature Mater. 12, 103–107 (2013). This error has been corrected in the HTML and PDF versions of the Letter.

References

  1. Tyryshkin, A. M. et al. Electron spin coherence exceeding seconds in high-purity silicon. Nature Mater. 11, 143–147 (2012).

    CAS  Article  Google Scholar 

  2. Balasubramanian, G. et al. Ultralong spin coherence time in isotopically engineered diamond. Nature Mater. 8, 383–387 (2009).

    CAS  Article  Google Scholar 

  3. Viola, L. & Lloyd, S. Dynamical suppression of decoherence in two-state quantum systems. Phys. Rev. A 58, 2733–2744 (1998).

    CAS  Article  Google Scholar 

  4. Bluhm, H. et al. Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 µs. Nature Phys. 7, 109–113 (2011).

    CAS  Article  Google Scholar 

  5. Steger, M. et al. Quantum information storage for over 180 s using donor spins in a 28Si ‘semiconductor vacuum’. Science 336, 1280–1283 (2012).

    CAS  Article  Google Scholar 

  6. Maurer, P. C. et al. Room-temperature quantum bit memory exceeding one second. Science 336, 1283–1286 (2012).

    CAS  Article  Google Scholar 

  7. Bollinger, J., Prestage, J., Itano, W. & Wineland, D. Laser-cooled-atomic frequency standard. Phys. Rev. Lett. 54, 1000–1003 (1985).

    CAS  Article  Google Scholar 

  8. Fisk, P. T. H. et al. Very high Q microwave spectroscopy on trapped 171Yb+ ions: application as a frequency standard. IEEE Trans. Instrum. Meas. 44, 113–116 (1995).

    CAS  Article  Google Scholar 

  9. George, R. E. et al. Electron spin coherence and electron nuclear double resonance of Bi donors in natural Si. Phys. Rev. Lett. 105, 067601 (2010).

    Article  Google Scholar 

  10. Morley, G. W. et al. The initialization and manipulation of quantum information stored in silicon by bismuth dopants. Nature Mater. 9, 725–729 (2010).

    CAS  Article  Google Scholar 

  11. Pla, J. J. et al. A single-atom electron spin qubit in silicon. Nature 489, 541–545 (2012).

    CAS  Article  Google Scholar 

  12. Haljan, P. et al. Entanglement of trapped-ion clock states. Phys. Rev. A 72, 062316 (2005).

    Article  Google Scholar 

  13. Langer, C. et al. Long-lived qubit memory using atomic ions. Phys. Rev. Lett. 95, 060502 (2005).

    CAS  Article  Google Scholar 

  14. Schenkel, T. et al. Electrical activation and electron spin coherence of ultralow dose antimony implants in silicon. Appl. Phys. Lett. 88, 112101 (2006).

    Article  Google Scholar 

  15. Vion, D. et al. Manipulating the quantum state of an electrical circuit. Science 296, 886–889 (2002).

    CAS  Article  Google Scholar 

  16. Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).

    Article  Google Scholar 

  17. Longdell, J., Alexander, A. & Sellars, M. Characterization of the hyperfine interaction in europium-doped yttrium orthosilicate and europium chloride hexahydrate. Phys. Rev. B 74, 195101 (2006).

    Article  Google Scholar 

  18. McAuslan, D., Bartholomew, J., Sellars, M. & Longdell, J. Reducing decoherence in optical and spin transitions in rare-earth-metal-ion-doped materials. Phys. Rev. A 85, 032339 (2012).

    Article  Google Scholar 

  19. Wolfowicz, G. et al. Decoherence mechanisms of 209Bi donor electron spins in isotopically pure 28Si. Phys. Rev. B 86, 245301 (2012).

    Article  Google Scholar 

  20. Mohammady, M. H., Morley, G. W., Nazir, A. & Monteiro, T. S. Analysis of quantum coherence in bismuth-doped silicon: a system of strongly coupled spin qubits. Phys. Rev. B 85, 094404 (2012).

    Article  Google Scholar 

  21. Morley, G. W. et al. Quantum control of hybrid nuclear–electronic qubits. Nature Mater. 12, 103–107 (2013).

    CAS  Article  Google Scholar 

  22. Schuster, D. et al. High-cooperativity coupling of electron–spin ensembles to superconducting cavities. Phys. Rev. Lett. 105, 140501 (2010).

    CAS  Article  Google Scholar 

  23. Kubo, Y. et al. Storage and retrieval of a microwave field in a spin ensemble. Phys. Rev. A 85, 012333 (2012).

    Article  Google Scholar 

  24. Riemann, H., Abrosimov, N. & Noetzel, N. Doping of silicon crystals with Bi and other volatile elements by the pedestal growth technique. ECS Trans. 3, 53–59 (2006).

    CAS  Article  Google Scholar 

  25. Feher, G. Electron spin resonance experiments on donors in silicon. I. Electronic structure of donors by the electron nuclear double resonance technique. Phys. Rev. 114, 1219–1244 (1959).

    CAS  Article  Google Scholar 

  26. Salikhov, K., Dzuba, S. & Raitsimring, A. The theory of electron spin-echo signal decay resulting from dipole–dipole interactions between paramagnetic centers in solids. J. Magn. Reson. 42, 255276 (1981).

    Google Scholar 

  27. Schweiger, A. & Jeschke, G. Principles of Pulse Electron Paramagnetic Resonance Ch. 8.1.5, 216 (Oxford Univ. Press, 2001).

    Google Scholar 

  28. Balian, S. J. et al. Measuring central-spin interaction with a spin-bath by pulsed ENDOR: towards suppression of spin diffusion decoherence. Phys. Rev. B 86, 104428 (2012).

    Article  Google Scholar 

  29. Witzel, W., Carroll, M., Morello, A., Cywinski, L. & Das Sarma, S. Electron spin decoherence in isotope-enriched silicon. Phys. Rev. Lett. 105, 187602 (2010).

    Article  Google Scholar 

  30. Fraval, E., Sellars, M. & Longdell, J. Dynamic decoherence control of a solid-state nuclear-quadrupole qubit. Phys. Rev. Lett. 95, 030506 (2005).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

The authors thank S. Simmons, T. Monteiro and S. Balian for discussions. This research is supported by the Engineering and Physical Sciences Research Council through the Materials World Network (EP/I035536/1) and a Doctoral Training Award, as well as by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007–2013)/ERC (grant agreement no. 279781). Work at Princeton was supported by the National Science Foundation through Materials World Network (DMR-1107606) and through the Princeton Materials Research Science and Engineering Center (DMR-0819860) and the National Security Agency/Laboratory for Physical Sciences through Lawrence Berkley National Laboratory (6970579). J.J.L.M. is supported by the Royal Society.

Author information

Authors and Affiliations

Authors

Contributions

G.W., A.M.T., R.E.G., S.A.L., M.L.W.T. and J.J.L.M. conceived and designed the experiments. G.W. and A.M.T. performed the experiments. G.W., A.M.T., S.A.L. and J.J.L.M. analysed the data. H.R., N.V.A., P.B., H-J.P. and M.L.W.T. provided materials. G.W. and J.J.L.M. wrote the paper with input from all authors.

Corresponding authors

Correspondence to Gary Wolfowicz or John J. L. Morton.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary Information (PDF 1572 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Wolfowicz, G., Tyryshkin, A., George, R. et al. Atomic clock transitions in silicon-based spin qubits. Nature Nanotech 8, 561–564 (2013). https://doi.org/10.1038/nnano.2013.117

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nnano.2013.117

Further reading

Search

Quick links

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research