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.

Triplet–singlet spin relaxation via nuclei in a double quantum dot

Abstract

The spin of a confined electron, when oriented originally in some direction, will lose memory of that orientation after some time. Physical mechanisms leading to this relaxation of spin memory typically involve either coupling of the electron spin to its orbital motion or to nuclear spins1,2,3,4,5,6,7. Relaxation of confined electron spin has been previously measured only for Zeeman or exchange split spin states, where spin-orbit effects dominate relaxation8,9,10; spin flips due to nuclei have been observed in optical spectroscopy studies11. Using an isolated GaAs double quantum dot defined by electrostatic gates and direct time domain measurements, we investigate in detail spin relaxation for arbitrary splitting of spin states. Here we show that electron spin flips are dominated by nuclear interactions and are slowed by several orders of magnitude when a magnetic field of a few millitesla is applied. These results have significant implications for spin-based information processing12.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Spin-selective tunnelling in a double quantum dot.
Figure 2: Dependence of the occupancy of the (1,1) state on measurement time, t M , and external field, B.
Figure 3: Detailed measurements of blockaded (1,1) occupation.
Figure 4: Decay of (1,1) occupancy as a function of detuning at various magnetic fields.

References

  1. Khaetskii, A. V. & Nazarov, Y. V. Spin relaxation in semiconductor quantum dots. Phys. Rev. B 61, 12639–12642 (2000)

    ADS  CAS  Article  Google Scholar 

  2. Erlingsson, S. I., Nazarov, Y. V. & Fal'ko, V. I. Nucleus-mediated spin-flip transitions in GaAs quantum dots. Phys. Rev. B 64, 195306 (2001)

    ADS  Article  Google Scholar 

  3. Khaetskii, A. V., Loss, D. & Glazman, L. Electron spin decoherence in quantum dots due to interaction with nuclei. Phys. Rev. Lett. 88, 186802 (2002)

    ADS  Article  Google Scholar 

  4. Merkulov, I. A., Efros, Al. L. & Rosen, M. Electron spin relaxation by nuclei in semiconductor quantum dots. Phys. Rev. B 65, 205309 (2002)

    ADS  Article  Google Scholar 

  5. de Sousa, R. & Das Sarma, S. Theory of nuclear-induced spectral diffusion: Spin decoherence of phosphorus donors in Si and GaAs quantum dots. Phys. Rev. B 68, 115322 (2003)

    ADS  Article  Google Scholar 

  6. Coish, W. A. & Loss, D. Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics. Phys. Rev. B 70, 195340 (2004)

    ADS  Article  Google Scholar 

  7. Golovach, V. N., Khaetskii, A. & Loss, D. Phonon-induced decay of the electron spin in quantum dots. Phys. Rev. Lett. 93, 016601 (2004)

    ADS  Article  Google Scholar 

  8. Fujisawa, T., Austing, D. G., Tokura, Y., Hirayama, Y. & Tarucha, S. Allowed and forbidden transitions in artificial hydrogen and helium atoms. Nature 419, 278–281 (2002)

    ADS  CAS  Article  Google Scholar 

  9. Elzerman, J. M. et al. Single-shot readout of an individual electron spin in a quantum dot. Nature 430, 431–435 (2004)

    ADS  CAS  Article  Google Scholar 

  10. Kroutvar, M. et al. Optically programmable electron spin memory using semiconductor quantum dots. Nature 432, 81–84 (2004)

    ADS  CAS  Article  Google Scholar 

  11. Bracker, A. S. et al. Optical pumping of the electronic and nuclear spin of single charge-tunable quantum dots. Phys. Rev. Lett. 94, 047402 (2005)

    ADS  CAS  Article  Google Scholar 

  12. Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A. 57, 120–126 (1998)

    ADS  CAS  Article  Google Scholar 

  13. Wald, K. R., Kouwenhoven, L. P., McEuen, P. L., Van der Vaart, N. C. & Foxon, C. T. Local dynamic nuclear polarization using quantum point contacts. Phys. Rev. Lett. 73, 1011–1014 (1994)

    ADS  CAS  Article  Google Scholar 

  14. Salis, G. Optical manipulation of nuclear spin by a two-dimensional electron gas. Phys. Rev. Lett. 86, 2677–2680 (2001)

    ADS  CAS  Article  Google Scholar 

  15. Kumada, N., Muraki, K., Hashimoto, K. & Hirayama, Y. Spin degree of freedom in the ν = 1 bilayer electron system investigated via nuclear spin relaxation. Phys. Rev. Lett. 94, 096802 (2005)

    ADS  CAS  Article  Google Scholar 

  16. Smet, J. H. et al. Gate-voltage control of spin interactions between electrons and nuclei in a semiconductor. Nature 415, 281–286 (2002)

    ADS  CAS  Article  Google Scholar 

  17. Ono, K. & Tarucha, S. Nuclear-spin-induced oscillatory current in spin-blockaded quantum dots. Phys. Rev. Lett. 92, 256803 (2004)

    ADS  Article  Google Scholar 

  18. Bracker, A. S. et al. Optical pumping of the electronic and nuclear spin of single charge-tunable quantum dots. Phys. Rev. Lett. 94, 047402 (2005)

    ADS  CAS  Article  Google Scholar 

  19. Petta, J. R. et al. Pulsed gate measurements of the singlet-triplet relaxation time in a two-electron double quantum dot. Preprint at http://arxiv.org/abs/cond-mat/0412048 2004.

  20. Ashoori, R. C. et al. N-electron ground-state energies of a quantum-dot in a magnetic field. Phys. Rev. Lett. 71, 613–616 (1993)

    ADS  CAS  Article  Google Scholar 

  21. Field, M. et al. Measurements of Coulomb blockade with a non-invasive voltage probe. Phys. Rev. Lett. 70, 1311–1314 (1993)

    ADS  CAS  Article  Google Scholar 

  22. DiCarlo, L. et al. Differential charge sensing and charge delocalization in a tunable double quantum dot. Phys. Rev. Lett. 92, 226801 (2004)

    ADS  CAS  Article  Google Scholar 

  23. Elzerman, J. M. et al. Few-electron quantum dot circuit with integrated charge readout. Phys. Rev. B 67, 161308 (2003)

    ADS  Article  Google Scholar 

  24. Petta, J. R., Johnson, A. C., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Manipulation of a single charge in a double quantum dot. Phys. Rev. Lett. 93, 186802 (2004)

    ADS  CAS  Article  Google Scholar 

  25. Ono, K., Austing, D. G., Tokura, Y. & Tarucha, S. Current rectification by Pauli exclusion in a weakly coupled double quantum dot system. Science 297, 1313–1317 (2002)

    ADS  CAS  Article  Google Scholar 

  26. Johnson, A. C., Petta, J. R., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Singlet-triplet spin blockade and charge sensing in a few-electron double quantum dot. Preprint at http://arxiv.org/abs/cond-mat/0410679 2004.

  27. Paget, D., Lampel, G., Sapoval, B. & Safarov, V. I. Low field electron-nuclear spin coupling in gallium-arsenide under optical-pumping conditions. Phys. Rev. B 15, 5780–5796 (1977)

    ADS  CAS  Article  Google Scholar 

  28. Dobers, M., von Klitzing, K., Schneider, J., Weimann, G. & Ploog, K. Electrical detection of nuclear magnetic-resonance in GaAs-AlxGa1-xAs heterostructures. Phys. Rev. Lett. 61, 1650–1653 (1988)

    ADS  CAS  Article  Google Scholar 

  29. Fujisawa, T. et al. Spontaneous emission spectrum in double quantum dot devices. Science 282, 932–935 (1998)

    ADS  CAS  Article  Google Scholar 

  30. Das Sarma, S., de Sousa, R., Hu, X. & Koiller, B. Spin quantum computation in silicon nanostructures. Solid State Commun. 133, 737–746 (2005)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank H. A. Engel and P. Zoller for discussions. This work was supported by the ARO, the DARPA-QuIST programme, and the NSF, including the Harvard NSEC.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to C. M. Marcus.

Ethics declarations

Competing interests

Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.

Supplementary information

Supplementary Methods

This section contains three parts. The first describes technical details of our experiment, the second discusses the effective nuclear field, and the third expands the theory leading up to equations (1) and (2) in the main text. (PDF 181 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Johnson, A., Petta, J., Taylor, J. et al. Triplet–singlet spin relaxation via nuclei in a double quantum dot. Nature 435, 925–928 (2005). https://doi.org/10.1038/nature03815

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature03815

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing