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.

  • Article
  • Published:

Driven coherent oscillations of a single electron spin in a quantum dot

Abstract

The ability to control the quantum state of a single electron spin in a quantum dot is at the heart of recent developments towards a scalable spin-based quantum computer. In combination with the recently demonstrated controlled exchange gate between two neighbouring spins, driven coherent single spin rotations would permit universal quantum operations. Here, we report the experimental realization of single electron spin rotations in a double quantum dot. First, we apply a continuous-wave oscillating magnetic field, generated on-chip, and observe electron spin resonance in spin-dependent transport measurements through the two dots. Next, we coherently control the quantum state of the electron spin by applying short bursts of the oscillating magnetic field and observe about eight oscillations of the spin state (so-called Rabi oscillations) during a microsecond burst. These results demonstrate the feasibility of operating single-electron spins in a quantum dot as quantum bits.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Device and ESR detection scheme.
Figure 2: ESR spin state spectroscopy.
Figure 3: The control cycle for coherent manipulation of the electron spin.
Figure 4: Coherent spin rotations.
Figure 5: Time evolution of the spin states.

Similar content being viewed by others

References

  1. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000)

    MATH  Google Scholar 

  2. Shor, P. W. in Proc. 35th Annu. Symp. on the Foundations of Computer Science (ed. Goldwasser, S.) 124–134 (IEEE Computer Society Press, Los Alamitos, California, 1994)

    Book  Google Scholar 

  3. Zoller, P. et al. Quantum information processing and communication, Strategic report on current status, visions and goals for research in Europe. Eur. Phys. J. D 36, 203–228 (2005)

    Article  ADS  CAS  Google Scholar 

  4. DiVincenzo, D. P. Quantum computation. Science 270, 255–261 (1995)

    Article  ADS  MathSciNet  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  6. Austing, D. G., Honda, T., Muraki, K., Tokura, Y. & Tarucha, S. Quantum dot molecules. Phys. B Cond. Matter 249–251, 206–209 (1998)

    Article  ADS  Google Scholar 

  7. Ciorga, M. et al. Addition spectrum of a lateral dot from Coulomb and spin-blockade spectroscopy. Phys. Rev. B 61, R16315 (2000)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Bayer, M. et al. Coupling and entangling of quantum states in quantum dot molecules. Science 291, 451–453 (2001)

    Article  ADS  CAS  Google Scholar 

  10. Atature, M. et al. Quantum-dot spin-state preparation with near-unity fidelity. Science 312, 551–553 (2006)

    Article  ADS  Google Scholar 

  11. Hanson, R. et al. Zeeman energy and spin relaxation in a one-electron quantum dot. Phys. Rev. Lett. 91, 196802 (2003)

    Article  ADS  CAS  Google Scholar 

  12. 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)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  14. Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005)

    Article  ADS  CAS  Google Scholar 

  15. Schleser, R. et al. Time-resolved detection of individual electrons in a quantum dot. Appl. Phys. Lett. 85, 2005–2007 (2004)

    Article  ADS  CAS  Google Scholar 

  16. Vandersypen, L. M. K. et al. Real-time detection of single-electron tunneling using a quantum point contact. Appl. Phys. Lett. 85, 4394–4396 (2004)

    Article  ADS  CAS  Google Scholar 

  17. Lu, W., Ji, Z. Q., Pfeiffer, L., West, K. W. & Rimberg, A. J. Real-time detection of electron tunnelling in a quantum dot. Nature 423, 422–425 (2003)

    Article  ADS  CAS  Google Scholar 

  18. Hanson, R. et al. Single-shot readout of electron spin states in a quantum dot using spin-dependent tunnel rates. Phys. Rev. Lett. 94, 196802 (2005)

    Article  ADS  CAS  Google Scholar 

  19. Dutt, M. V. G. et al. Stimulated and spontaneous optical generation of electron spin coherence in charged GaAs quantum dots. Phys. Rev. Lett. 94, 227403 (2005)

    Article  ADS  Google Scholar 

  20. Greilich, A. et al. Optical control of spin coherence in singly charged (In,Ga)As/GaAs quantum dots. Phys. Rev. Lett. 96, 227401 (2006)

    Article  ADS  CAS  Google Scholar 

  21. Poole, C. P. Electron Spin Resonance 2nd edn (Wiley, New York, 1983)

    Google Scholar 

  22. Xiao, M., Martin, I., Yablonovitch, E. & Jiang, H. W. Electrical detection of the spin resonance of a single electron in a silicon field-effect transistor. Nature 430, 435–439 (2004)

    Article  ADS  CAS  Google Scholar 

  23. Jelezko, F., Gaebel, T., Popa, I., Gruber, A. & Wrachtrup, J. Observation of coherent oscillations in a single electron spin. Phys. Rev. Lett. 92, 076401 (2004)

    Article  ADS  CAS  Google Scholar 

  24. Rugar, D., Budakian, R., Mamin, H. J. & Chui, B. W. Single spin detection by magnetic resonance force microscopy. Nature 430, 329–332 (2004)

    Article  ADS  CAS  Google Scholar 

  25. Engel, H. A. & Loss, D. Detection of single spin decoherence in a quantum dot via charge currents. Phys. Rev. Lett. 86, 4648–4651 (2001)

    Article  ADS  CAS  Google Scholar 

  26. Imamoglu, A. et al. Quantum information processing using quantum dot spins and cavity QED. Phys. Rev. Lett. 83, 4204–4207 (1999)

    Article  ADS  CAS  Google Scholar 

  27. Kato, Y., Myers, R. C., Gossard, A. C. & Awschalom, D. D. Coherent spin manipulation without magnetic fields in strained semiconductors. Nature 427, 50–53 (2003)

    Article  ADS  Google Scholar 

  28. Golovach, V. N., Borhani, M. & Loss, D. Electric dipole induced spin resonance in quantum dots. Preprint at www.arXiv.org/cond-mat/0601674 (2006).

  29. Tokura, Y., Van der Wiel, W. G., Obata, T. & Tarucha, S. Coherent single electron spin control in a slanting Zeeman field. Phys. Rev. Lett. 96, 047202 (2006)

    Article  ADS  Google Scholar 

  30. 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)

    Article  ADS  CAS  Google Scholar 

  31. Engel, H. A. et al. Measurement efficiency and n-shot readout of spin qubits. Phys. Rev. Lett. 93, 106804 (2004)

    Article  ADS  Google Scholar 

  32. Blaauboer, M. & DiVincenzo, D. P. Detecting entanglement using a double-quantum-dot turnstile. Phys. Rev. Lett. 95, 160402 (2005)

    Article  ADS  CAS  Google Scholar 

  33. Engel, H. A. & Loss, D. Fermionic bell-state analyzer for spin qubits. Science 309, 586–588 (2005)

    Article  ADS  CAS  Google Scholar 

  34. 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. Phys. Rev. B 72, 165308 (2005)

    Article  ADS  Google Scholar 

  35. Johnson, A. C. et al. Triplet-singlet spin relaxation via nuclei in a double quantum dot. Nature 435, 925–928 (2005)

    Article  ADS  CAS  Google Scholar 

  36. Koppens, F. H. L. et al. Control and detection of singlet-triplet mixing in a random nuclear field. Science 309, 1346–1350 (2005)

    Article  ADS  CAS  Google Scholar 

  37. Jouravlev, O. N. & Nazarov, Y. V. Electron transport in a double quantum dot governed by a nuclear magnetic field. Phys. Rev. Lett. 96, 176804 (2006)

    Article  ADS  Google Scholar 

  38. Potok, R. M. et al. Spin and polarized current from Coulomb blockaded quantum dots. Phys. Rev. Lett. 91, 016802 (2003)

    Article  ADS  CAS  Google Scholar 

  39. Willems van Beveren, L. H. W. et al. Spin filling of a quantum dot derived from excited-state spectroscopy. New J. Phys. 7, 182 (2005)

    Article  ADS  Google Scholar 

  40. Kogan, A. et al. Measurements of Kondo and spin splitting in single-electron transistors. Phys. Rev. Lett. 93, 166602 (2004)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  44. Vandersypen, L. M. K. & Chuang, I. L. NMR techniques for quantum control and computation. Rev. Mod. Phys. 76, 1037–1069 (2004)

    Article  ADS  Google Scholar 

  45. Klauser, D., Coish, W. A. & Loss, D. Nuclear spin state narrowing via gate-controlled Rabi oscillations in a double quantum dot. Phys. Rev. Lett. 96, 176804 (2006)

    Article  Google Scholar 

  46. Giedke, G., Taylor, J. M., D'Alessandro, D., Lukin, D. & Imamoglu, A. Quantum measurement of the nuclear spin polarization in quantum dots. Preprint at www.arXiv.org/quant-ph/0508144 (2005).

  47. Stepanenko, D., Burkard, G., Giedke, G. & Imamoglu, A. Enhancement of electron spin coherence by optical preparation of nuclear spins. Phys. Rev. Lett. 96, 136401 (2006)

    Article  ADS  Google Scholar 

  48. Salis, G. et al. Electrical control of spin coherence in semiconductor nanostructures. Nature 414, 619–622 (2001)

    Article  ADS  CAS  Google Scholar 

  49. Jiang, H. W. & Yablonovitch, E. Gate-controlled electron spin resonance in GaAs/AlxGa1-xAs heterostructures. Phys. Rev. B 64, 041307 (2001)

    Article  ADS  Google Scholar 

  50. Holleitner, A. W., Blick, R. H. & Eberl, K. Fabrication of coupled quantum dots for multiport access. Appl. Phys. Lett. 82, 1887–1889 (2003)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank W. Coish, J. Elzerman, D. Klauser, A. Lupascu, D. Loss and in particular J. Folk for discussions; R. Schouten, B. van der Enden and W. den Braver for technical assistance; The International Research Centre for Telecommunication and Radar at the Delft University of Technology for assistance with the stripline simulations. Supported by the Dutch Organization for Fundamental Research on Matter (FOM), the Netherlands Organization for Scientific Research (NWO) and the Defense Advanced Research Projects Agency Quantum Information Science and Technology programme.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to F. H. L. Koppens or L. M. K. Vandersypen.

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 Notes

This file contains Supplementary Figures, Supplementary Discussion, Supplementary Methods and additional references. (PDF 1549 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koppens, F., Buizert, C., Tielrooij, K. et al. Driven coherent oscillations of a single electron spin in a quantum dot. Nature 442, 766–771 (2006). https://doi.org/10.1038/nature05065

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature05065

This article is cited by

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