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.

  • Letter
  • Published:

Spin state tomography of optically injected electrons in a semiconductor

Nature volume 457, pages 702–705 (2009)Cite this article

Abstract

Spin is a fundamental property of electrons, with an important role in information storage1,2,3,4. For spin-based quantum information technology, preparation and read-out of the electron spin state are essential functions5,6,7,8,9,10,11,12,13. Coherence of the spin state is a manifestation of its quantum nature, so both the preparation and read-out should be spin-coherent. However, the traditional spin measurement technique based on Kerr rotation, which measures spin population using the rotation of the reflected light polarization that is due to the magneto-optical Kerr effect, requires an extra step of spin manipulation or precession to infer the spin coherence14,15,16,17,18,19,20. Here we describe a technique that generalizes the traditional Kerr rotation approach to enable us to measure the electron spin coherence directly without needing to manipulate the spin dynamics, which allows for a spin projection measurement on an arbitrary set of basis states. Because this technique enables spin state tomography, we call it tomographic Kerr rotation. We demonstrate that the polarization coherence of light is transferred to the spin coherence of electrons, and confirm this by applying the tomographic Kerr rotation method to semiconductor quantum wells with precessing and non-precessing electrons. Spin state transfer and tomography offers a tool for performing basis-independent preparation and read-out of a spin quantum state in a solid.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Figure 1: Operating principle of spin coherence transfer and tomography.
Figure 2: Spin state tomogram of precessing electrons.
Figure 3: Spin coherence transfer in the spin degenerate case.

Similar content being viewed by others

References

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

    Article  ADS  CAS  Google Scholar 

  2. 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 

  3. Awschalom, D. D., Loss, D. & Samarth, N. (eds) Semiconductor Spintronics and Quantum Computation (Springer, 2002)

    Book  Google Scholar 

  4. Hanson, R., Kouwenhoven, L. P., Petta, J. R., Tarucha, S. & Vandersypen, L. M. K. Spins in few-electron quantum dots. Rev. Mod. Phys. 79, 1217–1265 (2007)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  6. Young, R. et al. Single electron-spin memory with a semiconductor quantum dot. New J. Phys. 9, 365 (2007)

    Article  ADS  Google Scholar 

  7. Kikkawa, J. M. & Awschalom, D. D. Lateral drag of spin coherence in gallium arsenide. Nature 397, 139–141 (1999)

    Article  ADS  CAS  Google Scholar 

  8. 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)

    Article  ADS  CAS  Google Scholar 

  9. Berezovsky, J. et al. Nondestructive optical measurements of a single electron spin in a quantum dot. Science 314, 1916–1920 (2006)

    Article  ADS  CAS  Google Scholar 

  10. Atature, M., Dreiser, J., Badolato, A. & Imamoglu, A. Observation of Faraday rotation from a single confined spin. Nature Phys. 3, 101–105 (2007)

    Article  ADS  CAS  Google Scholar 

  11. Mikkelsen, M. H. et al. Optically detected coherent spin dynamics of a single electron in a quantum dot. Nature Phys. 3, 770–773 (2007)

    Article  ADS  CAS  Google Scholar 

  12. Kosaka, H. et al. Single photoelectron trapping, storage, and detection in a field effect transistor. Phys. Rev. B 67, 045104 (2003)

    Article  ADS  Google Scholar 

  13. Kosaka, H., Mitsumori, Y., Rikitake, Y. & Imamura, H. Polarization transfer from photon to electron spin in g factor engineered quantum wells. Appl. Phys. Lett. 90, 113511 (2007)

    Article  ADS  Google Scholar 

  14. Baumberg, J. J., Awschalom, D. D., Samarth, N., Luo, H. & Furdyna, J. K. Spin beats and dynamical magnetization in quantum structures. Phys. Rev. Lett. 72, 717–720 (1994)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  16. Gupta, J. A., Knobel, R., Samarth, N. & Awschalom, D. D. Ultrafast manipulation of electron spin coherence. Science 292, 2458–2461 (2001)

    Article  ADS  CAS  Google Scholar 

  17. 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 

  18. 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 

  19. Wu, Y. et al. Density matrix tomography through sequential coherent optical rotations of an exciton qubit in a single quantum dot. Phys. Rev. Lett. 96, 087402 (2006)

    Article  ADS  Google Scholar 

  20. Wu, Y. et al. Selective optical control of electron spin coherence in singly charged GaAs-Al0. 3Ga0. 7As quantum dots. Phys. Rev. Lett. 96, 097402 (2007)

    Article  ADS  Google Scholar 

  21. Meier, F. & Zakharchenya, B. P. (eds) Optical Orientation Ch. 2 (Elsevier, 1984)

    Google Scholar 

  22. Vrijen, R. & Yablonovitch, E. A spin-coherent semiconductor photodetector for quantum communication. Physica E 10, 569–575 (2001)

    Article  ADS  CAS  Google Scholar 

  23. Kosaka, H. et al. Coherent transfer of light polarization to electron spins in a semiconductor. Phys. Rev. Lett. 100, 096602 (2008)

    Article  ADS  Google Scholar 

  24. Xu, X. et al. Fast spin state initialization in a singly charged InAs-GaAs quantum dot by optical cooling. Phys. Rev. Lett. 99, 097401 (2007)

    Article  ADS  Google Scholar 

  25. Marie, X. et al. Hole spin quantum beats in quantum-well structures. Phys. Rev. B 60, 5811–5817 (1999)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the Strategic Information and Communications R & D Promotion Program (SCOPE No. 41402001) of the Ministry of Internal Affairs and Communications in Japan.

Author information

Authors and Affiliations

  1. Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, Sendai 980-8577, Japan

    Hideo Kosaka, Takahiro Inagaki, Yasuyoshi Mitsumori & Keiichi Edamatsu

  2. CREST-JST, Saitama 332-0012, Japan

    Hideo Kosaka, Yoshiaki Rikitake, Hiroshi Imamura & Yasuyoshi Mitsumori

  3. Department of Information Engineering, Sendai National College of Technology, Sendai 989-3128, Japan

    Yoshiaki Rikitake

  4. Nanotechnology Research Institute, AIST, Tsukuba 305-8568, Japan ,

    Hiroshi Imamura

Authors
  1. Hideo Kosaka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Takahiro Inagaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yoshiaki Rikitake
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hiroshi Imamura
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yasuyoshi Mitsumori
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Keiichi Edamatsu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hideo Kosaka.

Supplementary information

Supplementary Information

This file contains Supplementary Data (PDF 122 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kosaka, H., Inagaki, T., Rikitake, Y. et al. Spin state tomography of optically injected electrons in a semiconductor. Nature 457, 702–705 (2009). https://doi.org/10.1038/nature07729

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature07729

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

Advanced 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