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:

Single-atom gating of quantum-state superpositions

Nature Physics volume 4, pages 454–458 (2008)Cite this article

Abstract

The ultimate miniaturization of electronic devices will probably require local and coherent control of single electronic wavefunctions. Wavefunctions exist within both physical real space and an abstract state space with a simple geometric interpretation: this state space—or Hilbert space—is spanned by mutually orthogonal state vectors corresponding to the quantized degrees of freedom of the real-space system. Measurement of superpositions is akin to accessing the direction of a vector in Hilbert space, determining an angle of rotation equivalent to quantum phase. Here, we show that an individual atom inside a designed quantum corral1 can control this angle, producing arbitrary coherent superpositions of spatial quantum states. Using scanning tunnelling microscopy and nanostructures assembled atom-by-atom2, we demonstrate how single spins and quantum mirages3 can be harnessed to image the superposition of two electronic states. We also present a straightforward method to determine the atom path enacting phase rotations between any desired state vectors. A single atom thus becomes a real-space handle for an abstract Hilbert space, providing a simple technique for coherent quantum-state manipulation at the spatial limit of condensed matter.

Access through your institution
Buy or subscribe

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

Access options

Access through your institution

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

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

Figure 1: Designed degeneracy in a quantum corral.
Figure 2: Single-atom gating and read-out of quantum-state superpositions.
Figure 3: Complete indexing of two-dimensional Hilbert spaces.
Figure 4: Superposition coefficient maps.

Similar content being viewed by others

References

  1. Crommie, M. F., Lutz, C. P. & Eigler, D. M. Confinement of electrons to quantum corrals on a metal surface. Science 262, 218–220 (1993).

    Article  ADS  Google Scholar 

  2. Stroscio, J. A. & Eigler, D. M. Atomic and molecular manipulation with the scanning tunneling microscope. Science 254, 1319–1326 (1991).

    Article  ADS  Google Scholar 

  3. Manoharan, H. C., Lutz, C. P. & Eigler, D. M. Quantum mirages formed by coherent projection of electronic structure. Nature 403, 512–515 (2000).

    Article  ADS  Google Scholar 

  4. Kouwenhoven, L. & Marcus, C. Quantum dots. Phys. World 11, 35–39 (1998).

    Article  Google Scholar 

  5. Tans, S. J. et al. Individual single-wall carbon nanotubes as quantum wires. Nature 386, 474–477 (1997).

    Article  ADS  Google Scholar 

  6. Woodside, M. T. & McEuen, P. L. Scanned probe imaging of single-electron charge states in nanotube quantum dots. Science 296, 1098–1101 (2002).

    Article  ADS  Google Scholar 

  7. Eigler, D. M. et al. Information transport and computation in nanometre-scale structures. Phil. Trans. R. Soc. Lond. A 362, 1135–1147 (2004).

    Article  ADS  Google Scholar 

  8. Braun, K. F. & Rieder, K. H. Engineering electronic lifetimes in artificial atomic structures. Phys. Rev. Lett. 88, 096801 (2002).

    Article  ADS  Google Scholar 

  9. Rossi, E. & Morr, D. K. Spatially dependent Kondo effect in quantum corrals. Phys. Rev. Lett. 97, 236602–236604 (2006).

    Article  ADS  Google Scholar 

  10. Walls, J. D. & Heller, E. J. Spin–orbit coupling induced interference in quantum corrals. Nano Lett. 7, 3377–3382 (2007).

    Article  ADS  Google Scholar 

  11. Duan, L. M., Cirac, J. I. & Zoller, P. Geometric manipulation of trapped ions for quantum computation. Science 292, 1695–1697 (2001).

    Article  ADS  Google Scholar 

  12. Zanardi, P. & Lloyd, S. Topological protection and quantum noiseless subsystems. Phys. Rev. Lett. 90, 067902 (2003).

    Article  ADS  Google Scholar 

  13. Crommie, M. F., Lutz, C. P. & Eigler, D. M. Imaging standing waves in a two-dimensional electron gas. Nature 363, 524–527 (1993).

    Article  ADS  Google Scholar 

  14. Tersoff, J. & Hamann, D. R. Theory of the scanning tunneling microscope. Phys. Rev. B 31, 805–813 (1985).

    Article  ADS  Google Scholar 

  15. Aligia, A. A. Many-body theory of the quantum mirage. Phys. Rev. B 64, 121102 (2001).

    Article  ADS  Google Scholar 

  16. Porras, D., Fernández-Rossier, J. & Tejedor, C. Microscopic theory for quantum mirages in quantum corrals. Phys. Rev. B 63, 155406 (2001).

    Article  ADS  Google Scholar 

  17. Schmid, M. & Kampf, A. P. Mirages, anti-mirages, and further surprises in quantum corrals with non-magnetic impurities. Ann. Phys. (Leipzig) 12, 463–470 (2003).

    Article  ADS  Google Scholar 

  18. Aligia, A. A. & Lobos, A. M. Mirages and many-body effects in quantum corrals. J. Phys. Condens. Matter 17, S1095–S1122 (2005).

    Article  ADS  Google Scholar 

  19. Heller, E. J., Crommie, M. F., Lutz, C. P. & Eigler, D. M. Scattering and absorption of surface electron waves in quantum corrals. Nature 369, 464–466 (1994).

    Article  ADS  Google Scholar 

  20. Fiete, G. A. et al. Scattering theory of Kondo mirages and observation of single Kondo atom phase shift. Phys. Rev. Lett. 86, 2392–2395 (2001).

    Article  ADS  Google Scholar 

  21. Fiete, G. A. & Heller, E. J. Colloquium: Theory of quantum corrals and quantum mirages. Rev. Mod. Phys. 75, 933–948 (2003).

    Article  ADS  Google Scholar 

  22. Agam, O. & Schiller, A. Projecting the Kondo effect: Theory of the quantum mirage. Phys. Rev. Lett. 86, 484 (2001).

    Article  ADS  Google Scholar 

  23. Correa, A., Hallberg, K. & Balseiro, C. A. Mirages and enhanced magnetic interactions in quantum corrals. Europhys. Lett. 58, 899 (2002).

    Article  ADS  Google Scholar 

  24. Rahachou, A. I. & Zozoulenko, I. V. Elastic scattering of surface electron waves in quantum corrals: Importance of the shape of the adatom potential. Phys. Rev. B 70, 233409 (2004).

    Article  ADS  Google Scholar 

  25. Knorr, N., Schneider, M. A., Diekhoner, L., Wahl, P. & Kern, K. Kondo effect of single Co adatoms on Cu surfaces. Phys. Rev. Lett. 88, 096804 (2002).

    Article  ADS  Google Scholar 

  26. Lin, C. Y., Castro Neto, A. H. & Jones, B. A. Microscopic theory of the single impurity surface Kondo resonance. Phys. Rev. B 71, 35417 (2005).

    Article  ADS  Google Scholar 

  27. Eriksson, M. A. et al. Cryogenic scanning probe characterization of semiconductor nanostructures. Appl. Phys. Lett. 69, 671–673 (1996).

    Article  ADS  Google Scholar 

  28. Topinka, M. A. et al. Imaging coherent electron flow from a quantum point contact. Science 289, 2323–2326 (2000).

    Article  ADS  Google Scholar 

  29. Fallahi, P. et al. Imaging a single-electron quantum dot. Nano Lett. 5, 223–226 (2005).

    Article  ADS  Google Scholar 

  30. Kuhl, U., Persson, E., Barth, M. & Stöckmann, H.-J. Mixing of wavefunctions in rectangular microwave billiards. Eur. Phys. J. B 17, 253–259 (2000).

    Article  ADS  Google Scholar 

  31. Gokirmak, A., Wu, D.-H., Bridgewater, J. S. A. & Anlage, S. M. Scanned perturbation technique for imaging electromagnetic standing wave patterns of microwave cavities. Rev. Sci. Instrum. 69, 3410–3417 (1998).

    Article  ADS  Google Scholar 

  32. Crampin, S. Electron states in quantum corrals. Phil. Trans. R. Soc. Lond. A 362, 1149–1161 (2004).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the US Office of Naval Research, the US National Science Foundation, the US Department of Energy, the Research Corporation and the Stanford-IBM Center for Probing the Nanoscale. We acknowledge the US NDSEG program (C.R.M.) and the Alfred P. Sloan Foundation (H.C.M.) for fellowship support during this project. We thank D.-H. Lee, B. Sundaram, A. Bernevig, D. Haldane and D. Eigler for discussions and W. Mar for technical assistance.

Author information

Authors and Affiliations

  1. Department of Physics, Stanford University, Stanford, California 94305, USA

    Christopher R. Moon & Hari C. Manoharan

  2. IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, USA

    Christopher P. Lutz

Authors
  1. Christopher R. Moon
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Christopher P. Lutz
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Hari C. Manoharan
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Hari C. Manoharan.

Supplementary information

Supplementary Information

Supplementary Figures 1–2 (PDF 201 kb)

Supplementary Information

Supplementary Movie 1 (MOV 7599 kb)

Supplementary Information

Supplementary Movie 2 (MOV 4850 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moon, C., Lutz, C. & Manoharan, H. Single-atom gating of quantum-state superpositions. Nature Phys 4, 454–458 (2008). https://doi.org/10.1038/nphys930

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys930

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