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:

High-fidelity quantum driving

Nature Physics volume 8, pages 147–152 (2012)Cite this article

Abstract

Accurately controlling a quantum system is a fundamental requirement in quantum information processing and the coherent manipulation of molecular systems. The ultimate goal in quantum control is to prepare a desired state with the highest fidelity allowed by the available resources and the experimental constraints. Here we experimentally implement two optimal high-fidelity control protocols using a two-level quantum system comprising Bose–Einstein condensates in optical lattices. The first is a short-cut protocol that reaches the maximum quantum-transformation speed compatible with the Heisenberg uncertainty principle. In the opposite limit, we realize the recently proposed transitionless superadiabatic protocols in which the system follows the instantaneous adiabatic ground state nearly perfectly. We demonstrate that superadiabatic protocols are extremely robust against control parameter variations, making them useful for practical applications.

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: Schematic of a two-level quantum system and experimental realization.
Figure 2: Comparison between the driving protocols.
Figure 3: Superadiabatic dynamics in a two-level system.
Figure 4: Robustness and speed of the superadiabatic tangent protocol.

Similar content being viewed by others

References

  1. Walmsley, I. & Rabitz, H. Quantum physics under control. Phys. Today 56, 43–49 (August, 2003).

    Article  Google Scholar 

  2. Rice, S. A. & Zhao, M. Optical Control of Molecular Dynamics (Wiley, 2000).

    Google Scholar 

  3. Hänsch, T. W. Nobel Lecture: Passion for precision. Rev. Mod. Phys. 78, 1297–1309 (2006).

    Article  ADS  Google Scholar 

  4. Nielsen, M. & Chuang, I. Quantum Computation and Quantum Communication (Cambridge Univ. Press, 2000).

    MATH  Google Scholar 

  5. Wieman, C. E., Pritchard, D. E. & Wineland, D. J. Atom cooling, trapping, and quantum manipulation. Rev. Mod. Phys. 71, S253–S262 (1999).

    Article  Google Scholar 

  6. Poot, M. & van der Zant, H. S. J. Mechanical systems in the quantum regime. Preprint at http://arxiv.org/abs/1106.2060 (2011).

  7. Farhi, E. et al. A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292, 472–475 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  8. Berry, M. V. Two-state quantum asymptotics. Ann. NY Acad. Sci. 755, 303–317 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  9. Landau, L. On the theory of transfer of energy at collisions II. Phys. Z. Sow. 2, 46 (1932).

    Google Scholar 

  10. Zener, C. Non-adiabatic crossing of energy levels. Proc. R. Soc. A 137, 696–702 (1932).

    Article  ADS  Google Scholar 

  11. Caneva, T. et al. Optimal control at the quantum speed limit. Phys. Rev. Lett. 103, 240501 (2009).

    Article  ADS  Google Scholar 

  12. Peres, A. Quantum Theory: Concepts and Methods (Kluwer, 1993).

    MATH  Google Scholar 

  13. Levitin, L. B. Physical limitations of rate, depth, and minimum energy in information processing. Int. J. Theor. Phys. 21, 299–309 (1982).

    Article  Google Scholar 

  14. Bhattacharyya, K. Quantum decay and the Mandelstam–Tamm-energy inequality. J. Phys. A 16, 2993–2996 (1983).

    Article  ADS  Google Scholar 

  15. Giovannetti, V., Lloyd, S. & Maccone, L. Quantum limits to dynamical evolution. Phys. Rev. A 67, 052109 (2003).

    Article  ADS  Google Scholar 

  16. Demirplak, M. & Rice, S. A. Adiabatic population transfer with control fields. J. Phys. Chem. A 107, 9937–9945 (2003).

    Article  Google Scholar 

  17. Demirplak, M. & Rice, S. A. On the consistency, extremal, and global properties of counterdiabatic fields. J. Chem. Phys. 129, 154111 (2008).

    Article  ADS  Google Scholar 

  18. Berry, M. V. Transitionless quantum driving. J. Phys. A 42, 365303 (2009).

    Article  MathSciNet  Google Scholar 

  19. Lim, R. & Berry, M. V. Superadiabatic tracking of quantum evolution. J. Phys. A 24, 3255–3264 (1991).

    Article  ADS  Google Scholar 

  20. Morsch, O. & Oberthaler, M. Dynamics of Bose–Einstein condensates in optical lattices. Rev. Mod. Phys. 78, 179–215 (2006).

    Article  ADS  Google Scholar 

  21. Zenesini, A. et al. Time-resolved measurement of Landau–Zener tunneling in periodic potentials. Phys. Rev. Lett. 103, 090403 (2009).

    Article  ADS  Google Scholar 

  22. Tayebirad, G. et al. Time-resolved measurement of Landau–Zener tunneling in different bases. Phys. Rev. A 82, 013633 (2010).

    Article  ADS  Google Scholar 

  23. Carlini, A., Hosoya, A., Koike, T. & Okudaira, Y. Time-optimal quantum evolution. Phys. Rev. Lett. 96, 060503 (2006).

    Article  ADS  Google Scholar 

  24. Levitt, M. H. in Encyclopedia of Nuclear Magnetic Resonance (eds Grant, D. M. & Harris, R. K.) (Wiley, 1996).

    Google Scholar 

  25. Mellish, A. S., Duffy, G., McKenzie, C., Geursen, R. & Wilson, A. C. Nonadiabatic loading of a Bose–Einstein condensate into the ground state of an optical lattice. Phys. Rev. A 68, 051601(R) (2003).

    Article  ADS  Google Scholar 

  26. Roland, J. & Cerf, N. J. Quantum search by local adiabatic evolution. Phys. Rev. A 65, 042308 (2002).

    Article  ADS  Google Scholar 

  27. Chen, X., Lizuain, I., Ruschhaupt, A., Guéry-Odelin, D. & Muga, J. G. Shortcut to adiabatic passage in two- and three-level atoms. Phys. Rev. Lett. 105, 123003 (2010).

    Article  ADS  Google Scholar 

  28. Singer, K. et al. Trapped ions as quantum bits: Essential numerical tools. Rev. Mod. Phys. 82, 2609–2632 (2010).

    Article  ADS  Google Scholar 

  29. Wunderlich, Chr. et al. Robust state preparation of a single trapped ion by adiabatic passage. J. Mod. Opt. 54, 1541–1549 (2007).

    Article  ADS  Google Scholar 

  30. Sørensen, J. L. et al. Efficient coherent internal state transfer in trapped ions using stimulated Raman adiabatic passage. New J. Phys. 8, 261 (2006).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by CNISM through the Progetto Innesco 2007, the EU through grant No. 225187-NAMEQUAM and the collaboration between the University of Pisa and the University Paris Sud-11. R.F. and V.G. acknowledge support by MIUR through FIRB-IDEAS Project No. RBID08B3FM and by the E.U. through grants No. 234970-NANOCTM and No. 248629-SOLID. The authors thank D. Guéry-Odelin and M. Holthaus for fruitful discussions.

Author information

Authors and Affiliations

  1. INO-CNR, Largo Pontecorvo 3, 56127 Pisa, Italy

    Mark G. Bason, Matthieu Viteau, Paul Huillery, Ennio Arimondo, Donatella Ciampini & Oliver Morsch

  2. Dipartimento di Fisica ‘E. Fermi’, CNISM UdR, Università di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy

    Nicola Malossi, Ennio Arimondo & Donatella Ciampini

  3. Laboratoire Aimé Cotton, Univ. Paris-Sud 11, Campus d’Orsay Bat. 505, 91405 Orsay, France

    Paul Huillery

  4. Dipartimento di Fisica ‘E. Fermi’, Università di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy

    Ennio Arimondo, Donatella Ciampini & Riccardo Mannella

  5. NEST, Scuola Normale Superiore, and Istituto di Nanoscienze—CNR, 56126 Pisa, Italy

    Rosario Fazio & Vittorio Giovannetti

Authors
  1. Mark G. Bason
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matthieu Viteau
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nicola Malossi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Paul Huillery
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ennio Arimondo
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Donatella Ciampini
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Rosario Fazio
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Vittorio Giovannetti
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Riccardo Mannella
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Oliver Morsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

M.G.B., M.V., N.M., P.H. and D.C. carried out the experiments; V.G. and R.F. developed the composite pulse protocol; O.M. and R.M. developed the superadiabatic protocols and performed the numerical simulations; E.A., R.F. and O.M. wrote the paper. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Oliver Morsch.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bason, M., Viteau, M., Malossi, N. et al. High-fidelity quantum driving. Nature Phys 8, 147–152 (2012). https://doi.org/10.1038/nphys2170

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys2170

This article is cited by

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