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:

Manipulation of quantum paths for space–time characterization of attosecond pulses

Abstract

Attosecond extreme-ultraviolet pulses1 have a complex space–time structure2. However, at present, there is no method to observe this intricate detail; all measurements of the duration of attosecond pulses are, to some extent, spatially averaged1,3,4,5. A technique for determining the full space–time structure would enable a detailed study of the highly nonlinear processes that generate these pulses as a function of intensity without averaging6,7. Here, we introduce and demonstrate an all-optical method to measure the space–time characteristics of an isolated attosecond pulse. Our measurements show that intensity-dependent phase and quantum-path interference both play a key role in determining the pulse structure. In the generating medium, the attosecond pulse is strongly modulated in space and time. Propagation modifies but does not erase this modulation. Quantum-path interference of the single-atom response, previously obscured by spatial and temporal averaging, may enable measuring the laser-field-driven ion dynamics with sub-cycle resolution.

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: Illustration of the spatio-temporal measurement of an isolated attosecond pulse.
Figure 2: Spatio-temporal reconstruction of an isolated attosecond pulse.
Figure 3: Spatio-temporal snapshot of an isolated attosecond pulse.

Similar content being viewed by others

References

  1. Paul, P. M. et al. Observation of a train of attosecond pulses from high harmonic generation. Science 292, 1689–1692 (2001).

    Article  ADS  Google Scholar 

  2. Salières, P. et al. Feynman’s path-integral approach for intense-laser-atom interactions. Science 292, 902–905 (2001).

    Article  ADS  Google Scholar 

  3. Sansone, G. et al. Isolated single-cycle attosecond pulses. Science 314, 443–446 (2006).

    Article  ADS  Google Scholar 

  4. Kim, K. T. et al. Self-compression of attosecond high-order harmonic pulses. Phys. Rev. Lett. 99, 223904 (2007).

    Article  ADS  Google Scholar 

  5. Goulielmakis, E. et al. Single-cycle nonlinear optics. Science 320, 1614–1617 (2008).

    Article  ADS  Google Scholar 

  6. Zair, A. et al. Quantum path interferences in high-order harmonic generation. Phys. Rev. Lett. 100, 143902 (2008).

    Article  ADS  Google Scholar 

  7. Smirnova, O. et al. High harmonic interferometry of multi-electron dynamics in molecules. Nature 460, 972–977 (2009).

    Article  ADS  Google Scholar 

  8. Quéré, F., Itatani, J., Yudin, G. L. & Corkum, P. B. Attosecond spectral shearing interferometry. Phys. Rev. Lett. 90, 073902 (2003).

    Article  ADS  Google Scholar 

  9. Mairesse, Y. & Quéré, F. Frequency-resolved optical gating for complete reconstruction of attosecond bursts. Phys. Rev. A 71, 011401 (2005).

    Article  ADS  Google Scholar 

  10. Lee, D. G., Park, J. J., Sung, J. H. & Nam, C. H. Wave-front phase measurements of high-order harmonic beams by use of point-diffraction interferometry. Opt. Lett. 28, 480–482 (2003).

    Article  ADS  Google Scholar 

  11. Frumker, E., Paulus, G. G., Niikura, H., Villeneuve, D. M. & Corkum, P. B. Frequency-resolved high-harmonic wavefront characterization. Opt. Lett. 34, 3026–3028 (2009).

    Article  ADS  Google Scholar 

  12. Austin, D. R. et al. Lateral shearing interferometry of high-harmonic wavefronts. Opt. Lett. 36, 1746–1748 (2011).

    Article  ADS  Google Scholar 

  13. Chini, M., Gilbertson, S., Khan, S. D. & Chang, Z. Characterizing ultrabroadband attosecond lasers. Opt. Express 18, 13006–13016 (2010).

    Article  ADS  Google Scholar 

  14. Dudovich, N. et al. Measuring and controlling the birth of attosecond XUV pulses. Nature Phys. 2, 781–786 (2006).

    Article  ADS  Google Scholar 

  15. Doumy, G. et al. Attosecond synchronization of high-order harmonics from midinfrared drivers. Phys. Rev. Lett. 102, 093002 (2009).

    Article  ADS  Google Scholar 

  16. Dahlström, J. et al. Atomic and macroscopic measurements of attosecond pulse trains. Phys. Rev. A 80, 033836 (2009).

    Article  ADS  Google Scholar 

  17. Bertrand, J. B. et al. Ultrahigh-order wave mixing in noncollinear high harmonic generation. Phys. Rev. Lett. 106, 023001 (2011).

    Article  ADS  Google Scholar 

  18. Brugnera, L. et al. Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields. Phys. Rev. Lett. 107, 153902 (2011).

    Article  ADS  Google Scholar 

  19. Corkum, P. B. Plasma perspective on strong field multiphoton ionization. Phys. Rev. Lett. 71, 1994–1997 (1993).

    Article  ADS  Google Scholar 

  20. Lewenstein, M., Salières, P. & Ľ’Huillier, A. Phase of the atomic polarization in high-order harmonic generation. Phys. Rev. A 52, 4747–4754 (1995).

    Article  ADS  Google Scholar 

  21. Kane, D. J. & Trebino, R. Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating. IEEE Quant. Electron. 29, 571–579 (1993).

    Article  ADS  Google Scholar 

  22. Kane, D. J. Recent progress toward real-time measurement of ultrashort laser pulses. IEEE Quant. Electron. 35, 421–431 (1999).

    Article  ADS  Google Scholar 

  23. Trebino, R. Measuring the seemingly immeasurable. Nature Photon. 5, 189–192 (2011).

    Article  ADS  Google Scholar 

  24. Mairesse, Y. et al. Attosecond synchronization of high-harmonic soft x-rays. Science 302, 1540–1543 (2003).

    Article  ADS  Google Scholar 

  25. Smirnova, O. et al. Attosecond circular dichroism spectroscopy of polyatomic molecules. Phys. Rev. Lett. 102, 063601 (2009).

    Article  ADS  Google Scholar 

  26. Kienberger, R. et al. Atomic transient recorder. Nature 427, 817–821 (2004).

    Article  ADS  Google Scholar 

  27. Zair, A. et al. Molecular internal dynamics studied by quantum path interferences in high order harmonic generation. Preprint at http://arxiv.org/abs/1210.4814v1 (2012).

  28. Goulielmakis, E. et al. Real-time observation of valence electron motion. Nature 466, 739–743 (2010).

    Article  ADS  Google Scholar 

  29. Shiner, A. D. et al. Wavelength scaling of high harmonic generation efficiency. Phys. Rev. Lett. 103, 073902 (2009).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge the technical assistance of D. Crane and B. Avery. We also acknowledge financial support from NSERC, AFOSR and MURI Grant No. W911NF-07-1-0475. In addition, E.F. acknowledges support from the Marie Curie International Outgoing fellowship.

Author information

Authors and Affiliations

Authors

Contributions

K.T.K. and P.B.C. conceived the idea and designed the experiment. K.T.K., C.Z., A.D.S., S.E.K. and G.G. performed the experiment and collected the data. K.T.K. provided the theoretical analysis and analysed the experimental data. K.T.K., D.M.V. and P.B.C. prepared the initial manuscript. All authors contributed in writing the manuscript.

Corresponding author

Correspondence to P. B. Corkum.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 816 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, K., Zhang, C., Shiner, A. et al. Manipulation of quantum paths for space–time characterization of attosecond pulses. Nature Phys 9, 159–163 (2013). https://doi.org/10.1038/nphys2525

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1038/nphys2525

This article is cited by

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