Skip to main content

Thank you for visiting 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.

Interpreting attoclock measurements of tunnelling times


Resolving in time the dynamics of light absorption by atoms and molecules, and the electronic rearrangement this induces, is among the most challenging goals of attosecond spectroscopy. The attoclock is an elegant approach to this problem, which encodes ionization times in the strong-field regime. However, the accurate reconstruction of these times from experimental data presents a formidable theoretical task. Here, we solve this problem by combining analytical theory with ab initio numerical simulations. We apply our theory to numerical attoclock experiments on the hydrogen atom to extract ionization time delays and analyse their nature. Strong-field ionization is often viewed as optical tunnelling through the barrier created by the field and the core potential. We show that, in the hydrogen atom, optical tunnelling is instantaneous. We also show how calibrating the attoclock using the hydrogen atom opens the way to identifying possible delays associated with multielectron dynamics during strong-field ionization.

This is a preview of subscription content

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: The attoclock set-up.
Figure 2: Comparison of numerical and analytical calculations.
Figure 3: Offset angles θ extracted from photoelectron spectra as a function of intensity.
Figure 4: Attoclock spectra for long and short range potentials.
Figure 5: Reconstruction of ionization times.


  1. 1

    Schultze, M. et al. Delay in photoemission. Science 328, 1658–1662 (2010).

    ADS  Article  Google Scholar 

  2. 2

    Shafir, D. et al. Resolving the time when an electron exits a tunnelling barrier. Nature 485, 343–346 (2012).

    ADS  Article  Google Scholar 

  3. 3

    Goulielmakis, E. et al. Real-time observation of valence electron motion. Nature 466, 700–702 (2010).

    Article  Google Scholar 

  4. 4

    Eckle, P. et al. Attosecond ionization and tunneling delay time measurements in helium. Science 322, 1525–1529 (2008).

    ADS  Article  Google Scholar 

  5. 5

    Eckle, P. et al. Attosecond angular streaking. Nature Phys. 4, 565–570 (2008).

    Article  Google Scholar 

  6. 6

    Pfeiffer, A. N. et al. Breakdown of the independent electron approximation in sequential double ionization. New J. Phys. 13, 093008 (2011).

    ADS  Article  Google Scholar 

  7. 7

    Pfeiffer, A. P. et al. Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms. Nature Phys. 8, 76–80 (2012).

    ADS  Article  Google Scholar 

  8. 8

    Breidbach, J. & Cederbaum, L. S. Universal attosecond response to the removal of an electron. Phys. Rev. Lett. 94, 033901 (2005).

    ADS  Article  Google Scholar 

  9. 9

    Sukiasyan, S., Ishikawa, K. L. & Ivanov, M. Attosecond cascades and time delays in one-electron photoionization. Phys. Rev. A 86, 033423 (2012).

    ADS  Article  Google Scholar 

  10. 10

    Kheifets, A. S. & Ivanov, I. A. Delay in atomic photoionization. Phys. Rev. Lett. 105, 233002 (2010).

    ADS  Article  Google Scholar 

  11. 11

    Moore, L. R., Lysaght, M. A., Parker, J. S., van der Hart, H. W. & Taylor, K. T. Time delay between photoemission from the 2p and 2s subshells of neon. Phys. Rev. A 84, 061404 (2011).

    ADS  Article  Google Scholar 

  12. 12

    Klunder, K. et al. Probing single-photon ionization on the attosecond time scale. Phys. Rev. Lett. 106, 143002 (2011).

    ADS  Article  Google Scholar 

  13. 13

    Ivanov, M. & Smirnova, O. How accurate is the attosecond streak camera? Phys. Rev. Lett. 107, 213605 (2011).

    ADS  Article  Google Scholar 

  14. 14

    Pazourek, R., Nagele, S. & Burgdorfer, J. Time-resolved photoemission on the attosecond scale: Opportunities and challenges. Faraday Discuss. 163, 353–376 (2013).

    ADS  Article  Google Scholar 

  15. 15

    Dahlström, J. M., L’Huillier, A. & Maquet, A. Introduction to attosecond delays in photoionization. J. Phys. B 45, 183001 (2012).

    Article  Google Scholar 

  16. 16

    Ivanov, I. & Kheifets, A. Strong-field ionization of He by elliptically polarized light in attoclock configuration. Phys. Rev. A 89, 021402 (2014).

    ADS  Article  Google Scholar 

  17. 17

    Boge, R. et al. Probing nonadiabatic effects in strong-field tunnel ionization. Phys. Rev. Lett. 111, 103003 (2013).

    ADS  Article  Google Scholar 

  18. 18

    Shvetsov-Shilovski, N. I., Dimitrovski, D. & Madsen, L. B. Ionization in elliptically polarized pulses: Multielectron polarization effects and asymmetry of photoelectron momentum distributions. Phys. Rev. A 85, 023428 (2012).

    ADS  Article  Google Scholar 

  19. 19

    Torlina, L. & Smirnova, O. Time-dependent analytical R-matrix approach for strong-field dynamics. I. One-electron systems. Phys. Rev. A 86, 043408 (2012).

    ADS  Article  Google Scholar 

  20. 20

    Torlina, L. et al. Time-dependent analytical R-matrix approach for strong-field dynamics. II. Many-electron systems. Phys. Rev. A 86, 043409 (2012).

    ADS  Article  Google Scholar 

  21. 21

    Kaushal, J. & Smirnova, O. Nonadiabatic Coulomb effects in strong-field ionization in circularly polarized laser fields. Phys. Rev. A 88, 013421 (2013).

    ADS  Article  Google Scholar 

  22. 22

    Torlina, L., Kaushal, J. & Smirnova, O. Time-resolving electron–core dynamics during strong-field ionization in circularly polarized fields. Phys. Rev. A 88, 053403 (2013).

    ADS  Article  Google Scholar 

  23. 23

    Muller, H. G. An efficient propagation scheme for the time-dependent Schrödinger equation in the velocity gauge. Laser Phys. 9, 138–148 (1999).

    Google Scholar 

  24. 24

    Tao, L. & Scrinzi, A. Photo-electron momentum spectra from minimal volumes: The time-dependent surface flux method. New J. Phys. 14, 013021 (2012).

    ADS  Article  Google Scholar 

  25. 25

    Landsman, A. et al. Ultrafast resolution of tunneling delay time. Optica 1, 343–349 (2014).

    ADS  Article  Google Scholar 

  26. 26

    Nubbemeyer, T., Gorling, K., Saenz, A., Eichmann, U. & Sandner, W. Strong-field tunneling without ionization. Phys. Rev. Lett. 101, 233001 (2008).

    ADS  Article  Google Scholar 

  27. 27

    Kamor, A., Mauger, F., Chandre, C. & Uzer, T. How key periodic orbits drive recollisions in a circularly polarized laser field. Phys. Rev. Lett. 110, 253002 (2013).

    ADS  Article  Google Scholar 

  28. 28

    Wang, X. & Eberly, J. H. Elliptical polarization and probability of double ionization. Phys. Rev. Lett. 105, 083001 (2010).

    ADS  Article  Google Scholar 

  29. 29

    Carette, T., Dahlström, J. M., Argenti, L. & Lindroth, E. Multiconfigurational Hartree–Fock close-coupling ansatz: Application to the argon photoionization cross section and delays. Phys. Rev. A 87, 023420 (2013).

    ADS  Article  Google Scholar 

  30. 30

    Kheifets, A. S. Time delay in valence shell photoionization of noble gas atoms. Phys. Rev. A 87, 063404 (2013).

    ADS  Article  Google Scholar 

  31. 31

    Scrinzi, A. t-SURFF: Fully differential two-electron photo-emission spectra. New J. Phys. 14, 085008 (2012).

    ADS  Article  Google Scholar 

  32. 32

    Sukiasyan, S. et al. Signatures of bound-state-assisted nonsequential double ionization. Phys. Rev. A 80, 013412 (2009).

    ADS  Article  Google Scholar 

  33. 33

    Smirnova, O., Spanner, M. & Ivanov, M. Analytical solutions for strong field-driven atomic and molecular one- and two-electron continua and applications to strong-field problems. Phys. Rev. A 77, 033407 (2008).

    ADS  Article  Google Scholar 

Download references


We acknowledge stimulating discussions with U. Keller and A. Landsman. J.K., O.S. and M.I. acknowledge support of the EU Marie Curie ITN network CORINF, Grant Agreement No. 264951. F.M. and O.S. acknowledge support of the DFG project SM 292/3-1, S.S. and M.I. acknowledge support of the EPSRC Programme Grant EP/I032517/1, M.I. acknowledges the support of the United States Air Force Office of Scientific Research program No. FA9550-12-1-0482, O.S., L.T. and J.K. acknowledge support of the DFG grant SM 292/2-3. A.K. and I.I. acknowledge support of the Australian Research Council Grant DP120101805. A.Z. and A.S. acknowledge support from the DFG through excellence cluster Munich Center for Advanced Photonics (MAP) and from the Austrian Science Foundation project ViCoM (F41). O.S., M.I., F.M. and A.S. acknowledge the support of the European COST Action XLIC CM1204, H.G.M. acknowledges the hospitality of the Max Born Institute.

Author information




L.T., J.K. and O.S. derived the ARM method and performed the analytical study. F.M., H.G.M., M.I., A.Z., A.S., A.K., I.I. and S.S. performed the numerical simulations and checked the convergence and consistency of the results. F.M., O.S. and M.I. analysed the origins of negative ionization times. O.S. directed and coordinated the research. L.T., M.I. and O.S. wrote the paper. All authors discussed the results and provided contributions to the text of the manuscript.

Corresponding author

Correspondence to Olga Smirnova.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 523 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Torlina, L., Morales, F., Kaushal, J. et al. Interpreting attoclock measurements of tunnelling times. Nature Phys 11, 503–508 (2015).

Download citation

Further reading


Quick links