Ultrafast preparation and detection of ring currents in single atoms


Quantum particles can penetrate potential barriers by tunnelling1. If that barrier is rotating, the tunnelling process is modified2,3. This is typical for electrons in atoms, molecules or solids exposed to strong circularly polarized laser pulses4,5,6. Here we measure how the transmission probability through a rotating tunnel depends on the sign of the magnetic quantum number m of the electron and thus on the initial direction of rotation of its quantum phase. We further show that our findings agree with a semiclassical picture, in which the electron keeps part of that rotary motion on its way through the tunnel by measuring m-dependent modification of the electron emission pattern. These findings are relevant for attosecond metrology as well as for interpretation of strong-field electron emission from atoms and molecules7,8,9,10,11,12,13,14 and directly demonstrate the creation of ring currents in bound states of ions with attosecond precision. In solids, this could open a way to inducing and controlling ring-current-related topological phenomena15.

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Fig. 1: Experimental preparation of ring currents by m-dependent tunnel-ionization.
Fig. 2: Detection of ring currents by momentum-resolved m-dependent tunnel-ionization.
Fig. 3: Energy-resolved electron spectra showing ring current transport during tunnelling.


  1. 1.

    Keldysh, L. V. Ionization in the field of a strong electromagnetic wave. Sov. Phys. JETP 20, 1307–1314 (1965).

    MathSciNet  Google Scholar 

  2. 2.

    Ivanov, M., Spanner, M. & Smirnova, O. Anatomy of strong field ionization. J. Mod. Opt. 52, 165–184 (2005).

    ADS  Article  Google Scholar 

  3. 3.

    Yudin, G. & Ivanov, M. Nonadiabatic tunnel ionization: Looking inside a laser cycle. Phys. Rev. A 64, 13409 (2001).

    ADS  Article  Google Scholar 

  4. 4.

    Barth, I. & Smirnova, O. Nonadiabatic tunneling in circularly polarized laser fields: Physical picture and calculations. Phys. Rev. A 84, 63415 (2011).

    ADS  Article  Google Scholar 

  5. 5.

    Kaushal, J. & Smirnova, O. Nonadiabatic Coulomb effects in strong-field ionization in circularly polarized laser fields. Phys. Rev. A 88, 13421 (2013).

    ADS  Article  Google Scholar 

  6. 6.

    Zhu, X. et al. Helicity sensitive enhancement of strong-field ionization in circularly polarized laser fields. Opt. Express 24, 4196–4209 (2016).

    ADS  Article  Google Scholar 

  7. 7.

    Kaushal, J., Morales, F. & Smirnova, O. Opportunities for detecting ring currents using an attoclock setup. Phys. Rev. A 92, 63405 (2015).

    ADS  Article  Google Scholar 

  8. 8.

    Landsman, A. S. & Keller, U. Attosecond science and the tunnelling time problem. Phys. Rep. 547, 1–24 (2015).

    ADS  MathSciNet  Article  Google Scholar 

  9. 9.

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

    ADS  Article  Google Scholar 

  10. 10.

    Pedatzur, O. et al. Attosecond tunnelling interferometry. Nat. Phys. 11, 815–819 (2015).

    Article  Google Scholar 

  11. 11.

    Torlina, L. et al. Interpreting attoclock measurements of tunnelling times. Nat. Phys. 11, 503–508 (2015).

    Article  Google Scholar 

  12. 12.

    Garg, M. et al. Multi-petahertz electronic metrology. Nature 538, 359–363 (2016).

    ADS  Article  Google Scholar 

  13. 13.

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

    ADS  Article  Google Scholar 

  14. 14.

    Hassan, M. T. et al. Optical attosecond pulses and tracking the nonlinear response of bound electrons. Nature 530, 66–70 (2016).

    ADS  Article  Google Scholar 

  15. 15.

    Rechtsman, M. et al. Photonic Floquet topological insulators. Nature 496, 196–200 (2013).

    ADS  Article  Google Scholar 

  16. 16.

    Barth, I. & Manz, J. Electric ring currents in atomic orbitals and magnetic fields induced by short intense circularly polarized π laser pulses. Phys. Rev. A 75, 12510 (2007).

    ADS  Article  Google Scholar 

  17. 17.

    Fleischer, A. et al. Probing angular correlations in sequential double ionization. Phys. Rev. Lett. 107, 113003 (2011).

    ADS  Article  Google Scholar 

  18. 18.

    Fechner, L., Camus, N., Ullrich, J., Pfeifer, T. & Moshammer, R. Strong-field tunneling from a coherent superposition of electronic states. Phys. Rev. Lett. 112, 213001 (2014).

    ADS  Article  Google Scholar 

  19. 19.

    Barth, I. & Smirnova, O. Hole dynamics and spin currents after ionization in strong circularly polarized laser fields. J. Phys. B 47, 204020 (2014).

    ADS  Article  Google Scholar 

  20. 20.

    Barth, I. & Smirnova, O. Spin-polarized electrons produced by strong-field ionization. Phys. Rev. A 88, 13401 (2013).

    ADS  Article  Google Scholar 

  21. 21.

    Li, Y. et al. Nonadiabatic tunnel ionization in strong circularly polarized laser fields: counterintuitive angular shifts in the photoelectron momentum distribution. Opt. Express 23, 28801–28807 (2015).

    ADS  Article  Google Scholar 

  22. 22.

    Hartung, A. et al. Electron spin polarization in strong-field ionization of xenon atoms. Nat. Photon. 10, 526–528 (2016).

    ADS  Article  Google Scholar 

  23. 23.

    Herath, T., Yan, L., Lee, S. K. & Li, W. Strong-field ionization rate depends on the sign of the magnetic quantum number. Phys. Rev. Lett. 109, 43004 (2012).

    ADS  Article  Google Scholar 

  24. 24.

    Torlina, L. & Smirnova, O. Time-dependent analytical R-matrix approach for strong-field dynamics. I. One-electron systems. Phys. Rev. A 86, 43408 (2012).

    ADS  Article  Google Scholar 

  25. 25.

    Torlina, L., Kaushal, J. & Smirnova, O. Time-resolving electron-core dynamics during strong-field ionization in circularly polarized fields. Phys. Rev. A 88, 53403 (2013).

    ADS  Article  Google Scholar 

  26. 26.

    Torlina, L., Morales, F., Muller, H. G. & Smirnova, O. Ab initio verification of the analytical R-matrix theory for strong field ionization. J. Phys. B 47, 204021 (2014).

    ADS  Article  Google Scholar 

  27. 27.

    Jagutzki, O. et al. Multiple hit readout of a microchannel plate detector with a three-layer delay-line anode. IEEE Trans. Nucl. Sci. 49, 2477–2483 (2002).

    ADS  Article  Google Scholar 

  28. 28.

    Ullrich, J. et al. Recoil-ion and electron momentum spectroscopy: reaction-microscopes. Rep. Prog. Phys. 66, 1463–1545 (2003).

    ADS  Article  Google Scholar 

  29. 29.

    Eckart, S. et al. Nonsequential double ionization by counterrotating circularly polarized two-color laser fields. Phys. Rev. Lett. 117, 133202 (2016).

    ADS  Article  Google Scholar 

  30. 30.

    Pfeiffer, A. N. et al. Calculation of valence electron motion induced by sequential strong-field ionisation. Mol. Phys. 111, 2283–2291 (2013).

    ADS  Article  Google Scholar 

  31. 31.

    Nandor, M. J., Walker, M. A., Van Woerkom, L. D. & Muller, H. G. Detailed comparison of above-threshold-ionization spectra from accurate numerical integrations and high-resolution measurements. Phys. Rev. A 60, R1771–R1774 (1999).

    ADS  Article  Google Scholar 

  32. 32.

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

    Google Scholar 

  33. 33.

    Shvetsov-Shilovski, N. I. et al. Semiclassical two-step model for strong-field ionization. Phys. Rev. A 94, 13415 (2016).

    ADS  Article  Google Scholar 

  34. 34.

    Delone, N. B. & Krainov, V. P. Energy and angular electron spectra for the tunnel ionization of atoms by strong low-frequency radiation. J. Opt. Soc. Am. B 8, 1207–1211 (1991).

    ADS  Article  Google Scholar 

  35. 35.

    Lemell, C. et al. Low-energy peak structure in strong-field ionization by midinfrared laser pulses: Two-dimensional focusing by the atomic potential. Phys. Rev. A 85, 11403 (2012).

    ADS  Article  Google Scholar 

  36. 36.

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

    Article  Google Scholar 

  37. 37.

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

    Article  Google Scholar 

  38. 38.

    Bruner, B. D. et al. Multidimensional high harmonic spectroscopy of polyatomic molecules: detecting sub-cycle laser-driven hole dynamics upon ionization in strong mid-IR laser fields. Faraday Discuss. 194, 369–405 (2016).

    ADS  Article  Google Scholar 

  39. 39.

    Torlina, L. & Smirnova, O. Coulomb time delays in high harmonic generation. New J. Phys. 19, 23012 (2017).

    Article  Google Scholar 

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This work was supported by the DFG Priority Programme ‘Quantum Dynamics in Tailored Intense Fields’ (projects DO 604/29-1, BA 5623/1-1, IV 156/6-1, SM 292/5-1).

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S.E., M.K., M.R., A.H., J.R., F.T., K.F., N.S., K.H., L.Ph.H.S., T.J., M.S. and R.D. contributed to the experiment. S.E., M.K., M.R., K.L., I.B., J.K., F.M., M.I., O.S. and R.D. contributed to the theoretical results. S.E., M.K., T.J., M.S. and R.D. performed the analysis of the experimental data. All authors contributed to the manuscript.

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Correspondence to Sebastian Eckart or Reinhard Dörner.

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Eckart, S., Kunitski, M., Richter, M. et al. Ultrafast preparation and detection of ring currents in single atoms. Nature Phys 14, 701–704 (2018). https://doi.org/10.1038/s41567-018-0080-5

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