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Spatial molecular interferometry via multidimensional high-harmonic spectroscopy


Interferometry is a basic tool to resolve coherent properties in a wide range of light or matter wave phenomena. In the strong-field regime, interferometry serves as a fundamental building block in revealing ultrafast electron dynamics. In this work we manipulate strong-field-driven electron trajectories and probe the coherence of a molecular wavefunction by inducing an interferometer on a microscopic level. The two arms of the interferometer are controlled by a two-colour field, while the interference pattern is read via advanced, three-dimensional high-harmonic spectroscopy. This scheme recovers the spectral phase information associated with the structure of molecular orbitals, as well as the spatial properties of the interaction itself. Zooming into one of the most fundamental strong-field phenomena—field-induced tunnel ionization—we reconstruct the angle at which the electronic wavefunction tunnels through the barrier and follow its evolution with attosecond precision.

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Fig. 1: Schematic description of molecular interferometry.
Fig. 2: Reconstruction of the HHG phase as a function of molecular alignment angle.
Fig. 3: Recombination and ionization amplitude interferometry.
Fig. 4: Decoupling ionization and recombination amplitudes.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Ott, C. et al. Reconstruction and control of a time-dependent two-electron wave packet. Nature 516, 374–378 (2014).

    ADS  Article  Google Scholar 

  2. 2.

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

    Article  Google Scholar 

  3. 3.

    Sansone, G. et al. Electron localization following attosecond molecular photoionization. Nature 465, 763–766 (2010).

    Article  Google Scholar 

  4. 4.

    Calegari, F. et al. Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses. Science 346, 336–339 (2014).

    ADS  Article  Google Scholar 

  5. 5.

    Ghimire, S. et al. Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7, 138–141 (2011).

    Article  Google Scholar 

  6. 6.

    Vampa, G. et al. Linking high harmonics from gases and solids. Nature 522, 462–464 (2015).

    Article  Google Scholar 

  7. 7.

    Le, A.-T., Morishita, T. & Lin, C. Extraction of the species-dependent dipole amplitude and phase from high-order harmonic spectra in rare-gas atoms. Phys. Rev. A 78, 023814 (2008).

    ADS  Article  Google Scholar 

  8. 8.

    Lewenstein, M., Balcou, P., Ivanov, M. Y., L’huillier, A. & Corkum, P. B. Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49, 2117–2132 (1994).

    ADS  Article  Google Scholar 

  9. 9.

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

    ADS  Article  Google Scholar 

  10. 10.

    Smirnova, O. & Ivanov, M. in Attosecond and XUV Physics: Ultrafast Dynamics and Spectroscopy (eds Schultz, T. & Vrakking, M.) Ch. 7 (Wiley, 2014).

  11. 11.

    Haessler, S. et al. Attosecond imaging of molecular electronic wavepackets. Nat. Phys. 6, 200–206 (2010).

    Article  Google Scholar 

  12. 12.

    Vozzi, C. et al. Generalized molecular orbital tomography. Nat. Phys. 7, 823–827 (2011).

    Article  Google Scholar 

  13. 13.

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

    ADS  Article  Google Scholar 

  14. 14.

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

    ADS  Article  Google Scholar 

  15. 15.

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

    ADS  Article  Google Scholar 

  16. 16.

    Azoury, D. et al. Electronic wavefunctions probed by all-optical attosecond interferometry. Nat. Photon. 13, 54–59 (2019).

    ADS  Article  Google Scholar 

  17. 17.

    Mairesse, Y. et al. High-order harmonic transient grating spectroscopy in a molecular jet. Phys. Rev. Lett. 100, 143903 (2008).

    ADS  Article  Google Scholar 

  18. 18.

    Rupenyan, A., Bertrand, J. B., Villeneuve, D. M. & Wörner, H. J. All-optical measurement of high-harmonic amplitudes and phases in aligned molecules. Phys. Rev. Lett. 108, 033903 (2012).

    ADS  Article  Google Scholar 

  19. 19.

    Levesque, J. et al. Polarization state of high-order harmonic emission from aligned molecules. Phys. Rev. Lett. 99, 243001 (2007).

    ADS  Article  Google Scholar 

  20. 20.

    Mairesse, Y. et al. High harmonic spectroscopy of multichannel dynamics in strong-field ionization. Phys. Rev. Lett. 104, 213601 (2010).

    ADS  Article  Google Scholar 

  21. 21.

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

    Article  Google Scholar 

  22. 22.

    Shafir, D., Mairesse, Y., Villeneuve, D., Corkum, P. & Dudovich, N. Atomic wavefunctions probed through strong-field light–matter interaction. Nat. Phys. 5, 412–416 (2009).

    Article  Google Scholar 

  23. 23.

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

    Article  Google Scholar 

  24. 24.

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

    Article  Google Scholar 

  25. 25.

    Niikura, H., Dudovich, N., Villeneuve, D. & Corkum, P. Mapping molecular orbital symmetry on high-order harmonic generation spectrum using two-color laser fields. Phys. Rev. Lett. 105, 053003 (2010).

    ADS  Article  Google Scholar 

  26. 26.

    Boutu, W. et al. Coherent control of attosecond emission from aligned molecules. Nat. Phys. 4, 545–549 (2008).

    Article  Google Scholar 

  27. 27.

    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 

  28. 28.

    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 

  29. 29.

    Harvey, A. G., Brambila, D. S., Morales, F. & Smirnova, O. An R-matrix approach to electron–photon–molecule collisions: photoelectron angular distributions from aligned molecules. J. Phys. B 47, 215005 (2014).

    ADS  Article  Google Scholar 

  30. 30.

    Mašín, Z. et al. Electron correlations and pre-collision in the re-collision picture of high harmonic generation. J. Phys. B 51, 134006 (2018).

    ADS  Article  Google Scholar 

  31. 31.

    Pavičić, D., Lee, K. F., Rayner, D. M., Corkum, P. B. & Villeneuve, D. M. Direct measurement of the angular dependence of ionization for N2, O2, and CO2 in intense laser fields. Phys. Rev. Lett. 98, 243001 (2007).

    ADS  Article  Google Scholar 

  32. 32.

    Majety, V. P. & Scrinzi, A. Dynamic exchange in the strong field ionization of molecules. Phys. Rev. Lett. 115, 103002 (2015).

    ADS  Article  Google Scholar 

  33. 33.

    Murray, R., Spanner, M., Patchkovskii, S. & Ivanov, M. Y. Tunnel ionization of molecules and orbital imaging. Phys. Rev. Lett. 106, 173001 (2011).

    ADS  Article  Google Scholar 

  34. 34.

    Eckart, S. et al. Ultrafast preparation and detection of ring currents in single atoms. Nat. Phys. 14, 701–704 (2018).

    Article  Google Scholar 

  35. 35.

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

    Article  Google Scholar 

  36. 36.

    Kaushal, J., Morales, F. & Smirnova, O. Opportunities for detecting ring currents using an attoclock setup. Phys. Rev. A 92, 063405 (2015).

    ADS  Article  Google Scholar 

  37. 37.

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

    Article  Google Scholar 

  38. 38.

    Barth, I. & Smirnova, O. Spin-polarized electrons produced by strong-field ionization. Phys. Rev. A 88, 013401 (2013).

    ADS  Article  Google Scholar 

  39. 39.

    Wörner, H. J. et al. Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy. Science 334, 208–212 (2011).

    ADS  Article  Google Scholar 

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We thank G. Orenstein and M. Kruger for helpful discussions and Z. Masin for his theoretical support. N.D. is the incumbent of the Robin Chemers Neustein Professorial Chair. N.D. acknowledges the Minerva Foundation, the Israeli Science Foundation, the Crown Center of Photonics and the European Research Council for financial support. O.S. and M.I. acknowledge support of the DFG QUTIF grants. M.I. acknowledges support of EPSRC/DSTL MURI grant no. EP/N018680/1.

Author information




N.D., O.S., M.I. and B.P. supervised the study. A.J.U., H.S. and B.D.B. designed and built the experimental set-up. A.J.U., H.S. and O.P. carried out the measurements and analysed the data. M.I. and O.S. conceived and performed the theoretical calculations. A.C., S.L. and B.P. developed and studied the theoretical analysis of the Coulomb effects. A.J.U., H.S. and N.D. interpreted the experimental and theoretical results. All authors discussed the results and contributed to the final manuscript.

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Correspondence to Nirit Dudovich.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–14, detailed description of the theory, numeric calculations and discussion.

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Uzan, A.J., Soifer, H., Pedatzur, O. et al. Spatial molecular interferometry via multidimensional high-harmonic spectroscopy. Nat. Photonics 14, 188–194 (2020).

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