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.

Decoherence and revival in attosecond charge migration driven by non-adiabatic dynamics


Attosecond charge migration is a periodic evolution of the charge density at specific sites of a molecule on a timescale defined by the energy intervals between the electronic states involved. Here we report the observation of charge migration in neutral silane (SiH4) in 690 as, its decoherence within 15 fs and its revival after 40–50 fs, using X-ray attosecond transient-absorption spectroscopy. We observe the migration of charge as pairs of quantum beats with a characteristic spectral phase in the transient spectrum, in agreement with theory. The decay and revival of the degree of electronic coherence is found to be a result of both adiabatic and non-adiabatic dynamics in the populated Rydberg and valence states. The experimental results are supported by fully quantum-mechanical ab initio calculations that include both electronic and nuclear dynamics, which additionally support the experimental evidence that conical intersections can mediate the transfer of electronic coherence from an initial superposition state to another one involving a different lower-lying state.

Your institute does not have access to this article

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Overview of the experimental set-up, pump–probe scheme and data.
Fig. 2: Identifying the electronic states involved in charge migration.
Fig. 3: Non-adiabatic transfer of electronic coherence.
Fig. 4: Attosecond electron wavepacket, decoherence and revival.
Fig. 5: Encoding of the sign of transition-dipole moments in molecular ATAS.

Data availability

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


  1. Eyring, H., Walter, J. & Kimball, G. E. Quantum Chemistry (Wiley, 1944).

  2. Remacle, F. & Levine, R. D. An electronic time scale in chemistry. Proc. Natl. Acad. Sci. USA 103, 6793–6798 (2006).

    ADS  Article  Google Scholar 

  3. Cederbaum, L. S. & Zobeley, J. Ultrafast charge migration by electron correlation. Chem. Phys. Lett. 307, 205–210 (1999).

    ADS  Article  Google Scholar 

  4. Kuleff, A. I. & Cederbaum, L. S. Ultrafast correlation-driven electron dynamics. J. Phys. B At. Mol. Opt. Phys. 47, 124002 (2014).

    ADS  Article  Google Scholar 

  5. Kraus, P. M. & Wörner, H. J. Perspectives of attosecond spectroscopy for the understanding of fundamental electron correlations. Angew. Chem. Int. Ed. 57, 2–22 (2018).

    Article  Google Scholar 

  6. Wörner, H. J. et al. Charge migration and charge transfer in molecular systems. Struct. Dyn. 4, 061508 (2017).

    Article  Google Scholar 

  7. Vacher, M., Steinberg, L., Jenkins, A. J., Bearpark, M. J. & Robb, M. A. Electron dynamics following photoionization: decoherence due to the nuclear-wave-packet width. Phys. Rev. A 92, 040502 (2015).

    ADS  Article  Google Scholar 

  8. Arnold, C., Vendrell, O. & Santra, R. Electronic decoherence following photoionization: full quantum-dynamical treatment of the influence of nuclear motion. Phys. Rev. A 95, 033425 (2017).

    ADS  Article  Google Scholar 

  9. Despré, V., Golubev, N. V. & Kuleff, A. I. Charge migration in propiolic acid: a full quantum dynamical study. Phys. Rev. Lett. 121, 203002 (2018).

    ADS  Article  Google Scholar 

  10. Jia, D., Manz, J. & Yang, Y. De- and recoherence of charge migration in ionized iodoacetylene. J. Phys. Chem. Lett. 10, 4273–4277 (2019).

    Article  Google Scholar 

  11. Lünnemann, S., Kuleff, A. I. & Cederbaum, L. S. Ultrafast charge migration in 2-phenylethyl-N,N-dimethylamine. Chem. Phys. Lett. 450, 232–235 (2008).

    ADS  Article  Google Scholar 

  12. Remacle, F., Levine, R. & Ratner, M. A. Charge directed reactivity: a simple electronic model, exhibiting site selectivity, for the dissociation of ions. Chem. Phys. Lett. 285, 25–33 (1998).

    ADS  Article  Google Scholar 

  13. Lehr, L., Horneff, T., Weinkauf, R. & Schlag, E. Femtosecond dynamics after ionization: 2-phenylethyl-N,N-dimethylamine as a model system for nonresonant downhill charge transfer in peptides. J. Phys. Chem. A 109, 8074–8080 (2005).

    Article  Google Scholar 

  14. Kraus, P. M. et al. Measurement and laser control of attosecond charge migration in ionized iodoacetylene. Science 350, 790–795 (2015).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  16. Despré, V. et al. Attosecond hole migration in benzene molecules surviving nuclear motion. J. Phys. Chem. Lett. 6, 426–431 (2015).

    Article  Google Scholar 

  17. Yuan, K.-J. & Bandrauk, A. D. Exploring coherent electron excitation and migration dynamics by electron diffraction with ultrashort X-ray pulses. Phys. Chem. Chem. Phys. 19, 25846–25852 (2017).

    Article  Google Scholar 

  18. Jia, D. et al. Quantum control of electronic fluxes during adiabatic attosecond charge migration in degenerate superposition states of benzene. Chem. Phys. 482, 146–159 (2017).

    Article  Google Scholar 

  19. Vacher, M., Meisner, J., Mendive-Tapia, D., Bearpark, M. J. & Robb, M. A. Electronic control of initial nuclear dynamics adjacent to a conical intersection. J. Phys. Chem. A 119, 5165–5172 (2014).

    Article  Google Scholar 

  20. Lara-Astiaso, M., Palacios, A., Decleva, P., Tavernelli, I. & Martín, F. Role of electron-nuclear coupled dynamics on charge migration induced by attosecond pulses in glycine. Chem. Phys. Lett. 683, 357–364 (2017).

    ADS  Article  Google Scholar 

  21. Sun, S. et al. Nuclear motion driven ultrafast photodissociative charge transfer of the penna cation: an experimental and computational study. J. Phys. Chem. A 121, 1442–1447 (2017).

    Article  Google Scholar 

  22. Vacher, M., Bearpark, M. J., Robb, M. A. & Malhado, J. P. Electron dynamics upon ionization of polyatomic molecules: coupling to quantum nuclear motion and decoherence. Phys. Rev. Lett. 118, 083001 (2017).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  24. Timmers, H. et al. Disentangling conical intersection and coherent molecular dynamics in methyl bromide with attosecond transient absorption spectroscopy. Nat. Commun. 10, 3133 (2019).

    ADS  Article  Google Scholar 

  25. Kobayashi, Y., Chang, K. F., Zeng, T., Neumark, D. M. & Leone, S. R. Direct mapping of curve-crossing dynamics in IBr by attosecond transient absorption spectroscopy. Science 365, 79–83 (2019).

    ADS  Article  Google Scholar 

  26. Kraus, P. M. et al. High-harmonic probing of electronic coherence in dynamically aligned molecules. Phys. Rev. Lett. 111, 243005 (2013).

    ADS  Article  Google Scholar 

  27. Walt, S. G. et al. Dynamics of valence-shell electrons and nuclei probed by strong-field holography and rescattering. Nat. Commun. 8, 15651 (2017).

    ADS  Article  Google Scholar 

  28. Dutoi, A. D. & Cederbaum, L. S. An excited electron avoiding a positive charge. J. Phys. Chem. Lett. 2, 2300–2303 (2011).

    Article  Google Scholar 

  29. Neidel, C. et al. Probing time-dependent molecular dipoles on the attosecond time scale. Phys. Rev. Lett. 111, 033001 (2013).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  31. Kowalewski, M., Bennett, K., Dorfman, K. E. & Mukamel, S. Catching conical intersections in the act: monitoring transient electronic coherences by attosecond stimulated X-ray Raman signals. Phys. Rev. Lett. 115, 193003 (2015).

    ADS  Article  Google Scholar 

  32. Keefer, D., Schnappinger, T., de Vivie-Riedle, R. & Mukamel, S. Visualizing conical intersection passages via vibronic coherence maps generated by stimulated ultrafast X-ray Raman signals. Proc. Natl. Acad. Sci. USA 117, 24069–24075 (2020).

    ADS  Article  Google Scholar 

  33. Huppert, M., Jordan, I. & Wörner, H. J. Attosecond beamline with actively stabilized and spatially separated beam paths. Rev. Sci. Instrum. 86, 123106 (2015).

    ADS  Article  Google Scholar 

  34. Tachikawa, H. A full dimensional ab initio direct trajectory study on the ionization dynamics of SiH4. Phys. Chem. Chem. Phys. 4, 1135–1140 (2002).

    Article  Google Scholar 

  35. Püttner, R., Domke, M., Lentz, D. & Kaindl, G. Si 2p photoabsorption in SiH4 and SiD4: molecular distortion in core-excited silane. Phys. Rev. A 56, 1228–1239 (1997).

    ADS  Article  Google Scholar 

  36. Golubev, N. V., Vaníček, J. & Kuleff, A. I. Core-valence attosecond transient absorption spectroscopy of polyatomic molecules. Phys. Rev. Lett. 127, 123001 (2021).

    ADS  Article  Google Scholar 

  37. Meyer, H.-D., Manthe, U. & Cederbaum, L. S. The multi-configurational time-dependent Hartree approach. Chem. Phys. Lett. 165, 73–78 (1990).

    ADS  Article  Google Scholar 

  38. Meyer, H.-D., Gatti, F. & Worth, G. A. Multidimensional Quantum Dynamics: MCTDH Theory and Applications (Wiley, 2009).

  39. Köppel, H., Domcke, W. & Cederbaum, L. S. Multimode molecular dynamics beyond the Born–Oppenheimer approximation. Adv. Chem. Phys. 57, 59–246 (1984).

    Google Scholar 

  40. Pabst, S., Lein, M. & Wörner, H. J. Preparing attosecond coherences by strong-field ionization. Phys. Rev. A 93, 023412 (2016).

    ADS  Article  Google Scholar 

  41. Pabst, S., Greenman, L., Ho, P. J., Mazziotti, D. A. & Santra, R. Decoherence in attosecond photoionization. Phys. Rev. Lett. 106, 053003 (2011).

    ADS  Article  Google Scholar 

  42. Arnold, C. et al. Molecular electronic decoherence following attosecond photoionisation. J. Phys. B At. Mol. Opt. Phys. 53, 164006 (2020).

    ADS  Article  Google Scholar 

  43. Golubev, N. V., Begušić, T. & Vaníček, J. On-the-fly ab initio semiclassical evaluation of electronic coherences in polyatomic molecules reveals a simple mechanism of decoherence. Phys. Rev. Lett. 125, 083001 (2020).

    ADS  Article  Google Scholar 

  44. Fiete, G. A. & Heller, E. J. Semiclassical theory of coherence and decoherence. Phys. Rev. A 68, 022112 (2003).

    ADS  Article  Google Scholar 

  45. Yuan, G. et al. The role of transition dipole phase in atomic attosecond transient absorption from the multi-level model. Struct. Dyn. 6, 054102 (2019).

    Article  Google Scholar 

  46. Kobayashi, Y., Neumark, D. M. & Leone, S. R. Theoretical analysis of the role of complex transition dipole phase in XUV transient-absorption probing of charge migration. Opt. Express 30, 5673–5682 (2022).

    ADS  Article  Google Scholar 

  47. Kling, M. F., von den Hoff, P., Znakovskaya, I. & de Vivie-Riedle, R. (Sub-)femtosecond control of molecular reactions via tailoring the electric field of light. Phys. Chem. Chem. Phys. 15, 9448–9467 (2013).

    Article  Google Scholar 

  48. Golubev, N. V. & Kuleff, A. I. Control of charge migration in molecules by ultrashort laser pulses. Phys. Rev. A 91, 051401 (2015).

    ADS  Article  Google Scholar 

  49. Cooper, G., Burton, G. R., W. F., C. & Brion, C. Absolute oscillator strengths for the photoabsorption of silane in the valence and Si 2p and 2s regions (7.5–350 eV). Chem. Phys. 196, 293–306 (1995).

    Article  Google Scholar 

  50. Jarque, E. C. et al. Universal route to optimal few- to single-cycle pulse generation in hollow-core fiber compressors. Sci. Rep. 8, 2256 (2018).

    ADS  Article  Google Scholar 

  51. Harada, T., Takahashi, K., Sakuma, H. & Osyczka, A. Optimum design of a grazing-incidence flat-field spectrograph with a spherical varied-line-space grating. Appl. Opt. 38, 2743–2748 (1999).

    ADS  Article  Google Scholar 

Download references


We thank A. Schneider and M. Seiler for their technical support, D. Hammerland for laser support, D. Stefano for the coating of the Nb mirrors, J. Leitner and J. R. Mößinger for performing part of the test calculations, N. C. Geib for providing access to the Pypret reconstruction package, as well as V. U. Lanfaloni for the preparation of Fig. 1a. D.T.M. and H.J.W. gratefully acknowledge funding from the ERC Consolidator Grant (project no. 772797-ATTOLIQ) and from the Swiss National Science Foundation through projects 200021_172946 and the NCCR-MUST. V.D. and A.I.K. thank the DFG for the financial support, provided through the QUTIF Priority Programme, and N.V.G. acknowledges support from the Branco Weiss Fellowship—Society in Science, administered by ETH Zürich.

Author information

Authors and Affiliations



H.J.W. proposed the study. D.T.M. developed the experimental set-up, performed the measurements and analysed the data. V.D., N.V.G. and A.I.K. developed the theoretical models, and V.D. and N.V.G. carried out the calculations. H.J.W. supervised the experimental and A.I.K. the theoretical part of the project. H.J.W. and D.T.M. wrote the manuscript with input from all coauthors.

Corresponding authors

Correspondence to Alexander I. Kuleff or Hans Jakob Wörner.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Attosecond soft-X-ray pulse spectrum and absorbance of silane.

The black dotted and solid lines are the measured probe-pulse spectra before and after the silane is introduced into the target gas cell, respectively. The absorbance of the unpumped silane gas can therefore be calculated and is shown as the purple line. As the CCD detector is made of silicon, its quantum efficiency drops by a factor of two above ~ 100 eV which is evident in the black lines. This effect is eliminated when calculating the absorbance and, therefore, does not affect the results shown in all other figures, including the main text.

Source data

Extended Data Fig. 2 Time-frequency analysis of the attosecond transient-absorption spectra showing evidence of coherence transfer.

The top-left panel shows the pseudo Wigner-Ville distribution of the ΔOD at 105.6 eV. The vertical white lines indicate the two frequencies at which Gabor filters are applied to the entire transient-absorption data set. The results of these Gabor filters are shown in the three panels below. The amplitudes are shown above the phases, sharing a common color scale. Amplitude thresholding has been applied to the phases to ease the identification of the phase of the relevant signals. For completeness, the top right panel shows the unthresholded phase of the 0.72 PHz Gabor filter, exhibiting a pronounced change in structure for delays above 10 fs (highlighted by a white horizontal line).

Source data

Supplementary information

Supplementary Information

Supplementary Sections ‘Experimental methods’ and ‘Theoretical modelling’, Figs. 1–9 and Tables 1–4.

Supplementary Video S1

Electron density difference between the excited and unexcited molecule (ρES(t) − ρGS) as a function of the time delay since excitation, based on the results of the MCTDH and EOM-CCSD/aug-cc-pVTZ calculations. Nuclear motion is not displayed. The isosurfaces of the density difference have the same isovalues as in Fig. 3a. The periods of most intense attosecond charge migration are shown at a slower speed for clarity.

Supplementary Video S2

Projection of the vibrational wavepackets of all electronic states in the MCTDH model onto the ν3 symmetric and one ν4 asymmetric stretching modes. Although the ν4 dynamics are clearly responsible for the diabatic population transfer, the wavepackets of these modes do not show pronounced motion and remain well overlapped around the Frank–Condon region. Meanwhile, the ν3 dynamics are very periodic and show clear decay of the overlap of Rydberg and valence vibrational wavepackets, followed by a revival around a delay of 50 fs.

Source data

Source Data Fig. 1

.csv format files containing numeric data of Fig.1c

Source Data Fig. 2

.csv format files containing numeric data of Fig.2a & c

Source Data Fig. 3

.csv format files containing numeric data of Fig.3a & b

Source Data Fig. 4

.csv format files containing numeric data of Fig.4a–f

Source Data Fig. 5

.csv format files containing numeric data of Fig.5a–c

Source Data Extended Data Fig. 1

.csv format files containing numeric data of EDF1.

Source Data Extended Data Fig. 2

.csv format files containing numeric data of EDF2a & b.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Matselyukh, D.T., Despré, V., Golubev, N.V. et al. Decoherence and revival in attosecond charge migration driven by non-adiabatic dynamics. Nat. Phys. (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI:


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