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
Subscribe to Nature+
Get immediate online access to the entire Nature family of 50+ journals
Subscribe to Journal
Get full journal access for 1 year
only $8.25 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
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.
Eyring, H., Walter, J. & Kimball, G. E. Quantum Chemistry (Wiley, 1944).
Remacle, F. & Levine, R. D. An electronic time scale in chemistry. Proc. Natl. Acad. Sci. USA 103, 6793–6798 (2006).
Cederbaum, L. S. & Zobeley, J. Ultrafast charge migration by electron correlation. Chem. Phys. Lett. 307, 205–210 (1999).
Kuleff, A. I. & Cederbaum, L. S. Ultrafast correlation-driven electron dynamics. J. Phys. B At. Mol. Opt. Phys. 47, 124002 (2014).
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).
Wörner, H. J. et al. Charge migration and charge transfer in molecular systems. Struct. Dyn. 4, 061508 (2017).
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).
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).
Despré, V., Golubev, N. V. & Kuleff, A. I. Charge migration in propiolic acid: a full quantum dynamical study. Phys. Rev. Lett. 121, 203002 (2018).
Jia, D., Manz, J. & Yang, Y. De- and recoherence of charge migration in ionized iodoacetylene. J. Phys. Chem. Lett. 10, 4273–4277 (2019).
Lünnemann, S., Kuleff, A. I. & Cederbaum, L. S. Ultrafast charge migration in 2-phenylethyl-N,N-dimethylamine. Chem. Phys. Lett. 450, 232–235 (2008).
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).
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).
Kraus, P. M. et al. Measurement and laser control of attosecond charge migration in ionized iodoacetylene. Science 350, 790–795 (2015).
Calegari, F. et al. Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses. Science 346, 336–339 (2014).
Despré, V. et al. Attosecond hole migration in benzene molecules surviving nuclear motion. J. Phys. Chem. Lett. 6, 426–431 (2015).
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).
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).
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).
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).
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).
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).
Goulielmakis, E. et al. Real-time observation of valence electron motion. Nature 466, 739–743 (2010).
Timmers, H. et al. Disentangling conical intersection and coherent molecular dynamics in methyl bromide with attosecond transient absorption spectroscopy. Nat. Commun. 10, 3133 (2019).
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).
Kraus, P. M. et al. High-harmonic probing of electronic coherence in dynamically aligned molecules. Phys. Rev. Lett. 111, 243005 (2013).
Walt, S. G. et al. Dynamics of valence-shell electrons and nuclei probed by strong-field holography and rescattering. Nat. Commun. 8, 15651 (2017).
Dutoi, A. D. & Cederbaum, L. S. An excited electron avoiding a positive charge. J. Phys. Chem. Lett. 2, 2300–2303 (2011).
Neidel, C. et al. Probing time-dependent molecular dipoles on the attosecond time scale. Phys. Rev. Lett. 111, 033001 (2013).
Ott, C. et al. Reconstruction and control of a time-dependent two-electron wave packet. Nature 516, 374–378 (2014).
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).
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).
Huppert, M., Jordan, I. & Wörner, H. J. Attosecond beamline with actively stabilized and spatially separated beam paths. Rev. Sci. Instrum. 86, 123106 (2015).
Tachikawa, H. A full dimensional ab initio direct trajectory study on the ionization dynamics of SiH4. Phys. Chem. Chem. Phys. 4, 1135–1140 (2002).
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).
Golubev, N. V., Vaníček, J. & Kuleff, A. I. Core-valence attosecond transient absorption spectroscopy of polyatomic molecules. Phys. Rev. Lett. 127, 123001 (2021).
Meyer, H.-D., Manthe, U. & Cederbaum, L. S. The multi-configurational time-dependent Hartree approach. Chem. Phys. Lett. 165, 73–78 (1990).
Meyer, H.-D., Gatti, F. & Worth, G. A. Multidimensional Quantum Dynamics: MCTDH Theory and Applications (Wiley, 2009).
Köppel, H., Domcke, W. & Cederbaum, L. S. Multimode molecular dynamics beyond the Born–Oppenheimer approximation. Adv. Chem. Phys. 57, 59–246 (1984).
Pabst, S., Lein, M. & Wörner, H. J. Preparing attosecond coherences by strong-field ionization. Phys. Rev. A 93, 023412 (2016).
Pabst, S., Greenman, L., Ho, P. J., Mazziotti, D. A. & Santra, R. Decoherence in attosecond photoionization. Phys. Rev. Lett. 106, 053003 (2011).
Arnold, C. et al. Molecular electronic decoherence following attosecond photoionisation. J. Phys. B At. Mol. Opt. Phys. 53, 164006 (2020).
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).
Fiete, G. A. & Heller, E. J. Semiclassical theory of coherence and decoherence. Phys. Rev. A 68, 022112 (2003).
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).
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).
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).
Golubev, N. V. & Kuleff, A. I. Control of charge migration in molecules by ultrashort laser pulses. Phys. Rev. A 91, 051401 (2015).
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).
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).
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).
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.
The authors declare no competing interests.
Peer review information
Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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.
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).
Supplementary Sections ‘Experimental methods’ and ‘Theoretical modelling’, Figs. 1–9 and Tables 1–4.
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.
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.
.csv format files containing numeric data of Fig.1c
.csv format files containing numeric data of Fig.2a & c
.csv format files containing numeric data of Fig.3a & b
.csv format files containing numeric data of Fig.4a–f
.csv format files containing numeric data of Fig.5a–c
.csv format files containing numeric data of EDF1.
.csv format files containing numeric data of EDF2a & b.
About this article
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). https://doi.org/10.1038/s41567-022-01690-0