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

Abstract

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.

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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.

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Acknowledgements

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

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Contributions

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.

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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.

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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

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