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Complete characterization of sub-Coulomb-barrier tunnelling with phase-of-phase attoclock


Laser-induced electron tunnelling—which triggers a broad range of ultrafast phenomena such as the generation of attosecond light pulses, photoelectron diffraction and holography—has laid the foundation for strong-field physics and attosecond science. Using the attoclock constructed by single-colour elliptically polarized laser fields, previous experiments have measured the tunnelling rates, exit positions, exit velocities and delay times for some specific electron trajectories, which are mostly created at the field peak instant, that is, when the laser electric field and the formed potential barrier are stationary in terms of the derivative versus time. From the view of wave-particle dualism, the electron phase under a classically forbidden, tunnelling barrier has not been measured, which is at the heart of quantum tunnelling physics. Here we present a robust measurement of tunnelling dynamics including the electron sub-barrier phase and amplitude. We combine the attoclock technique with two-colour phase-of-phase (POP) spectroscopy to accurately calibrate the angular streaking relation and to probe the non-stationary tunnelling dynamics by manipulating a rapidly changing potential barrier. This POP attoclock directly links the measured phase of the two-colour relative phase with the ionization instant for the photoelectron with any final momentum on the detector, allowing us to reconstruct the imaginary tunnelling time and the accumulated phase under the barrier. The POP attoclock provides a general time-resolved approach to accessing the underlying quantum dynamics in intense light–matter interactions.

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Fig. 1: POP attoclock photoelectron spectroscopy.
Fig. 2: Experimental results of the POP attoclock.
Fig. 3: Calculated POP spectra.
Fig. 4: Sub-barrier tunnelling dynamics.

Data availability

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


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Y.L. acknowledges the finance support by the National Science Foundation of China (grant nos. 92050201, 918850111 and 11774013). M.H. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 801459 (FP-RESOMUS) and the Swiss National Science Foundation through the NCCR MUST.

Author information

Authors and Affiliations



M.H., P.G., and Z.G. performed the experiments. M.H., Y.F. and Y L. analysed and interpreted the data. Simulations were implemented by M. H. This project was coordinated by Y. L.. All authors discussed the results and wrote the paper.

Corresponding author

Correspondence to Yunquan Liu.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Photonics thanks Karen Hatsagortsyan, Anatoli Kheifets and the other, anonymous, reviewer(s) 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.

Supplementary information

Supplementary Information

Supplementary Figs. 1–6 and Discussion.

Supplementary Video 1

Animated measured angle-resolved energy spectrum in the POP attoclock.

Supplementary Video 2

Animated calculated angle-resolved energy spectrum in the POP attoclock using the CTMC model without including Coulomb potential.

Supplementary Video 3

Animated calculated angle-resolved energy spectrum in the POP attoclock using the CTMC model including Coulomb potential.

Supplementary Video 4

Animated calculated angle-resolved energy spectrum in the POP attoclock using the SFA model by numerical integration method.

Supplementary Video 5

Animated calculated angle-resolved energy spectrum in the POP attoclock using the CCSFA model.

Supplementary Video 6

Animated calculated angle-resolved energy spectrum in the POP attoclock using the TDSE method.

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Han, M., Ge, P., Wang, J. et al. Complete characterization of sub-Coulomb-barrier tunnelling with phase-of-phase attoclock. Nat. Photon. 15, 765–771 (2021).

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