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Attosecond-resolved non-dipole photoionization dynamics

Nature Photonics volume 18, pages 311–317 (2024)Cite this article

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Abstract

Light–matter interactions are usually described within the electric-dipole approximation, where the magnetic-field component and the spatial variation of the light electric field over the relevant electronic length scales are both ignored. Non-dipole effects in photoionization were revealed to be tiny from the infrared to the soft X-ray domains, and all non-dipole observations reported so far were limited to single-pulse, single-colour measurements. Here we advance attosecond time-resolved spectroscopy into the non-dipole interaction regime. Using a self-referenced attosecond photoelectron interferometry on helium atoms, we resolve the electron subcycle motion along the light propagation direction in the 15 pm range driven by the magnetic component of a near-infrared laser field. Furthermore, we measure a time delay of 15 ± 10 as between the electric-dipole and electric-quadrupole transitions by resolving the asymmetry of the photoelectron forward–backward yields with attosecond resolution. These fundamental findings are supported by ab initio calculations based on the non-dipole time-dependent Schrödinger equation.

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Fig. 1: Attosecond non-dipole photoelectron interferometry.
Fig. 2: Photoelectron energy spectra in the forward and backward propagation directions.
Fig. 3: Magnetic-field-induced forward–backward shift of interference fringes.
Fig. 4: Electric-quadrupole-induced time-delay-dependent forward/backward asymmetry of spectral amplitude.

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Data availability

The data generated and analysed in this study are available via the ETH Zurich Research Collection at https://doi.org/10.3929/ethz-b-000638773.

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Acknowledgements

We thank A. Schneider and M. Seiler for their technical support. This work was supported by the National Key Research and Development Program of China (grant no. 2019YFA0308 300), and the National Natural Science Foundation of China (grant nos. 12374264, 12021004, 12074265 and 91950202). M.H. acknowledges the funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement no. 801459 (FP-RESOMUS). This work was supported by ETH Zürich and the Swiss National Science Foundation through projects 200021_172946 and the NCCR-MUST. The computing work in this paper is supported by the Public Service Platform of High Performance Computing provided by Network and Computing Center of Huazhong University of Science and Technology (HUST).

Author information

Author notes

  1. These authors contributed equally: Jintai Liang, Meng Han and Yijie Liao.

Authors and Affiliations

  1. Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, Wuhan, China

    Jintai Liang, Yijie Liao, Yueming Zhou & Peixiang Lu

  2. Laboratorium für Physikalische Chemie, ETH Zürich, Zürich, Switzerland

    Meng Han, Jia-bao Ji, Chung Sum Leung, Kiyoshi Ueda & Hans Jakob Wörner

  3. J. R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, KS, USA

    Meng Han

  4. Institute of Quantum Precision Measurement, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen, China

    Wei-Chao Jiang

  5. Department of Chemistry, Tohoku University, Sendai, Japan

    Kiyoshi Ueda

  6. School of Physical Science and Technology, ShanghaiTech University, Shanghai, China

    Kiyoshi Ueda

  7. Optics Valley Laboratory, Hubei, China

    Peixiang Lu

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Contributions

Y.Z. and M.H. conceived the study. M.H. performed the experiments with the support of J.-b.J. and C.S.L. The data were analysed and interpreted by J.L., Y.L., Y.Z., M.H., K.U. and H.J.W. Simulations were implemented by J.L. and Y.L., with the help of W.-C.J. This work was supervised by Y.Z., P.L. and H.J.W. The paper was written by J.L., M.H., Y.Z., K.U. and H.J.W., with the input of all co-authors.

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Correspondence to Meng Han, Yueming Zhou or Peixiang Lu.

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Extended data

Extended Data Fig. 1 Calibration of IR intensity.

Measured photoelectron spectrum as a function of the time delay between the XUV and IR fields without the attosecond phase stability. The white arrow denotes the maximal energy shift, which is employed to determine the IR peak intensity.

Extended Data Fig. 2 Data analysis.

a Measured photoelectron spectra at θ = 70∘ (blue solid line) and θ = 110∘ (purple line) for helium ionization by the combination of XUV and IR fields. The dashed line represents the fitted background of the photoelectron spectra. b The photoelectron spectra by subtracting the background from the measured spectra. c The comparison of the spectra and the Gaussian fitting of the peaks (green dashed lines). d-f The Gaussian fitting for the photoelectron spectra with the window width of δE = 0.015 (d), δE = 0.02 (e) and δE = 0.025 (f). The vertical dashed lines in c-f mark the peak positions determined by the Gaussian fitting.

Extended Data Fig. 3 Supplementary experimental data.

a-c Measured time-delay averaged photoelectron spectra for photoionization of helium by the combination of the XUV and IR fields at different angles. d-f The same as a-c but at the different time delays for θ = 70∘ (blue solid line) and θ = 110∘ (purple line). The green dashed lines show the Gaussian fitting of the peaks. The vertical dashed lines mark the peak positions determined by the Gaussian fitting.

Extended Data Fig. 4 Measured delay- and angle-resolved photoelectron spectrum.

a Measured delay- and angle-resolved photoelectron spectrum for peak1 (Ek = [10.0, 11.4] eV). b Normalized photoelectron spectrum, \({{{\mathscr{I}}}}(\theta ,\tau ;{E}_{k})={{{\mathscr{M}}}}(\theta ,\tau ;{E}_{k})-\overline{{{{\mathscr{M}}}}}(\theta ;{E}_{k})\), shown in Eq.(6) of the main text. c The asymmetry of the normalized photoelectron spectrum, \({{{\mathscr{I}}}}(\theta ,\tau ;{E}_{k})-{{{\mathscr{I}}}}(\pi -\theta ,\tau ;{E}_{k})\).

Extended Data Fig. 5 Supplementary photoelectron angular distribution and asymmetric distribution.

a Measured delay- and angle-resolved photoelectron spectrum for Ek = [6.7, 8.4] eV. b-d Same as Fig. 4b–d of main text, but for the results of Ek = [6.7, 8.4] eV. e-h Same as a-d, but for the results of Ek = [13.1, 14.8] eV.

Extended Data Fig. 6 TDSE results of the photoelectron energy spectra.

a, Vector potentials of the laser pulses in our calculations. The wavelength and the intensity of the IR field are 800 nm and 5.88 × 1013W/cm2. The centre frequency of XUV pulse is ωXUV=2 a.u., and its intensity is 1 × 1013W/cm2. b c, Photoelectron energy spectra for He ionization obtained by numerically solving TDSE. The blue and red lines are the results for θ = π/4 and θ = 3π/4, respectively. b and c display the results for XUV pulse alone and combination of XUV and IR fields, respectively.

Extended Data Fig. 7 Light-induced electron displacement predicted by nSFA and TDSE.

a Displacement ΔαM(τ) as a function of the time delay between the IR and XUV fields. The intensity and wavelength for the IR field is I = 5.88 × 1013W/cm2 and 800 nm, respectively. The final momentum of the electron is \({p}_{z}=p\sin \theta\) = 1.0 a.u. b The forward-backward momentum shift as a function of the emission angle. c, The forward-backward (θ = 70∘/110∘) momentum shift as a function of the time-delay between the XUV and IR pulses. In b and c the photoelectron energy is 11eV. The solid lines are the prediction from nSFA.

Extended Data Fig. 8 Interference picture.

Schematic representation of the interference between the electric dipole and quadrupole transitions. a The sketch of the PDD and PDQ channels. b The sketch of the PDD and PQD channels. The PDD produces photoelectron with partial waves s and d0. The PQD and PDQ channels produce photoelectrons with partial waves p±1 and f±1. Note that in each channel the transition amplitudes for p1 and p−1 are equal. It is the same for f1 and f−1.

Extended Data Fig. 9 Photoionization time delays.

a CC phase of the electric quadrupole CC transitions. The solid line represents the analytical expression of the CC phase as given in Eq.((33)). The markers represents the results obtained by numerical method. The symbols ‘ × ’ and ‘ + ’ represent the CC phase of electric quadrupole transition for final state with the angular momentum of the final state as l = 1 (p) and l = 3 (f), respectively. b Time delays extracted from the oscillation of the asymmetry parameter by considering different interfering paths, as labelled in the legend. c Times delays extracted from the oscillation of the asymmetry parameters (lines with rhombuses) and photoelectron yield (lines with circles). The solid and dashed lines represent the results from TDSE calculations and obtained by the lowest-order perturbation theory, respectively. d Time delay between the electric-dipole and -quadrupole transitions ΔτQ−D as a function of photoelectron energy. The solid and dashed lines represent the results from TDSE calculations and obtained by the lowest-order perturbation theory, respectively. The symbols with the error bar are the experimental results. The error bar represents the 95% confidence level by the sine fitting.

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Liang, J., Han, M., Liao, Y. et al. Attosecond-resolved non-dipole photoionization dynamics. Nat. Photon. 18, 311–317 (2024). https://doi.org/10.1038/s41566-023-01349-z

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