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All data in this study are available from the corresponding author upon request.
References
Krausz, F. & Ivanov, M. Attosecond physics. Rev. Mod. Phys. 81, 163–234 (2009).
Article ADS Google Scholar
Lewenstein, M., Balcou, Ph., Ivanov, M. Yu., L’huillier, A. & Corkum, P. B. Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49, 2117–2132 (1994).
Article ADS CAS PubMed Google Scholar
Antoine, P., L’huillier, A. & Lewenstein, M. Attosecond pulse trains using high–order harmonics. Phys. Rev. Lett. 77, 1234–1237 (1996).
Article ADS CAS PubMed Google Scholar
Paul, P. M. et al. Observation of a train of attosecond pulses from high harmonic generation. Science 292, 1689–1692 (2001).
Article ADS CAS PubMed Google Scholar
Hentschel, M. et al. Attosecond metrology. Nature 414, 509–513 (2001).
Article ADS CAS PubMed Google Scholar
Maroju, P. K. et al. Attosecond pulse shaping using a seeded free-electron laser. Nature 578, 386–391 (2020).
Article ADS CAS PubMed Google Scholar
Maroju, P. K. et al. Attosecond coherent control of electronic wave packets in two-colour photoionization using a novel timing tool for seeded free-electron laser. Nat. Photon. 17, 200–207 (2023).
Article ADS CAS Google Scholar
Huang, S. et al. Generating single-spike hard X-ray pulses with nonlinear bunch compression in free-electron lasers. Phys. Rev. Lett. 119, 154801 (2017).
Article ADS CAS PubMed Google Scholar
Marinelli, A. et al. Experimental demonstration of a single-spike hard-X-ray free-electron laser starting from noise. Appl. Phys. Lett. 111, 151101 (2017).
Article ADS Google Scholar
Malyzhenkov, A. et al. Single-and two-color attosecond hard X-ray free-electron laser pulses with nonlinear compression. Phys. Rev. Res. 2, 042018(R) (2020).
Article Google Scholar
Zhang, Z. et al. Experimental demonstration of enhanced self-amplified spontaneous emission by photocathode temporal shaping and self-compression in a magnetic wiggler. New J. Phys. 22, 083030 (2020).
Article ADS Google Scholar
Duris, J. et al. Tunable isolated attosecond X-ray pulses with gigawatt peak power from a free-electron laser. Nat. Photon. 14, 30–36 (2020).
Article ADS MathSciNet CAS Google Scholar
Prat, E. et al. Coherent sub-femtosecond soft X-ray free-electron laser pulses with nonlinear compression. APL Photon. 8, 111302 (2023).
Article ADS Google Scholar
Li, S. et al. “Beam à la carte”: laser heater shaping for attosecond pulses in a multiplexed X-ray free-electron laser. Appl. Phys. Lett. 125, 191101 (2024).
Article ADS CAS Google Scholar
Yan, J. et al. Terawatt-attosecond hard X-ray free-electron laser at high repetition rate. Nat. Photon. 18, 1293–1298 (2024).
Article ADS CAS Google Scholar
Inoue, I. et al. Experimental demonstration of attosecond hard X-ray pulses. Nat. Photon. https://doi.org/10.1038/s41566-026-02026-7 (2026).
Prat, E., Malyzhenkov, A., Orlandi, G. L., Weilbach, T. & Reiche, S. Enhanced generation of single-spike hard X-ray free-electron laser pulses with lower charge and shorter electron beams in the injector. Phys. Rev. Res. 7, L042060 (2025).
Article CAS Google Scholar
Li, S. et al. Attosecond coherent electron motion in Auger-Meitner decay. Science 375, 285–290 (2022).
Article ADS CAS PubMed Google Scholar
Driver, T. et al. Attosecond delays in X-ray molecular ionization. Nature 632, 762–767 (2024).
Article ADS CAS PubMed Google Scholar
Guo, Z. et al. Experimental demonstration of attosecond pump–probe spectroscopy with an X-ray free-electron laser. Nat. Photon.18, 691–697 (2024).
Article ADS CAS Google Scholar
Li, S. et al. Attosecond-pump attosecond-probe X-ray spectroscopy of liquid water. Science 383, 1118–1122 (2024).
Article ADS CAS PubMed Google Scholar
Hartmann, N. et al. Attosecond time–energy structure of X-ray free-electron laser pulses. Nat. Photon. 12, 215–220 (2018).
Article ADS CAS Google Scholar
Li, S. et al. Characterizing isolated attosecond pulses with angular streaking. Opt. Express 26, 4531–4547 (2018).
Article ADS CAS PubMed Google Scholar
Franz, P. et al. Terawatt-scale attosecond X-ray pulses from a cascaded superradiant free-electron laser. Nat. Photon. 18, 698–703 (2024).
Article ADS CAS Google Scholar
Rohringer, N. et al. Atomic inner-shell X-ray laser at 1.46 nanometres pumped by an X-ray free-electron laser. Nature 481, 488–491 (2012).
Article ADS CAS PubMed Google Scholar
Yoneda, H. et al. Atomic inner-shell laser at 1.5-ångström wavelength pumped by an X-ray free-electron laser. Nature 524, 446–449 (2015).
Article ADS CAS PubMed Google Scholar
Driver, T. et al. Attosecond response of molecules to impulsive ionization. Nat. Phys. 22, 1459–1466 (2026).
Mukamel, S. Principles of Nonlinear Optical Spectroscopy Vol. 6 (Oxford Univ. Press, 1995).
Sun, Y., Li, H., Ichii, Y. & Zhu, D. An ultrastable hard X-ray attosecond split-delay line. Preprint at arxiv.org/abs/2505.06865 (2025).
Ding, Y., Huang, Z. & Ocko, S. A. Transverse-coherence properties of the fel at the lcls. In Proc. FEL2010, 151–154. (JACoW Publishing, 2010).
Gutt, C. et al. Single shot spatial and temporal coherence properties of the slac linac coherent light source in the hard X-ray regime. Phys. Rev. Lett. 108, 024801 (2012).
Article ADS CAS PubMed Google Scholar
Ghimire, S. et al. Nonsequential two-photon absorption from the K shell in solid zirconium. Phys. Rev. A 94, 043418 (2016).
Article ADS Google Scholar
Tamasaku, K. et al. Nonlinear spectroscopy with X-ray two-photon absorption in metallic copper. Phys. Rev. Lett. 121, 083901 (2018).
Article ADS CAS PubMed Google Scholar
Osaka, T. et al. Hard X-ray intensity autocorrelation using direct two-photon absorption. Phys. Rev. Res. 4, L012035 (2022).
Article CAS Google Scholar
Göppert-Mayer, M. Über Elementarakte mit zwei Quantensprüngen. Annal. Phys. 401, 273–294 (1931).
Article ADS Google Scholar
Zhu, D. et al. A single-shot transmissive spectrometer for hard X-ray free electron lasers. Appl. Phys. Lett. 101, 034103 (2012).
Article ADS Google Scholar
Bonifacio, R., De Salvo, L., Pierini, P., Piovella, N. & Pellegrini, C. Spectrum, temporal structure, and fluctuations in a high-gain free-electron laser starting from noise. Phys. Rev. Lett. 73, 70–73 (1994).
Article ADS CAS PubMed Google Scholar
Pellegrini, C., Marinelli, A. & Reiche, S. The physics of X-ray free-electron lasers. Rev. Mod. Phys. 88, 015006 (2016).
Article ADS Google Scholar
Baxevanis, P., Duris, J., Huang, Z. & Marinelli, A. Time-domain analysis of attosecond pulse generation in an X-ray free-electron laser. Phys. Rev. Accel. Beams 21, 110702 (2018).
Article ADS CAS Google Scholar
Shwartz, S. et al. X-ray second harmonic generation. Phys. Rev. Lett. 112, 163901 (2014).
Article ADS CAS PubMed Google Scholar
Osaka, T. et al. Background-free intensity autocorrelation for femtosecond X-ray pulses. Phys. Rev. Lett. 136, 195002 (2026).
Article CAS PubMed Google Scholar
Zhu, D. & Reis, D. A. Attosecond X-ray laser vision. Nat. Photon. 18, 1232–1233 (2024).
Article ADS CAS Google Scholar
Alexander, O. et al. Attosecond impulsive stimulated X-ray Raman scattering in liquid water. Sci. Adv. 10, eadp0841(2024).
Article PubMed PubMed Central Google Scholar
Linker, T. M. et al. Attosecond inner-shell lasing at ångström wavelengths. Nature 642, 934–940 (2025).
Article ADS CAS PubMed PubMed Central Google Scholar
Simmermacher, M. et al. Real-space imaging of the electron-pair density hole in molecular Auger–Meitner decay. Nat. Phys. 22, 1473–1478 (2026).
Article CAS PubMed PubMed Central Google Scholar
Volkov, M. et al. Attosecond screening dynamics mediated by electron localization in transition metals. Nat. Phys. 15, 1145–1149 (2019).
Article CAS Google Scholar
Schumacher, Z. et al. Ultrafast electron localization and screening in a transition metal dichalcogenide. Proc. Natl. Acad. Sci. USA 120, e2221725120(2023).
Article CAS PubMed PubMed Central Google Scholar
Varillas, R.B. et al. Roadmap on attosecond science. Preprint at arxiv.org/abs/2604.15085 (2026).
Alonso-Mori, R. et al. The X-ray correlation spectroscopy instrument at the linac coherent light source. J. Synchrotron Radiat. 22, 508–513 (2015).
Article CAS PubMed PubMed Central Google Scholar
Mozzanica, A. et al. Characterization results of the JUNGFRAU full scale readout ASIC. J. Instrum. 11, C02047 (2016).
Article Google Scholar
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Acknowledgements
Y.S. acknowledges the discussions with M. H. Seaberg in delay line designs and sample setup.
Funding
Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under contract no. DE-AC02-76SF00515. A.M. and R.R. acknowledge funding from the DOE-BES Accelerator and Detector Research Program. D.A.R., S.G., C.O.-S., J.P.C. and M.F.K. were supported by US Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division through the AMOS program. I.I. was supported by the Japan Society for the Promotion of Science KAKENHI and JST PRESTO (24K21199, 26H02025, P-MJPR24J1).
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Sun, Y., Robles, R., Linker, T.M. et al. Hard X-ray attosecond metrology. Nature (2026). https://doi.org/10.1038/s41586-026-11245-5
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DOI: https://doi.org/10.1038/s41586-026-11245-5