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# Clocking Auger electrons

## Abstract

Intense X-ray free-electron lasers (XFELs) can rapidly excite matter, leaving it in inherently unstable states that decay on femtosecond timescales. The relaxation occurs primarily via Auger emission, so excited-state observations are constrained by Auger decay. In situ measurement of this process is therefore crucial, yet it has thus far remained elusive in XFELs owing to inherent timing and phase jitter, which can be orders of magnitude larger than the timescale of Auger decay. Here we develop an approach termed ‘self-referenced attosecond streaking’ that provides subfemtosecond resolution in spite of jitter, enabling time-domain measurement of the delay between photoemission and Auger emission in atomic neon excited by intense, femtosecond pulses from an XFEL. Using a fully quantum-mechanical description that treats the ionization, core-hole formation and Auger emission as a single process, the observed delay yields an Auger decay lifetime of $$2.2_{ - 0.3}^{ + 0.2}$$ fs for the KLL decay channel.

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• ### Artificial intelligence for online characterization of ultrashort X-ray free-electron laser pulses

Scientific Reports Open Access 24 October 2022

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## Data availability

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

## Code availability

Interested parties may contact A.K.K. (kazan356@rambler.ru) to obtain a copy of the simulation code used to verify the quantum treatment of Auger decay for our experiment.

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## Acknowledgements

We thank the staff at the Linac Coherent Light Source for preparing and operating the free-electron laser. Use of the Linac Coherent Light Source at the SLAC National Accelerator Laboratory, is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract number DE-AC02-76SF00515. D.C.H., M.M., R.S. and A.L.C. acknowledge funding through the Clusters of Excellence ‘The Hamburg Centre for Ultrafast Imaging’ (EXC 1074 project ID 194651731) and ‘CUI: Advanced Imaging of Matter’ (EXC 2056 project ID 390715994) of the Deutsche Forschungsgemeinschaft. J.T.C. acknowledges support by Science Foundation Ireland (grant number 16/RI/3696) and the SEAI (grant number 19/RDD/556). L.F.D. and C.R. acknowledge support from the National Science Foundation under grant number 1605042 and the US Department of Energy under grant DE-FG02-04ER15614. W.H. acknowledges financial support from a Marie Curie International Outgoing Fellowship and by the BaCaTeC programme. M.I. acknowledges funding from the Volkswagen Foundation within a Peter Paul Ewald-Fellowship. N.M.K. acknowledges hospitality and financial support from the theory group in cooperation with the SQS work package of European XFEL (Hamburg). A.R.M. and S.J. acknowledge funding through BMBF grant 05K16GU2. T. Mazza and M.M. acknowledge support by Deutsche Forschungsgemeinschaft Grant No. SFB925/A1. A.A.-H., C. Bostedt and G.D. were supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division under contract DE-AC02-06CH11357.

## Author information

Authors

### Contributions

L.F.D. and G.D. proposed the measurement of Auger lifetimes at the Linac Coherent Light Source and A.L.C. conceived the self-referenced streaking approach that enabled these measurements. The experiment and supporting experiments were performed by A.A.-H., C. Bostedt, J.B., H.B., M.B., A.C., S.C., A.L.C., R.C., J.T.C., L.F.D., G.D., K.F., I.G., D.C.H., M.C.H., M.I., R.K., A.R.M., F.T., W.H., T. Mazza, M.M., H.P., C.R., A.S., P.A.W., M.W. and K.Z. The mid-infrared laser for streaking was provided by M.C.H. and J.R. Electron beam tuning and diagnostics were provided by Y.D., T. Maxwell and C. Behrens D.C.H., C. Bostedt, W.H., N.M.K., A.K.K., M.M., H.S., G.D., C. Behrens and A.L.C. were primarily responsible for interpreting the experimental results. D.C.H., M.W., A.S., A.C., R.S., C.Behrens and A.L.C. analysed the data. N.M.K. and A.K.K. performed theoretical calculations. D.C.H., C. Bostedt, C. Behrens and A.L.C. were primarily responsible for writing the paper. All authors contributed to the final version of the manuscript.

### Corresponding authors

Correspondence to D. C. Haynes or A. L. Cavalieri.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Physics thanks Lorenz Cederbaum, Markus Guehr 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.

## Extended data

### Extended Data Fig. 1 Distribution of maximally streaked kinetic energies.

The changes in photoelectron kinetic energy in the sector corresponding to maximal streaking phase are plotted in the histogram. The red line shows the numerically determined least-square fit, from which we extract the peak of the distribution. By the normally distributed nature of timing jitter, highest number of shots will overlap at or near the peak of the pulse envelope, so that the peak of the histogram ought to correspond to those conditions.

### Extended Data Fig. 2 Generalized ellipse.

An arbitrary ellipse is shown (blue line) with the x- and y-axes highlighted (black lines), in addition to the parameters y1 and y2 (red dotted lines).

### Extended Data Fig. 3 Critical angle θc.

The measured value of y2 is shown (blue line) for a range of critical angles θc. The red dotted line represents the value of θc that was used in the final analysis.

### Extended Data Fig. 4 Sectors for calculation of the parameters y1 and y2.

A zoomed-in section of the data is shown. Overlaid on the density map, the red points are those contained in each of the sectors used to find the parameters. The black crosses represent the measured values y1 and y2, which are highlighted by the red dotted lines. From these data, y1 and y2 were measured at 7.9 eV and 20.9 eV respectively.

### Extended Data Fig. 5 The distribution of parameters y1 and y2.

The red dashed lines highlight the mean value and the black dashed lines display the statistical width of each distribution.

## Supplementary information

### Supplementary Information

Supplementary Discussion and Fig. 1.

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Haynes, D.C., Wurzer, M., Schletter, A. et al. Clocking Auger electrons. Nat. Phys. 17, 512–518 (2021). https://doi.org/10.1038/s41567-020-01111-0

• Accepted:

• Published:

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• DOI: https://doi.org/10.1038/s41567-020-01111-0

• ### Artificial intelligence for online characterization of ultrashort X-ray free-electron laser pulses

• Kristina Dingel
• Thorsten Otto
• Wolfram Helml

Scientific Reports (2022)