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# Coherent control of ultrafast extreme ultraviolet transient absorption

## Abstract

Ultrafast extreme ultraviolet (XUV) transient absorption is the process by which atoms and molecules absorb light on a timescale faster than the lifetime of the states involved. Coherent control uses quantum coherences to manipulate quantum pathways in light–matter interactions. Here we combine the two. We show that we can control the absorption spectral lineshape, changing it from Lorentzian to Fano to inverted Lorentzian and back again. The control is achieved by creating quantum coherence in the ground electronic state of hydrogen molecules, long before the arrival of the ultrafast XUV pulse. We show that the absorption can become negative at 12 eV, which is the optical gain. These observations provide new insights into the control of spectral lineshapes and open the way for achieving lasing without inversion in the XUV spectral range.

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## Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

## Code availability

The code used in this study is available from the corresponding authors upon reasonable request.

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## Acknowledgements

We thank D. Crane and R. Kroeker for technical support. We acknowledge fruitful discussions with A. Korobenko, G. Xin, A. Stolow, M. Spanner, B. Bernhardt and V. Schuster. This research is supported by the NSERC Discovery Grant program (RGPIN-327147-2012; D.M.V.), and by the US Army Research Office through award W911NF-14-1-0383 (D.M.V.). We acknowledge support of the Joint Centre for Extreme Photonics (P.B.C. and D.M.V.), the DFG (grant no. MI 2434/1-1; Y.M.), and the start-up grant of ShanghaiTech University (P.P.).

## Author information

Authors

### Contributions

P.P. and D.M.V. conceived and planned the experiment. P.P., Y.M. and X.D. conducted the measurements. P.P. and D.M.V. analysed and interpreted the data. M.L. and M.B. provided the theoretical supporting calculations. A.Y.N., P.B.C. and D.M.V. supervised the project. P.P. wrote the manuscript, with inputs from all the authors.

### Corresponding authors

Correspondence to Peng Peng or D. M. Villeneuve.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Photonics thanks the anonymous reviewers for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1–10 and Sections 1–5.

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Peng, P., Mi, Y., Lytova, M. et al. Coherent control of ultrafast extreme ultraviolet transient absorption. Nat. Photon. 16, 45–51 (2022). https://doi.org/10.1038/s41566-021-00907-7

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• DOI: https://doi.org/10.1038/s41566-021-00907-7