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Amplification of intense light fields by nearly free electrons

A Publisher Correction to this article was published on 18 June 2018

This article has been updated


Light can be used to modify and control properties of media, as in the case of electromagnetically induced transparency or, more recently, for the generation of slow light or bright coherent extreme ultraviolet and X-ray radiation. Particularly unusual states of matter can be created by light fields with strengths comparable to the Coulomb field that binds valence electrons in atoms, leading to nearly free electrons oscillating in the laser field and yet still loosely bound to the core1,2. These are known as Kramers–Henneberger states3, a specific example of laser-dressed states2. Here, we demonstrate that these states arise not only in isolated atoms4,5, but also in rare gases, at and above atmospheric pressure, where they can act as a gain medium during laser filamentation. Using shaped laser pulses, gain in these states is achieved within just a few cycles of the guided field. The corresponding lasing emission is a signature of population inversion in these states and of their stability against ionization. Our work demonstrates that these unusual states of neutral atoms can be exploited to create a general ultrafast gain mechanism during laser filamentation.

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Fig. 1: Kramers–Henneberger potential and simulated absorption spectra of an Ar atom dressed by a strong IR pulse.
Fig. 2: Forward emission spectrum from different pulse shapes filamenting in argon at 9 bar.
Fig. 3: A comparison between simulated and experimental emission spectra from a 10 fs rise, 10 fs plateau, 10 fs decay laser pulse shape.
Fig. 4: The forward emission spectra of trapezoid pulse shapes in krypton at 9 bar, with increasing pulse energy.

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Change history

  • 18 June 2018

    In the version of this Letter originally published, the units of the bottom three values in the Fig. 1d legend were incorrect; they should have been W cm–2. This has now been corrected.


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The authors acknowledge the valuable contributions of M. Moret, for advanced technical assistance with the experimental set-up, S. Courvoisier, for technical assistance with graphical formatting, and L. Woeste, for constructive advice. J.P, J.G. and S.H. acknowledge funding from SNF NCCR MUST grant. J.P and J.K acknowledge funding from ERC grant Filatmo. M.M. acknowledges funding from MHV fellowship grant number: PMPDP2-145444 and NCCR MUST Women's Postdoc Awards. M.I. acknowledges the support of the DFG QUTIF grant number IV 152/7-1.

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Authors and Affiliations



J-P.W. and M.I. conceived the experiment. M.I., F.M., M.R., T.B. and O.S. performed the calculations and developed the theoretical interpretation. N.B. performed filamentation propagation simulations. M.M., S.H., J.K. and J.G. designed the experimental apparatus. A.P. and A.L. designed and implemented the pulse-shaping process. M.M., A.P., A.L, J.G. and S.H. performed the experiment and pulse measurements. M.M., A.P. and J.K. analysed and processed the experimental data. All authors contributed to the writing of the manuscript.

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Correspondence to Mary Matthews.

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Matthews, M., Morales, F., Patas, A. et al. Amplification of intense light fields by nearly free electrons. Nature Phys 14, 695–700 (2018).

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