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Real-time observation of valence electron motion


The superposition of quantum states drives motion on the atomic and subatomic scales, with the energy spacing of the states dictating the speed of the motion. In the case of electrons residing in the outer (valence) shells of atoms and molecules which are separated by electronvolt energies, this means that valence electron motion occurs on a subfemtosecond to few-femtosecond timescale (1 fs = 10−15 s). In the absence of complete measurements, the motion can be characterized in terms of a complex quantity, the density matrix. Here we report an attosecond pump–probe measurement of the density matrix of valence electrons in atomic krypton ions1. We generate the ions with a controlled few-cycle laser field2 and then probe them through the spectrally resolved absorption of an attosecond extreme-ultraviolet pulse3, which allows us to observe in real time the subfemtosecond motion of valence electrons over a multifemtosecond time span. We are able to completely characterize the quantum mechanical electron motion and determine its degree of coherence in the specimen of the ensemble. Although the present study uses a simple, prototypical open system, attosecond transient absorption spectroscopy should be applicable to molecules and solid-state materials to reveal the elementary electron motions that control physical, chemical and biological properties and processes.

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Figure 1: Probing intra-atomic electron motion by attosecond absorption spectroscopy.
Figure 2: Transient absorption spectra of krypton ions.
Figure 3: Build-up of electronic coherence in Kr + produced by optical field ionization (theory).
Figure 4: Attosecond absorption spectroscopy reveals intra-atomic electron wave-packet motion in Kr+.
Figure 5: Reconstruction of valence-shell electron wave-packet motion.


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We thank U. Kleineberg, M. Hofstetter and M. Fiess for invaluable contributions. This work was supported by the Max Planck Society, the Nobel Program of King Saud University and the DFG Cluster of Excellence: Munich Centre for Advanced Photonics ( E.G. acknowledges a Marie-Curie Reintegration grant (MERG-CT-2007-208643). A.W., S.Z. and M.F.K. acknowledge support by the Emmy Noether programme of the DFG. Z.-H.L., T.P. and S.R.L. acknowledge support from the Air Force Office of Scientific Research (FA9550-04-1-0242), the National Science Foundation (CHE-0742662 and EEC-0310717) and the Director, Office of Science, Office of Basic Energy Sciences, US Department of Energy (DE-AC02-05-CH11231). T.P. acknowledges support from the MPRG program of the MPG. R.S. is supported by the Office of Basic Energy Sciences, Office of Science, US Department of Energy (DE-AC02-06CH11357). Part of this work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory (DE-AC52-07NA27344). S.R.L. gratefully acknowledges appointment as a Miller Research Professor in the Miller Institute for Basic Research in Science.

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E.G., Z.-H.L. and A.W. conceived and designed the experiments; E.G., A.W. and Z.-H.L. performed the measurements; A.W., Z.-H.L., E.G., T.P., S.Z., A.M.A., M.F.K., S.R.L and F.K. evaluated, analysed and interpreted the experimental data; and R.S., N.R. and V.S.Y. performed the theoretical modelling. All authors discussed the results and contributed to the final manuscript.

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Correspondence to Eleftherios Goulielmakis, Stephen R. Leone or Ferenc Krausz.

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Goulielmakis, E., Loh, ZH., Wirth, A. et al. Real-time observation of valence electron motion. Nature 466, 739–743 (2010).

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