Attosecond nonlinear polarization and light–matter energy transfer in solids


Electric-field-induced charge separation (polarization) is the most fundamental manifestation of the interaction of light with matter and a phenomenon of great technological relevance. Nonlinear optical polarization1,2 produces coherent radiation in spectral ranges inaccessible by lasers and constitutes the key to ultimate-speed signal manipulation. Terahertz techniques3,4,5,6,7,8 have provided experimental access to this important observable up to frequencies of several terahertz9,10,11,12,13. Here we demonstrate that attosecond metrology14 extends the resolution to petahertz frequencies of visible light. Attosecond polarization spectroscopy allows measurement of the response of the electronic system of silica to strong (more than one volt per ångström) few-cycle optical (about 750 nanometres) fields. Our proof-of-concept study provides time-resolved insight into the attosecond nonlinear polarization and the light–matter energy transfer dynamics behind the optical Kerr effect and multi-photon absorption. Timing the nonlinear polarization relative to the driving laser electric field with sub-30-attosecond accuracy yields direct quantitative access to both the reversible and irreversible energy exchange between visible–infrared light and electrons. Quantitative determination of dissipation within a signal manipulation cycle of only a few femtoseconds duration (by measurement and ab initio calculation) reveals the feasibility of dielectric optical switching at clock rates above 100 terahertz. The observed sub-femtosecond rise of energy transfer from the field to the material (for a peak electric field strength exceeding 2.5 volts per ångström) in turn indicates the viability of petahertz-bandwidth metrology with a solid-state device.

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Figure 1: Attosecond spectroscopy of the nonlinear polarization.
Figure 2: Sub-femtosecond-resolved optical Kerr effect in silica.
Figure 3: The nonlinear optical polarization response of silica at critical field strengths.
Figure 4: Energy exchange between strong optical fields and electrons in real time.


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We acknowledge discussions with M. Stockman and V. Apalkov. This work was supported by the Max Planck Society and the Deutsche Forschungsgemeinschaft Cluster of Excellence: Munich Centre for Advanced Photonics ( M.S. was supported by a Marie Curie International Outgoing Fellowship (FP7-PEOPLE-2011-IOF). E.M.B. acknowledges funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement number 290605 (PSI-FELLOW/COFUND) and from the Swiss National Science Foundation through NCCR MUST. This research is based upon work supported by the US Air Force Office of Scientific Research under award number FA9550-16-1-0073 and used computational resources of the K computer provided by the RIKEN Advanced Institute for Computational Science through the HPCI System Research project (Project ID: hp140103).

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F.K. and M.S. initiated, conceived and supervised the study. A.S. and E.M.B. developed the experimental method. A.S., E.M.B. and C.J. (in close cooperation with T.L., O.R., M.J., W.S. and V.S.) prepared and performed the experiment. S.A.S., H.F., K.Y. and N.K. accomplished the theoretical modelling. A.S., E.M.B., V.S.Y., R.K., N.K., M.S. and F.K. analysed and interpreted the experimental data. All authors discussed the results and contributed to the final manuscript.

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Correspondence to M. Schultze or F. Krausz.

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Sommer, A., Bothschafter, E., Sato, S. et al. Attosecond nonlinear polarization and light–matter energy transfer in solids. Nature 534, 86–90 (2016).

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