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Multi-petahertz electronic metrology

Abstract

The frequency of electric currents associated with charge carriers moving in the electronic bands of solids determines the speed limit of electronics and thereby that of information and signal processing1. The use of light fields to drive electrons promises access to vastly higher frequencies than conventionally used, as electric currents can be induced and manipulated on timescales faster than that of the quantum dephasing of charge carriers in solids2. This forms the basis of terahertz (1012 hertz) electronics in artificial superlattices2, and has enabled light-based switches3,4,5 and sampling of currents extending in frequency up to a few hundred terahertz. Here we demonstrate the extension of electronic metrology to the multi-petahertz (1015 hertz) frequency range. We use single-cycle intense optical fields (about one volt per ångström) to drive electron motion in the bulk of silicon dioxide, and then probe its dynamics by using attosecond (10−18 seconds) streaking6,7 to map the time structure of emerging isolated attosecond extreme ultraviolet transients and their optical driver. The data establish a firm link between the emission of the extreme ultraviolet radiation and the light-induced intraband, phase-coherent electric currents that extend in frequency up to about eight petahertz, and enable access to the dynamic nonlinear conductivity of silicon dioxide. Direct probing, confinement and control of the waveform of intraband currents inside solids on attosecond timescales establish a method of realizing multi-petahertz coherent electronics. We expect this technique to enable new ways of exploring the interplay between electron dynamics and the structure of condensed matter on the atomic scale.

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Figure 1: Attosecond pulse metrology in bulk SiO2.
Figure 2: Interband versus intraband dynamics in SiO2.
Figure 3: Control of multi-petahertz currents in SiO2.
Figure 4: Phase coherence of multi-petahertz currents and the dynamic conductivity of SiO2.

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References

  1. Caulfield, H. J. & Dolev, S. Why future supercomputing requires optics. Nat. Photon. 4, 261–263 (2010)

    Article  CAS  Google Scholar 

  2. Leo, K. High-Field Transport in Semiconductor Superlattices (Springer, 2003)

  3. Schiffrin, A. et al. Optical-field-induced current in dielectrics. Nature 493, 70–74 (2012)

    Article  CAS  ADS  Google Scholar 

  4. Krüger, M., Schenk, M. & Hommelhoff, P. Attosecond control of electrons emitted from a nanoscale metal tip. Nature 475, 78–81 (2011)

    Article  Google Scholar 

  5. Somma, C., Reimann, K., Flytzanis, C., Elsaesser, T. & Woerner, M. High-field terahertz bulk photovoltaic effect in lithium niobate. Phys. Rev. Lett. 112, 146602 (2014)

    Article  CAS  ADS  Google Scholar 

  6. Itatani, J. et al. Attosecond streak camera. Phys. Rev. Lett. 88, 173903 (2002)

    Article  CAS  ADS  Google Scholar 

  7. Goulielmakis, E. et al. Direct measurement of light waves. Science 305, 1267–1269 (2004)

    Article  CAS  ADS  Google Scholar 

  8. Braun, F. Electrical oscillations and wireless telegraphy. In Nobel Lectures, Physics 1901–1921 (Elsevier, 1967)

  9. Gaal, P. et al. Internal motions of a quasiparticle governing its ultrafast nonlinear response. Nature 450, 1210–1213 (2007)

    Article  CAS  ADS  Google Scholar 

  10. Huber, R. et al. How many-particle interactions develop after ultrafast excitation of an electron-hole plasma. Nature 414, 286–289 (2001)

    Article  CAS  ADS  Google Scholar 

  11. Gudde, J., Rohleder, M., Meier, T., Koch, S. W. & Hofer, U. Time-resolved investigation of coherently controlled electric currents at a metal surface. Science 318, 1287–1291 (2007)

    Article  CAS  ADS  Google Scholar 

  12. Liu, C. D. et al. Carrier-envelope phase effects of a single attosecond pulse in two-color photoionization. Phys. Rev. Lett. 111, 123901 (2013)

    Article  ADS  Google Scholar 

  13. Ghimire, S. et al. Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7, 138–141 (2011)

    Article  CAS  Google Scholar 

  14. Luu, T. T. et al. Extreme ultraviolet high-harmonic spectroscopy of solids. Nature 521, 498–502 (2015)

    Article  CAS  ADS  Google Scholar 

  15. Vampa, G. et al. Linking high harmonics from gases and solids. Nature 522, 462–464 (2015)

    Article  CAS  ADS  Google Scholar 

  16. Hohenleutner, M. et al. Real-time observation of interfering crystal electrons in high-harmonic generation. Nature 523, 572–575 (2015)

    Article  CAS  ADS  Google Scholar 

  17. Schubert, O. et al. Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations. Nat. Photon. 8, 119–123 (2014)

    Article  CAS  ADS  Google Scholar 

  18. Wu, M. X., Ghimire, S., Reis, D. A., Schafer, K. J. & Gaarde, M. B. High-harmonic generation from Bloch electrons in solids. Phys. Rev. A 91, 043839 (2015)

    Article  ADS  Google Scholar 

  19. Kira, M. & Koch, S. W. Semiconductor Quantum Optics (Cambridge Univ. Press, 2012)

  20. Golde, D., Meier, T. & Koch, S. W. High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations. Phys. Rev. B 77, 075330 (2008)

    Article  ADS  Google Scholar 

  21. Haug, H. & Koch, S. W. Quantum Theory of the Optical and Electronic Properties of Semiconductors 5th edn (World Scientific, 2009)

  22. Schultze, M. et al. Attosecond band-gap dynamics in silicon. Science 346, 1348–1352 (2014)

    Article  CAS  ADS  Google Scholar 

  23. McDonald, C. R., Vampa, G., Corkum, P. B. & Brabec, T. Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals. Phys. Rev. A 92, 033845 (2015)

    Article  ADS  Google Scholar 

  24. Tamaya, T., Ishikawa, A., Ogawa, T. & Tanaka, K. Diabatic mechanisms of higher-order harmonic generation in solid-state materials under high-intensity electric fields. Phys. Rev. Lett. 116, 016601 (2016)

    Article  CAS  ADS  Google Scholar 

  25. Hassan, M. T. et al. Optical attosecond pulses and tracking the nonlinear response of bound electrons. Nature 530, 66–70 (2016)

    Article  CAS  ADS  Google Scholar 

  26. Mairesse, Y. & Quere, F. Frequency-resolved optical gating for complete reconstruction of attosecond bursts. Phys. Rev. A 71, 011401(R) (2005)

    Article  ADS  Google Scholar 

  27. Corkum, P. B. Plasma perspective on strong-field multiphoton ionization. Phys. Rev. Lett. 71, 1994–1997 (1993)

    Article  CAS  ADS  Google Scholar 

  28. Goulielmakis, E. et al. Single-cycle nonlinear optics. Science 320, 1614–1617 (2008)

    Article  CAS  ADS  Google Scholar 

  29. Benko, C. et al. Extreme ultraviolet radiation with coherence time greater than 1 s. Nat. Photon. 8, 530–536 (2014)

    Article  CAS  ADS  Google Scholar 

  30. Mics, Z. et al. Thermodynamic picture of ultrafast charge transport in graphene. Nat. Commun. 6, 7655 (2015)

    Article  CAS  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by a European Research Council grant (Attoelectronics-258501), the Deutsche Forschungsgemeinschaft Cluster of Excellence, Munich Centre for Advanced Photonics, the Max Planck Society and the European Research Training Network MEDEA.

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Authors

Contributions

M.G. and M.Z. conducted the experiments; E.G. planned the experiments and supervised the project; M.G., H.L., T.K., T.T.L. and A.G. conducted the simulations; and M.G. and E.G. interpreted the experimental data and contributed to the preparation of the manuscript.

Corresponding author

Correspondence to E. Goulielmakis.

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The authors declare no competing financial interests.

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Reviewer Information

Nature thanks M. Chini, U. Höfer and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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This file contains Supplementary Text and Data 1-11, Supplementary Figures 1-21 and additional references. (PDF 3595 kb)

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Garg, M., Zhan, M., Luu, T. et al. Multi-petahertz electronic metrology. Nature 538, 359–363 (2016). https://doi.org/10.1038/nature19821

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