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.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Caulfield, H. J. & Dolev, S. Why future supercomputing requires optics. Nat. Photon. 4, 261–263 (2010)
Leo, K. High-Field Transport in Semiconductor Superlattices (Springer, 2003)
Schiffrin, A. et al. Optical-field-induced current in dielectrics. Nature 493, 70–74 (2012)
Krüger, M., Schenk, M. & Hommelhoff, P. Attosecond control of electrons emitted from a nanoscale metal tip. Nature 475, 78–81 (2011)
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)
Itatani, J. et al. Attosecond streak camera. Phys. Rev. Lett. 88, 173903 (2002)
Goulielmakis, E. et al. Direct measurement of light waves. Science 305, 1267–1269 (2004)
Braun, F. Electrical oscillations and wireless telegraphy. In Nobel Lectures, Physics 1901–1921 (Elsevier, 1967)
Gaal, P. et al. Internal motions of a quasiparticle governing its ultrafast nonlinear response. Nature 450, 1210–1213 (2007)
Huber, R. et al. How many-particle interactions develop after ultrafast excitation of an electron-hole plasma. Nature 414, 286–289 (2001)
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)
Liu, C. D. et al. Carrier-envelope phase effects of a single attosecond pulse in two-color photoionization. Phys. Rev. Lett. 111, 123901 (2013)
Ghimire, S. et al. Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7, 138–141 (2011)
Luu, T. T. et al. Extreme ultraviolet high-harmonic spectroscopy of solids. Nature 521, 498–502 (2015)
Vampa, G. et al. Linking high harmonics from gases and solids. Nature 522, 462–464 (2015)
Hohenleutner, M. et al. Real-time observation of interfering crystal electrons in high-harmonic generation. Nature 523, 572–575 (2015)
Schubert, O. et al. Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations. Nat. Photon. 8, 119–123 (2014)
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)
Kira, M. & Koch, S. W. Semiconductor Quantum Optics (Cambridge Univ. Press, 2012)
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)
Haug, H. & Koch, S. W. Quantum Theory of the Optical and Electronic Properties of Semiconductors 5th edn (World Scientific, 2009)
Schultze, M. et al. Attosecond band-gap dynamics in silicon. Science 346, 1348–1352 (2014)
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)
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)
Hassan, M. T. et al. Optical attosecond pulses and tracking the nonlinear response of bound electrons. Nature 530, 66–70 (2016)
Mairesse, Y. & Quere, F. Frequency-resolved optical gating for complete reconstruction of attosecond bursts. Phys. Rev. A 71, 011401(R) (2005)
Corkum, P. B. Plasma perspective on strong-field multiphoton ionization. Phys. Rev. Lett. 71, 1994–1997 (1993)
Goulielmakis, E. et al. Single-cycle nonlinear optics. Science 320, 1614–1617 (2008)
Benko, C. et al. Extreme ultraviolet radiation with coherence time greater than 1 s. Nat. Photon. 8, 530–536 (2014)
Mics, Z. et al. Thermodynamic picture of ultrafast charge transport in graphene. Nat. Commun. 6, 7655 (2015)
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.
The authors declare no competing financial interests.
Nature thanks M. Chini, U. Höfer and the other anonymous reviewer(s) for their contribution to the peer review of this work.
About this article
Cite this article
Garg, M., Zhan, M., Luu, T. et al. Multi-petahertz electronic metrology. Nature 538, 359–363 (2016) doi:10.1038/nature19821
Nature Communications (2019)
APL Materials (2019)
Applied Sciences (2019)
ACS Photonics (2019)
Optics Express (2019)