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The time it takes a bound electron to respond to the electromagnetic force of light sets a fundamental speed limit on the dynamic control of matter and electromagnetic signal processing. Time-integrated measurements of the nonlinear refractive index of matter indicate that the nonlinear response of bound electrons to optical fields is not instantaneous; however, a complete spectral characterization of the nonlinear susceptibility tensors--which is essential to deduce the temporal response of a medium to arbitrary driving forces using spectral measurements--has not yet been achieved. With the establishment of attosecond chronoscopy, the impulsive response of positive-energy electrons to electromagnetic fields has been explored through ionization of atoms and solids by an extreme-ultraviolet attosecond pulse or by strong near-infrared fields. However, none of the attosecond studies carried out so far have provided direct access to the nonlinear response of bound electrons. Here we demonstrate that intense optical attosecond pulses synthesized in the visible and nearby spectral ranges allow sub-femtosecond control and metrology of bound-electron dynamics. Vacuum ultraviolet spectra emanating from krypton atoms, exposed to intense waveform-controlled optical attosecond pulses, reveal a finite nonlinear response time of bound electrons of up to 115 attoseconds, which is sensitive to and controllable by the super-octave optical field. Our study could enable new spectroscopies of bound electrons in atomic, molecular or lattice potentials of solids, as well as light-based electronics operating on sub-femtosecond timescales and at petahertz rates.

Investigations using single-cycle intense optical fields to drive electron motion in bulk silicon dioxide show that the light-induced electric currents extend in frequency up to about 8 petahertz. The speed of electronics, and hence of computing, is limited by the frequencies of the electric currents that are used. Light fields can induce and manipulate electric currents at vastly higher frequencies than are achievable in conventional devices, and Eleftherios Goulielmakis and colleagues now extend this approach to reach an even faster regime. They use single-cycle intense optical fields to drive electron motion in the bulk of silicon dioxide and show that the light-induced intraband electric currents extend in frequency up to about eight petahertz. This demonstration of real-time access to the dynamic nonlinear conductivity of silicon dioxide, with the ability to directly probe and control the intraband currents on attosecond timescales, establishes intense light fields as a platform for multi-petahertz coherent electronics and points to new opportunities for fundamental studies of electron dynamics in condensed matter. 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 angstrom) 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.

Extreme ultraviolet (EUV) high-harmonic radiation emerging from laser-driven atoms, molecules or plasmas underlies powerful attosecond spectroscopy techniques and provides insight into fundamental structural and dynamic properties of matter. The advancement of these spectroscopy techniques to study strong-field electron dynamics in condensed matter calls for the generation and manipulation of EUV radiation in bulk solids, but this capability has remained beyond the reach of optical sciences. Recent experiments and theoretical predictions paved the way to strong-field physics in solids by demonstrating the generation and optical control of deep ultraviolet radiation in bulk semiconductors, driven by femtosecond mid-infrared fields or the coherent up-conversion of terahertz fields to multi-octave spectra in the mid-infrared and optical frequencies. Here we demonstrate that thin films of SiO2 exposed to intense, few-cycle to sub-cycle pulses give rise to wideband coherent EUV radiation extending in energy to about 40 electronvolts. Our study indicates the association of the emitted EUV radiation with intraband currents of multi-petahertz frequency, induced in the lowest conduction band of SiO2. To demonstrate the applicability of high-harmonic spectroscopy to solids, we exploit the EUV spectra to gain access to fine details of the energy dispersion profile of the conduction band that are as yet inaccessible by photoemission spectroscopy in wide-bandgap dielectrics. In addition, we use the EUV spectra to trace the attosecond control of the intraband electron motion induced by synthesized optical transients. Our work advances lightwave electronics in condensed matter into the realm of multi-petahertz frequencies and their attosecond control, and marks the advent of solid-state EUV photonics.