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.

The advent of visible-infrared laser pulses carrying a substantial fraction of their energy in a single field oscillation cycle has opened a new era in the experimental investigation of ultrafast processes in semiconductors and dielectrics (bulk as well as nanostructured), motivated by the quest for the ultimate frontiers of electron-based signal metrology and processing. Exploring ways to approach those frontiers requires insight into the physics underlying the interaction of strong high-frequency (optical) fields with electrons moving in periodic potentials. This Colloquium aims at providing this insight. Introduction to the foundations of strong-field phenomena defines and compares regimes of field-matter interaction in periodic systems, including (perfect) crystals as well as optical and semiconductor superlattices, followed by a review of recent experimental advances in the study of strong-field dynamics in crystals and nanostructures. Avenues toward measuring and controlling electronic processes up to petahertz frequencies are discussed.

The optical properties of monolayer and bilayer transition metal dichalcogenide semiconductors are governed by excitons in different spin and valley configurations, providing versatile aspects for van der Waals heterostructures and devices. Here, we present experimental and theoretical studies of exciton energy splittings in external magnetic field in neutral and charged WSe2 monolayer and bilayer crystals embedded in a field effect device for active doping control. We develop theoretical methods to calculate the exciton g-factors from first principles for all possible spin-valley configurations of excitons in monolayer and bilayer WSe2 including valley-indirect excitons. Our theoretical and experimental findings shed light on some of the characteristic photoluminescence peaks observed for monolayer and bilayer WSe2. In more general terms, the theoretical aspects of our work provide additional means for the characterization of single and few-layer transition metal dichalcogenides, as well as their heterostructures, in the presence of external magnetic fields.

The electric field of a laser pulse can be described as Here we report the first method permitting absolute CEP detection with a solid-state detector applicable in ambient conditions. Recently, we have shown that the strong electric field of an intense, linearly-polarized, visible/near-infrared (VIS/NIR), few-cycle laser pulse can rapidly increase the (ac) conductivity of a solid insulator, allowing electric currents to be induced and switched with the field of visible light [22]. In these experiments, we exposed amorphous silicon dioxide (bandgap g 9 eV E ≈ ) to a strong, controlled electric field ( ) F t of a few-cycle pulse with a carrier photon energy of ∆ is a consequence of dispersive pulse broadening inside the glass wedges. However, in our experiments P ( ) Q l ∆ was still detectable above the noise level for values of 400 µm l ∆ > , corresponding to a pulse duration of more than 9 fs (FWHM of the time-dependent cycle-averaged intensity). Subsequently, PQ was calibrated with respect to the absolute CEP of the laser pulse via stereo-ATI measurements performed with identical pulses [4]. After the measurement of P ( ) Q l ∆ with the solid-state device, a mirror was inserted into the beam path, deflecting the 5 pulses into a stereo-ATI apparatus located -together with the solid-state detector -in the same vacuum chamber (Fig. 1). Here, the CEP of the incident laser pulse was detected by analyzing the kinetic energy distribution of electrons that are photoemitted from Xe atoms, see Methods Summary. An uncertainty due to a Gouy phase shift in both foci can be neglected since in both experiments, the sample was placed exactly in the region of the highest laser intensity.We set 17 different propagation lengths l ∆ , ranging from 21.5 µm − to 27.5 µm +. For each of them, 500 single-shot stereo-ATI measurements were performed. Because consecutive laser pulses had a CEP-shift of π , which is only required for the accurate detection of P ( ) Q l ∆ , only spectra from odd-numbered pulses were considered for the stereo-ATI measurements. As shown in [4], CEϕ can then be reconstructed by calculating two asymmetry parameters ( , ) X Y by integrating the averaged time-of-flight spectra L,R TOF ( ) n t of the electrons photoemitted from Xe atoms by the intense few-cycle VIS/NIR pulses in two different regions. The parametric plot of ( , ) X Y in Fig. 2(a) was obtained by calculating, for each. The photoelectron spectra L,R TOF ( ) n twere measured with the left (L) and right (R) micro-channel plates (MCPs) of the set-up in Fig. 1 We have compared the results of the solid-state-based phase retrieval with the predictions of two quantum mechanical models. The first model, which was earlier employed in Ref.[24] to describe the ultrafast increase in conductivity of SiO 2 nanojunctions, is based on the nearestneighbor tight-binding approximation. The second model, presented in detail in Ref.[25], describes quantum dynamics in a one-dimensional pseudopotential (see the Methods Summary for details). In both models, the electric fi...