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Solid attosecond science Attosecond techniques exploit the electric field surrounding femtosecond laser pulses to steer electrons, and are widely applied to atoms or molecules in the gas phase. Electrons liberated by few-cycle laser pulses from solids are also predicted to show strong sensitivity to the phase of the light, but observation of this effect has been elusive. Krüger et al . demonstrate the phenomenon in the spectra of electrons laser-emitted from a nanoscale tungsten tip; current modulation of up to 100% and interference are observed, depending on the carrier envelope phase of the laser. This work should facilitate sub-femtosecond, sub-nanometre probing of collective electron dynamics in a range of solid-state systems. Attosecond science is based on steering electrons with the electric field of well controlled femtosecond laser pulses 1 . It has led to the generation of extreme-ultraviolet pulses 2 with a duration of less than 100 attoseconds (ref. 3 ; 1 as = 10 −18  s), to the measurement of intramolecular dynamics (by diffraction of an electron taken from the molecule under scrutiny 4 , 5 ) and to ultrafast electron holography 6 . All these effects have been observed with atoms or molecules in the gas phase. Electrons liberated from solids by few-cycle laser pulses are also predicted 7 , 8 to show a strong light-phase sensitivity, but only very small effects have been observed 14 . Here we report that the spectra of electrons undergoing photoemission from a nanometre-scale tungsten tip show a dependence on the carrier-envelope phase of the laser, with a current modulation of up to 100 per cent. Depending on the carrier-envelope phase, electrons are emitted either from a single sub-500-attosecond interval of the 6-femtosecond laser pulse, or from two such intervals; the latter case leads to spectral interference. We also show that coherent elastic re-scattering of liberated electrons takes place at the metal surface. Owing to field enhancement at the tip, a simple laser oscillator reaches the peak electric field strengths required for attosecond experiments at 100-megahertz repetition rates, rendering complex amplified laser systems dispensable. Practically, this work represents a simple, extremely sensitive carrier-envelope phase sensor, which could be shrunk in volume to about one cubic centimetre. Our results indicate that the attosecond techniques developed with (and for) atoms and molecules can also be used with solids. In particular, we foresee subfemtosecond, subnanometre probing of collective electron dynamics (such as plasmon polaritons 9 ) in solid-state systems ranging in scale from mesoscopic solids to clusters and to single protruding atoms.

Light-driven electronic excitation is a cornerstone for energy and information transfer. In the interaction of intense and ultrafast light fields with solids, electrons may be excited irreversibly, or transiently during illumination only. As the transient electron population cannot be observed after the light pulse is gone, it is referred to as virtual, whereas the population that remains excited is called real 1 – 4 . Virtual charge carriers have recently been associated with high-harmonic generation and transient absorption 5 – 8 , but photocurrent generation may stem from real as well as virtual charge carriers 9 – 14 . However, a link between the generation of the carrier types and their importance for observables of technological relevance is missing. Here we show that real and virtual charge carriers can be excited and disentangled in the optical generation of currents in a gold–graphene–gold heterostructure using few-cycle laser pulses. Depending on the waveform used for photoexcitation, real carriers receive net momentum and propagate to the gold electrodes, whereas virtual carriers generate a polarization response read out at the gold–graphene interfaces. On the basis of these insights, we further demonstrate a proof of concept of a logic gate for future lightwave electronics. Our results offer a direct means to monitor and excite real and virtual charge carriers. Individual control over each type of carrier will markedly increase the integrated-circuit design space and bring petahertz signal processing closer to reality 15 , 16 . Light-field control of real and virtual charge carriers in a gold–graphene–gold heterostructure is demonstrated, and used to create a logic gate for application in lightwave electronics.

Scattering of a tightly focused electron beam by an atom forms one of the bases of modern electron microscopy. A fundamental symmetry breaking occurs when the target atom is displaced from the beam center. This displacement results in a deflection of the beam and an asymmetric angular distribution of the scattered electrons. Here we propose a concept to control the sign and magnitude of the scattering asymmetry by shaping the incident high-energy electron wave packet in momentum space on the atto- to picosecond time scale. The shaping controls the ultrafast real-space dynamics of the wave packet, shifting the balance between two competing contributions of the impact-parameter-dependent quantum interference and the momentum distribution of the wave packet on the target. We find a strong sensitivity of the elastic scattering on the wave packet properties, an effect that will allow wave-packet and target characterization in ultrafast electron microscopy.

Electron and ion beams are indispensable tools in numerous fields of science and technology, ranging from radiation therapy to microscopy and lithography. Advanced beam control facilitates new functionalities. Here, we report the guiding and splitting of charged particle beams using ponderomotive forces created by the motion of charged particles through electrostatic optics printed on planar substrates. Shape and strength of the potential can be locally tailored by the lithographically produced electrodes’ layout and the applied voltages, enabling the control of charged particle beams within precisely engineered effective potentials. We demonstrate guiding of electrons and ions for a large range of energies (from 20 to 5000 eV) and masses (from 5 · 10 −4 to 131 atomic mass units) as well as electron beam splitting for energies up to the keV regime as a proof-of-concept for more complex beam manipulation. There is interest in controlling particle beams using electric fields and using them in compact devices. Here the authors demonstrate guiding and splitting of charged particle (electron and ion) beams on a chip designed with special structures.

Ultrafast control of electron dynamics in solid state systems has recently found particular attention. By increasing the electric field strength of laser pulses, the light-matter interaction in solids might turn from a perturbative into a novel non-perturbative regime, where interband transitions from the valence to the conduction band become strongly affected by intraband motion. We have demonstrated experimentally and numerically that this combined dynamics can be controlled in graphene with the electric field waveform of phase-stabilized few-cycle laser pulses (Higuchi et al 2017 Nature 550 224-8; Heide et al 2018 Phys. Rev. Lett. 121 207401). Here we show new experimental data and matching simulation results at comparably low optical fields, which allows us to focus on the highly interesting transition regime where the light-matter interaction turns from perturbative to non-perturbative. We find a 5th order power-law scaling of the laser induced waveform-dependent current at low optical fields, which breaks down for higher optical fields, indicating the transition.

In different applications the Gouy phase is used to describe broadband lasers, but new 3D measurements of the spatial dependence of a focused laser pulse show serious deviations from the Gouy phase. Precise knowledge of the behaviour of the phase of light in a focused beam is fundamental to understanding and controlling laser-driven processes. More than a hundred years ago, an axial phase anomaly for focused monochromatic light beams was discovered and is now commonly known as the Gouy phase 1 , 2 , 3 , 4 . Recent theoretical work has brought into question the validity of applying this monochromatic phase formulation to the broadband pulses becoming ubiquitous today 5 , 6 . Based on electron backscattering at sharp nanometre-scale metal tips, a method is available to measure light fields with sub-wavelength spatial resolution and sub-optical-cycle time resolution 7 , 8 , 9 . Here we report such a direct, three-dimensional measurement of the spatial dependence of the optical phase of a focused, 4-fs, near-infrared pulsed laser beam. The observed optical phase deviates substantially from the monochromatic Gouy phase—exhibiting a much more complex spatial dependence, both along the propagation axis and in the radial direction. In our measurements, these significant deviations are the rule and not the exception for focused, broadband laser pulses. Therefore, we expect wide ramifications for all broadband laser–matter interactions, such as in high-harmonic and attosecond pulse generation, femtochemistry 10 , ophthalmological optical coherence tomography 11 , 12 and light-wave electronics 13 .

The injection of directional currents in solids with strong optical fields has attracted tremendous attention as a route to realize ultrafast electronics based on the quantum-mechanical nature of electrons at femto- to attosecond timescales. Such currents are usually the result of an asymmetric population distribution imprinted by the temporal symmetry of the driving field. Here we compare two experimental schemes that allow control over the amplitude and direction of light-field-driven currents excited in graphene. Both schemes rely on shaping the incident laser field with one parameter only: either the carrier-envelope phase (CEP) of a single laser pulse or the relative phase between pulses oscillating at angular frequencies and 2 , both for comparable laser parameters. We observe that the efficiency in generating a current via two-color-control exceeds that of CEP control by more than two orders of magnitude (7 nA vs. 18 pA), as the + 2 field exhibits significantly more asymmetry in its temporal shape. We support this finding with numerical simulations that clearly show that two-color current control in graphene is superior, even down to single-cycle pulse durations. We expect our results to be relevant to experimentally access fundamental properties of any solid at ultrafast timescales, as well as for the emerging field of petahertz electronics.

We theoretically investigate the dependence of the enhancement of optical near-fields at nanometric tips on the shape, size, and material of the tip. We confirm the strong dependence of the field enhancement factor on the radius of curvature. In addition, we find a surprisingly strong increase of field enhancement with increasing opening angle of the nanotips. For gold and tungsten nanotips in the experimentally relevant parameter range (radius of curvature at laser wavelength), we obtain field enhancement factors of up to for Au and for W for large opening angles. We confirm this strong dependence on the opening angle for many other materials featuring a wide variety in their dielectric response. For dielectrics, the opening angle dependence is traced back to the electrostatic force of the induced surface charge at the tip shank. For metals, the plasmonic response strongly increases the field enhancement and shifts the maximum field enhancement to smaller opening angles.

When graphene is exposed to a strong few-cycle optical field, a directional electric current can be induced depending on the carrier-envelope phase of the field. This phenomenon has successfully been explained by the charge dynamics in reciprocal space, namely an asymmetry in the conduction band population left after the laser excitation. However, the corresponding real-space perspective has not been explored so far although it could yield knowledge about the atomic origin of the macroscopic currents. In this work, by adapting the nearest-neighbor tight-binding model including overlap integrals and the semiconductor Bloch equation, we reveal the spatial distributions of the light-field-driven currents on the atomic scale and show how they are related to the light-induced changes of charge densities. The atomic-scale currents flow dominantly through the network of the π bonds and are the strongest at the bonds parallel to the field polarization, where an increase of the charge density is observed. The real-space maps of the currents and changes in charge densities are elucidated using simple symmetries connecting real and reciprocal space. We also discuss the strong-field-driven Rabi oscillations appearing in the atomic-scale charge densities. This work highlights the importance of real-space measurements and stimulates future time-resolved atomic-scale experimental studies with high-energy electrons or x-rays, for examples.

We investigate two-electron interference in free space using two laser-triggered needle tips as independent electron sources, a fermionic realisation of the landmark Hanbury Brown and Twiss interferometer. We calculate the two-electron interference pattern in a quantum path formalism taking into account the fermionic nature and the spin configuration of the electrons. We also estimate the Coulomb repulsion in the setup in a semiclassical approach. We find that antibunching resulting from Pauli’s exclusion principle and repulsion stemming from the Coulomb interaction can be clearly distinguished.