The propagation and transport of electrons in crystals is a fundamental process pertaining to the functioning of most electronic devices. Microscopic theories describe this phenomenon as being based on the motion of Bloch wave packets. These wave packets are superpositions of individual Bloch states with the group velocity determined by the dispersion of the electronic band structure near the central wavevector in momentum space. This concept has been verified experimentally in artificial superlattices by the observation of Bloch oscillations—periodic oscillations of electrons in real and momentum space. Here we present a direct observation of electron wave packet motion in a real-space and real-time experiment, on length and time scales shorter than the Bloch oscillation amplitude and period. We show that attosecond metrology (1 as = 10^-18 seconds) now enables quantitative insight into weakly disturbed electron wave packet propagation on the atomic length scale without being hampered by scattering effects, which inevitably occur over macroscopic propagation length scales. We use sub-femtosecond (less than 10^-15 seconds) extreme-ultraviolet light pulses to launch photoelectron wave packets inside a tungsten crystal that is covered by magnesium films of varied, well-defined thicknesses of a few ångströms. Probing the moment of arrival of the wave packets at the surface with attosecond precision reveals free-electron-like, ballistic propagation behaviour inside the magnesium adlayer—constituting the semi-classical limit of Bloch wave packet motion. Real-time access to electron transport through atomic layers and interfaces promises unprecedented insight into phenomena that may enable the scaling of electronic and photonic circuits to atomic dimensions. In addition, this experiment allows us to determine the penetration depth of electrical fields at optical frequencies at solid interfaces on the atomic scal

High-harmonic generation by a highly non-linear interaction of infrared laser fields with matter allows for the generation of attosecond pulses in the XUV spectral regime. This process, well established for atoms, has been recently extended to the condensed phase. Remarkably well pronounced harmonics up to order ∼ 30 have been observed for dielectrics. We present the first ab-initio multiscale simulation of solid-state high-harmonic generation. We find that mesoscopic effects of the extended system, in particular the realistic sampling of the entire Brillouin zone, the pulse propagation in the dense medium, and the inhomogeneous illumination of the crystal have a strong effect on the formation of clean harmonic spectra. Our results provide a novel explanation for the formation of clean harmonics and have implications for a wide range of non-linear optical processes in dense media.PACS numbers: 42.65. Ky, 42.50.Hz, 72.20.Ht The generation of high harmonics (HHG) in the nonlinear interaction of intense ultrashort infrared (IR) laser pulses with matter has turned out to be a highly successful route towards the generation of attosecond pulses in the EUV and XUV spectral regimes [1][2][3][4]. It has become the workhorse of investigation of a vast array of electronic processes on the attosecond time scale [5]. Expanding the range of accessible photon energies and intensities faces, however, fundamental limitations. Experimental and theoretical investigations have established a scaling of the cut-off energy E cut ∝ λ 2 for HHG from atoms in the gas phase raising hopes to reach ever higher photon energies by increasing the wavelength λ of the driving laser pulse. However, the intensity in the cut-off region was found to scale unfavorably I cut ∝ λ −5.3 due to the large spatial dispersion of the electron wave packet upon return to its parent atom [6][7][8][9][10]. Propagation effects in gas filled capillaries have been found to partially offset this suppression at high λ [11].Extending HHG to the condensed phase promises to overcome some of these limitations to enable compact and brighter light sources and to open up the novel field of solid-state photonics on the attosecond scale. The recent observation of HHG in solids for intensities below the damage threshold [12][13][14][15][16][17][18] suggests opportunities for controlling electronic dynamics [16,17] and for an alloptical reconstruction of the band structure [19].The observed solid-state HHG substantially differs from the corresponding atomic spectra. For example, while for atoms the cut-off frequency ω HHG cut scales linearly with the (peak) intensity I 0 of the driving pulse [20,21] One major puzzle has remained so far unresolved: while many experiments display remarkably "clean" harmonic spectra with pronounced peaks near multiples of the driving frequency (odd multiples when inversion symmetry is preserved) all the way up to the cutoff frequency, corresponding simulations display a noisy spectrum lacking any clear harmonic structure over a wide range of fre...

Attosecond science is based on electron dynamics driven by a strong optical electric field and has evolved beyond its original scope in gas-phase atomic and molecular physics to solid-state targets. In this review, we discuss a nanoscale attosecond physics laboratory that has enabled the first observations of strong-field-driven photoemission and recollision at a solid surface: laser-triggered metallic nanotips. In addition to the research questions of rather fundamental nature, femtosecond electron sources with outstanding beam qualities have resulted from this research, which has prompted follow-up application in the sensing of electric fields and lightwave electronics, ultrafast microscopy and diffraction, and fundamental matter-wave quantum optics. We review the theoretical and experimental concepts underlying near-field enhancement, photoemission regimes and electron acceleration mechanisms. Nanotips add new degrees of freedom to well known strong-field phenomena from atomic physics. For example, they enable the realization of a true sub-optical-cycle acceleration regime where recollision is suppressed. We also discuss the possibility of high-harmonic generation due to laser irradiation of metallic nanostructures.

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We discuss the interaction of ultrashort near-infrared laser pulses with sharp metal tips at moderate nominal intensities (I 0 ∼ 10 11 W cm −2 ). As external electric fields are strongly enhanced at such tips (enhancement factor ∼10) our system turns out to be an ideal miniature laboratory to investigate strong-field effects at solid surfaces. We analyse the electron-energy spectra as a function of the strength of the laser field and the static extraction field and present an intuitive model for their interpretation. The size of the effective field acting on the metal electrons can be determined from the electron spectra. The latter are also reproduced by time-dependent density functional theory (TDDFT) simulations.The emerging field of attosecond science is based on the ability to control electronic wavepackets with the help of well-controlled few-cycle laser pulses [1]. The key effect is the recollision of an electronic wavepacket with the parent matter within a fraction of the laser cycle after its generation through ionization [2,3]. Prominent dynamical processes based on recollision are high-harmonic generation (HHG) and high-order above-threshold ionization (ATI), observed with atomic and molecular gases. The exquisite control over the recolliding wavepacket allows one to take, for example, diffraction images of the parent molecule [4,5] and to achieve attosecond time resolution for electronic processes [6][7][8]. Recently, laser-electricfield-driven recollision processes were also observed with solid-state systems, namely at dielectric nanoparticles [9] and at sharp metal tips [10,11].For versatile imaging techniques applied to atomic, molecular and solid-state systems it would be of great interest to vary the parameters of the returning electron over a large energy range. The same holds true in the process of the generation of high-harmonic photons, which is currently being optimized to match certain flux and energy requirements (see, e.g., [12,13]). Improving and extending the ability to control the motion of the electronic wavepacket requires additional control knobs for the strong fields driving the wavepacket. One obvious choice would be the addition of a static (dc) electric field. Theory suggests [14][15][16] that the application of relatively small static fields, one to four orders of magnitude weaker than the maximum laser field, already leads to a modification of the path of the recolliding wavepacket and, hence, to changes of the resulting HHG spectrum. For example, the maximum HHG energy could be tripled if a static field with a field strength 10% that of the maximum laser field was applied [16]. Although considerably smaller than the amplitude of the moderately strong laser itself, application of such a (macroscopic) static field with a strength of a fraction of a GV m −1 is unfeasible, rendering this control tool exceedingly difficult to employ in laser-atom or laser-molecule interactions.When nanostructures are irradiated with laser light, optical field enhancement takes place. The laser ele...

We theoretically investigate the generation of ultrafast currents in insulators induced by strong few-cycle laser pulses. Ab initio simulations based on time-dependent density functional theory give insight into the atomic-scale properties of the induced current signifying a femtosecond-scale insulator-metal transition. We observe the transition from nonlinear polarization currents during the laser pulse at low intensities to tunnelinglike excitation into the conduction band at higher laser intensities. At high intensities, the current persists after the conclusion of the laser pulse considered to be the precursor of the dielectric breakdown on the femtosecond scale. We show that the transferred charge sensitively depends on the orientation of the polarization axis relative to the crystal axis, suggesting that the induced charge separation reflects the anisotropic electronic structure. We find good agreement with very recent experimental data on the intensity and carrier-envelope phase dependence [A. Schiffrin et al., Nature (London) 493, 70 (2013).

We demonstrate coherent control of multiphoton and above-threshold photoemission from a single solid-state nanoemitter driven by a fundamental and a weak second harmonic laser pulse. Depending on the relative phase of the two pulses, electron emission is modulated with a contrast of the oscillating current signal of up to 94%. Electron spectra reveal that all observed photon orders are affected simultaneously and similarly. We confirm that photoemission takes place within 10 fs. Accompanying simulations indicate that the current modulation with its large contrast results from two interfering quantum pathways leading to electron emission.

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 5 nm ⩾ at 800 nm laser wavelength), we obtain field enhancement factors of up to 35 ∼ for Au and 12 ∼ 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.