Multi-petahertz electronic metrology

Garg, Manish; Zhan, Minjie; Luu, Tran Trung; Lakhotia, Harshit; Klostermann, Till; Guggenmos, Alexander; Goulielmakis, Eleftherios

doi:10.1038/nature19821

Cited by 305 publications

(253 citation statements)

References 29 publications

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“…Further studies of HHG from solids might benefit substantially from extending our current model beyond the Markovian approximation [17,19] by taking into account non-Markovian scattering processes. Experimentally, time-domain characterization of the HHG from solids [65] could help to verify theoretical studies. In addition, high-order harmonic spectroscopy in solids could serve as an important tool in determining the phase relaxation times that were measured previously via conventional techniques such as four-wave mixing experiments, Rayleigh scattering and speckle analysis, THz spectroscopy, etc.…”

Section: Discussionmentioning

confidence: 99%

High-order harmonic generation in solids: A unifying approach

2016

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There have been several experimental reports showing high-order harmonic generation from solids, but there has been no unifying theory presented as of yet for all these experiments. Here we report on the systematic investigation of high-order harmonic generation within the semiconductor Bloch equations, taking into account multiple bands and relaxation processes phenomenologically. In addition to reproducing key experiments, we show the following: (i) Electronic excitations, direct-indirect excitation pathways, and relaxation processes are responsible for high-order harmonic generation and control using midinfrared drivers in zinc oxide. We describe an intuitive picture explaining a two-color experiment involving noninversion symmetric crystals. (ii) High-order harmonic generation can be considered as a general feature of ultrafast strong-field-driven electronic dynamics in solids. We demonstrate this statement by predicting high-order harmonic spectra of solids that have not been studied yet.

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Section: Discussionmentioning

confidence: 99%

High-order harmonic generation in solids: A unifying approach

2016

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“…Fortunately, this few-femtosecond reversibility seems frequently available in attosecond physics. For example, photoemission takes less than hundreds of attoseconds 7,27,30,31 , Auger decays have few-femtosecond time constants 45,46 , laser-driven interband/intraband Bloch oscillations [47][48][49] occur within each optical cycle, all linear and nonlinear optical effects (for example, second/third/higher-harmonic generation) [49][50][51][52] involve cycle-reversible atomicscale charge-density displacements 24 and macroscopic currents in dielectrics can be initiated and controlled on sub-cycle timescales 53,54 . Recombination might also be ultrafast in a condensed-matter environment.…”

Section: Competing Interestsmentioning

confidence: 99%

Diffraction and microscopy with attosecond electron pulse trains

2017

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Attosecond spectroscopy1-7 can resolve electronic processes directly in time, but a movie-like space-time recording is impeded by the too long wavelength (~100 times larger than atomic distances) or the source-sample entanglement in re-collision techniques [8][9][10][11] . Here we advance attosecond metrology to picometre wavelength and sub-atomic resolution by using free-space electrons instead of higher-harmonic photons 1-7 or re-colliding wavepackets [8][9][10][11] . A beam of 70-keV electrons at 4.5-pm de Broglie wavelength is modulated by the electric field of laser cycles into a sequence of electron pulses with sub-optical-cycle duration. Time-resolved diffraction from crystalline silicon reveals a < 10-as delay of Bragg emission and demonstrates the possibility of analytic attosecond-ångström diffraction. Real-space electron microscopy visualizes with sub-light-cycle resolution how an optical wave propagates in space and time. This unification of attosecond science with electron microscopy and diffraction enables space-time imaging of light-driven processes in the entire range of sample morphologies that electron microscopy can access.Our concepts for generating attosecond electron pulses, direct streaking-oscilloscope characterization, atomic diffraction and proof-of-principle attosecond electron microscopy of electromagnetic fields are depicted in Fig. 1. A femtosecond laser 12 triggers electron emission from a photocathode (yellow) and produces electron pulses of ~1 ps duration at a central energy of E el = 70 keV (ref.13 ). The de Broglie wavelength is λ el ≈ 4.5 pm and spacecharge effects are avoided by using fewer than one electron per pulse at the sample. A first laser beam ('modulation') is used to compress the electron pulse into a sub-cycle pulse train. For this purpose, we let the laser beam and the electron beam intersect at a 50-nm-thick silicon nitride membrane that lets the electrons pass through. The membrane is also transparent to the laser beam (1,030 nm wavelength), but the refractive index of ~2 in combination with thin-layer interferences generates a phase shift between the incoming and outgoing electromagnetic waves. Therefore, the periodic electromagnetic acceleration and deceleration of the propagating electrons in the optical field cycles before and after the membrane do not cancel out after passage through the laser focus, as would happen in free space 13 . In the end, there remains a time-dependent overall momentum kick that is proportional to the change of vector potential at the membrane and therefore dependent on the optical phase. In contrast to metal foils 13,14 , graphite 15 or nanostructures 16 , a dielectric membrane has negligible linear or nonlinear optical absorption and can therefore sustain an extreme level of power and fields, enabling strong/effective compression and metrology.In the experiment, we let the electron beam (0.48 × speed of light) and the laser beam (p-polarized, ~15 mW, peak field ~5 × 10 7 V m -1 ) hit the membrane under 35° and 60° from the surface...

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“…As the creation of polarization and charge carriers, as well as their acceleration inside the bands are strongly coupled, both emission sources contribute simultaneously to the total emission

E_{out} false(t false) \propto \frac{\partial}{\partial t} P false(t false) + J false(t false)

. The frequency spectrum is obtained by a Fourier transform of

E_{out} false(t false)

and reads

\begin{matrix} true \\ right I_{out} false(ω false) = | E_{out} {(ω) false|}^{2} \propto {false| ω P (ω) + normali J (ω) false|}^{2} . \end{matrix}

Questions concerning the relative importance of the emission sources in a strongly excited semiconductor as well as the interplay between them are a topic of ongoing discussions . Nevertheless, both emission sources are intrinsically coupled and equally important as demonstrated in Refs.…”

Section: Microscopic Theory Of Strong‐field Excitations In Semiconducmentioning

confidence: 99%

“…Strong‐field excitations generally involve such significant complications, which makes the use of simplified trajectory models limited. So far, only full many‐body approaches have quantitatively explained details of HHG experiments …”

Section: Microscopic Theory Of Strong‐field Excitations In Semiconducmentioning

confidence: 99%

Ultrahigh Off‐Resonant Field Effects in Semiconductors

Huttner

Kira

Koch

2017

Laser & Photonics Reviews

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The excitation of semiconductors with short, off-resonant, high-power terahertz pulses yields extremely nonlinear, ultrafast, dynamical processes including very-high harmonic generation, the occurence of high-order sidebands, dynamical Bloch oscillations, as well as quasi-particle collisions. This review overviews the experimental findings and the microscopic theory used for the consistent quantitative analysis of the observations.

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Multi-petahertz electronic metrology

Cited by 305 publications

References 29 publications

High-order harmonic generation in solids: A unifying approach

High-order harmonic generation in solids: A unifying approach

Diffraction and microscopy with attosecond electron pulse trains

Ultrahigh Off‐Resonant Field Effects in Semiconductors

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