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Heide, Christian

Publications and source records attributed to Heide, Christian.

Ultrafast high-harmonic spectroscopy of solids

High-harmonic spectroscopy, an ultrafast all-optical technique initially conceptualized in atomic and molecular systems, has now emerged as a powerful platform for studying the structure and dynamics of condensed matter. Unlike that in the gas phase, solid-state high-harmonic generation relies on the fundamental response from high atomic density and periodicity, leading to interband transitions and coherent driving of electrons and holes in their respective bands. These mechanisms make high-harmonic spectroscopy particularly sensitive to the electronic band structure, topological properties and many-body correlations in condensed media. An advantage of high-harmonic spectroscopy over other spectroscopic methods is its ability to probe ultrafast phenomena, capturing femto- to attosecond dynamics of multi-band and strongly correlated electron interactions in solids. Furthermore, in this Review, we discuss the latest experimental and theoretical advances in ultrafast high-harmonic spectroscopy of solids and provide perspectives for future research in this field.

High-harmonic generation↗

Petahertz electronics

Petahertz, or lightwave, electronics uses tailored optical waveforms to control charge carriers in an electronic circuit at petahertz frequencies. This may enable faster processing than conventional pulsed electronics, which cannot be scaled beyond gigahertz frequencies. In recent years, petahertz-scale currents driven by optical fields have been measured in solid-state systems and nanoscale structures, with several proof-of-principle demonstrations of sub-optical-cycle current generation and optical-field-resolved waveform detection at the sub-femtosecond to few-femtosecond scale. Recent work has taken the first steps towards digital and quantum operation by exploring optical-field-driven logic and memory functionality. Here, in this Review, we discuss the progress towards sub-cycle field-driven current injection, highlighting key theoretical concepts, experimental milestones, and questions remaining as we push towards realizing petahertz electronics for ultrafast optical waveform analysis, digital logic, communications, and quantum computation.

Heide, Christian↗

Strong-Field Bloch Electron Interferometry for Band-Structure Retrieval

When Bloch electrons in a solid are exposed to a strong optical field, they are coherently driven in their respective bands where they acquire a quantum phase as the imprint of the band shape. If an electron approaches an avoided crossing formed by two bands, it may be split by undergoing a Landau-Zener transition. We here employ subsequent Landau-Zener transitions to realize strong-field Bloch electron interferometry (SFBEI), allowing us to reveal band structure information. In particular, we measure the Fermi velocity (band slope) of graphene in the vicinity of the K points as 1.07±0.04 nm fs –1 . As a result, we expect SFBEI for band structure retrieval to apply to a wide range of material systems and experimental conditions, making it suitable for studying transient changes in band structure with femtosecond temporal resolution at ambient conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

High-harmonic generation from artificially stacked 2D crystals

Here, we report a coherent layer-by-layer build-up of high-order harmonic generation (HHG) in artificially stacked transition metal dichalcogenides (TMDC) crystals in their various stacking configurations. In the experiments, millimeter-sized single crystalline monolayers are synthesized using the gold foil-exfoliation method, followed by artificially stacking on a transparent substrate. High-order harmonics up to the 19th order are generated by the interaction with a mid-infrared (MIR) driving laser. We find that the generation is sensitive to both the number of layers and their relative orientation. For AAAA stacking configuration, both odd- and even-orders exhibit a quadratic increase in intensity as a function of the number of layers, which is a signature of constructive interference of high-harmonic emission from successive layers. Particularly, we observe some deviations from this scaling at photon energies above the bandgap, which is explained by self-absorption effects. For AB and ABAB stacking, even-order harmonics remain below the detection level, consistent with the presence of inversion symmetry. Our study confirms our capability of producing nonperturbative high-order harmonics from stacked layered materials subjected to intense MIR fields without damaging samples. Our results have implications for optimizing solid-state HHG sources at the nanoscale and developing high-harmonics as an ultrafast probe of artificially stacked layered materials. Because the HHG process is a strong-field driven process, it has the potential to probe high-momentum and energy states in the bandstructure combined with atomic-scale sensitivity in real space, making it an attractive probe of novel material structures such as the Moiré pattern.

2D materials↗

Floquet engineering of strongly driven excitons in monolayer tungsten disulfide

Interactions of quantum materials with strong-laser fields can induce exotic nonequilibrium electronic states. Monolayer transition-metal dichalcogenides, a new class of direct-gap semiconductors with prominent quantum confinement, offer exceptional opportunities toward Floquet engineering of quasiparticle electron-hole states, or excitons. Strong-field driving has a potential to achieve enhanced control of electronic band structure, thus a possibility to open a new realm of exciton light-matter interactions. However, experimental implementation of strongly-driven excitons has so far remained out of reach. Here, we use mid-infrared laser pulses below the optical bandgap to excite monolayer tungsten disulfide up to a field strength of 0.3 V/nm, and demonstrate strong-field light dressing of excitons in the excess of a hundred millielectronvolt. Our high-sensitivity transient absorption spectroscopy further reveals formation of a virtual absorption feature below the 1s-exciton resonance, which is assigned to a light-dressed sideband from the dark 2p-exciton state. Quantum-mechanical simulations substantiate the experimental results and enable us to retrieve real-space movies of the exciton dynamics. Here, this study advances our understanding of the exciton dynamics in the strong-field regime, and showcases the possibility of harnessing ultrafast, strong-field phenomena in device applications of two-dimensional materials.

36 MATERIALS SCIENCE↗

In-Situ Nanoscale Focusing of Extreme Ultraviolet Solid-State High Harmonics

Extreme ultraviolet light delivering radiation with a wavelength shorter than approximately 100 nm is now available from solid-state sources. However, despite exceptional progress, efficient focusing of extreme ultraviolet photons to their ultimate diffraction limit remains a formidable challenge because of the precision of the focusing by curved, optical surfaces. Here we integrate coherent short-wavelength high-order harmonics from a MgO crystal, with a high-numerical-aperture, nanostructured, focusing element etched onto the surface of the crystal itself. We focus extreme ultraviolet light, seventh harmonic of an 800-nm laser, with a zone plate of numerical aperture 0.35, down to a waist radius of 150 nm, with 18% focusing efficiency. The estimated intensity approaches 10 7 W/cm 2 . Future developments may demonstrate nanoscale laser ablation and miniaturization of extreme ultraviolet coherent sources on a chip.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Intense infrared lasers for strong-field science

The advent of chirped-pulse amplification in the 1980s and femtosecond Ti:sapphire lasers in the 1990s enabled transformative advances in intense laser–matter interaction physics. Whereas most of experiments have been conducted in the limited near-infrared range of 0.8–1 μm, theories predict that many physical phenomena such as high harmonic generation in gases favor long laser wavelengths in terms of extending the high-energy cutoff. Significant progress has been made in developing few-cycle, carrier-envelope phase-stabilized, high-peak-power lasers in the 1.6–2 μm range that has laid the foundation for attosecond X ray sources in the water window. Even longer wavelength lasers are becoming available that are suitable to study light filamentation, high harmonic generation, and laser–plasma interaction in the relativistic regime. Long-wavelength lasers are suitable for sub-bandgap strong-field excitation of a wide range of solid materials, including semiconductors. In the strong-field limit, bulk crystals also produce high-order harmonics. In this review, we first introduce several important wavelength scaling laws in strong-field physics, then describe recent breakthroughs in short- (1.4–3 μm), mid- (3–8 μm), and long-wave (8–15 μm) infrared laser technology, and finally provide examples of strong-field applications of these novel lasers. Furthermore, some of the broadband ultrafast infrared lasers will have profound effects on medicine, environmental protection, and national defense, because their wavelengths cover the water absorption band, the molecular fingerprint region, as well as the atmospheric infrared transparent window.

43 PARTICLE ACCELERATORS↗

Probing topological phase transitions using high-harmonic generation

We report the prediction and realization of topological insulators have sparked great interest in experimental approaches to the classification of materials. The phase transition between non-trivial and trivial topological states is important, not only for basic materials science but also for next-generation technology, such as dissipation-free electronics. It is therefore crucial to develop advanced probes that are suitable for a wide range of samples and environments. Here we demonstrate that circularly polarized laser-field-driven high-harmonic generation is distinctly sensitive to the non-trivial and trivial topological phases in the prototypical three-dimensional topological insulator bismuth selenide. The phase transition is chemically initiated by reducing the spin–orbit interaction strength through the substitution of bismuth with indium atoms. We find strikingly different high-harmonic responses of trivial and non-trivial topological surface states that manifest themselves as a conversion efficiency and elliptical dichroism that depend both on the driving laser ellipticity and the crystal orientation. The origins of the anomalous high-harmonic response are corroborated by calculations using the semiconductor optical Bloch equations with pairs of surface and bulk bands. As a purely optical approach, this method offers sensitivity to the electronic structure of the material, including its nonlinear response, and is compatible with a wide range of samples and sample environments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Light-field control of real and virtual charge carriers

We report 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. Virtual charge carriers have recently been associated with high-harmonic generation and transient absorption, but photocurrent generation may stem from real as well as virtual charge carriers. 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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Electronic Coherence and Coherent Dephasing in the Optical Control of Electrons in Graphene

Electronic coherence is of utmost importance for the access and control of quantum-mechanical solid-state properties. Using a purely electronic observable, the photocurrent, we measure a lower bound of the electronic coherence time of 22 ± 4 fs in graphene. The photocurrent is ideally suited to measure electronic coherence, as it is a direct result of coherent quantum-path interference, controlled by the delay between two ultrashort two-color laser pulses. The maximum delay for which interference between the population amplitude injected by the first pulse interferes with that generated by the second pulse determines the electronic coherence time. In particular, numerical simulations reveal that the experimental data yields a lower bound on the electronic coherence time, masked by coherent dephasing due to the broadband absorption in graphene. Overall, we expect that our results will significantly advance the understanding of coherent quantum control in solid-state systems ranging from excitation with weak fields to strongly driven systems.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Polarization Flipping of Even-Order Harmonics in Monolayer Transition-Metal Dichalcogenides

We present a systematic study of the crystal-orientation dependence of high-harmonic generation in monolayer transition-metal dichalcogenides, WS 2 and MoSe 2 , subjected to intense linearly polarized midinfrared laser fields. The measured spectra consist of both odd- and even-order harmonics, with a high-energy cutoff extending beyond the 15th order for a laser-field strength around ~1 V/nm. In WS 2 , we find that the polarization direction of the odd-order harmonics smoothly follows that of the laser field irrespective of the crystal orientation, whereas the direction of the even-order harmonics is fixed by the crystal mirror planes. Furthermore, the polarization of the even-order harmonics shows a flip in the course of crystal rotation when the laser field lies between two of the crystal mirror planes. By numerically solving the semiconductor Bloch equations for a gapped-graphene model, we qualitatively reproduce these experimental features and find the polarization flipping to be associated with a significant contribution from interband polarization. In contrast, high-harmonic signals from MoSe 2 exhibit deviations from the laser-field following of odd-order harmonics and crystal-mirror-plane following of even-order harmonics. We attribute these differences to the competing roles of the intraband and interband contributions, including the deflection of the electron-hole trajectories by nonparabolic crystal bands.

36 MATERIALS SCIENCE↗

Optical current generation in graphene: CEP control vs. ω + 2 ω control

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 ω and 2ω, 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 ω + 2ω 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.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗