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The nonlinear Hall effect (NLHE) with time-reversal symmetry constitutes the appearance of a transverse voltage quadratic in the applied electric field. It is a secondorder electronic transport phenomenon that induces frequency doubling and occurs in non-centrosymmetric crystals with large Berry curvature – an emergent magnetic field encoding the geometric properties of electronic wavefunctions. The design of (opto)electronic devices based on the NLHE is however hindered by the fact that this nonlinear effect typically appears at low temperatures and in complex compounds characterized by Dirac or Weyl electrons Here, we show a strong room temperature NLHE in the centrosymmetric elemental material bismuth synthesized in the form of technologically relevant polycrystalline thin films. The (111) surface electrons of this material are equipped with a Berry curvature triple that activates side jumps and skew scatterings generating nonlinear transverse currents. We also report a boost of the zero field nonlinear transverse voltage in arc-shaped bismuth stripes due to a extrinsic geometric classical counterpart of the NLHE This electrical frequency doubling in curved geometries is then extended to optical second harmonic generation in the terahertz (THz) spectral range. The strong nonlinear electrodynamical responses of the surface states are further demonstrated by a concomitant highly efficient THz third harmonic generation which we achieve in a broad range of frequencies in Bi and Bi-based heterostructures. Combined with the possibility of growth on CMOS-compatible and mechanically flexible substrates, these results highlight the potential of Bi thin films for THz (opto)electronic applications.

Ultrafast optical control of quantum systems is an emerging field of physics. In particular, the possibility of light-driven superconductivity has attracted much of attention. To identify non-equilibrium superconductivity, it is necessary to measure fingerprints of superconductivity on ultrafast timescales. Recently non-linear THz third harmonic generation (THG) was shown to directly probe the collective degrees of freedoms of the superconducting condensate, including the Higgs mode. Here we extend this idea to light-driven non-equilibrium states in superconducting La2-xSrxCuO4 establishing an optical pump-THz-THG drive protocol to access the transient superconducting (SC) order-parameter quench and recovering on few-picosecond timescales. We show in particular the ability of two-dimensional (2D) TH spectroscopy to disentangle the effects of optically-excited quasiparticles from the pure order-parameter dynamics, that are unavoidably mixed in the pump-driven linear THz response. Benchmarking the gap dynamics to existing experiments shows the ability of driven THG spectroscopy to overcome these limitations in ordinary pump-probe protocols.

Water possesses strong absorption in the THz range due to intermolecular vibrational modes in a network of hydrogen-bonded water molecules. Its THz response is also sensitive to the coupling of water to other molecules, i.e. the hydration shell of a protein. Probing the nonlinear properties of hydration water can provide insight into protein solvent dynamics, and in the case of intrinsically disordered proteins, its subsequent role in the liquid-liquid phase separation (LLPS). Such characterization at low THz frequencies (< 3 THz) remains yet limited, due to the scarcity of brilliant light sources in this range. Here, we present the nonlinear characterization at 0.5 THz of water and FUS protein solution in a liquid transmission cell, using a THz time-domain spectroscopy (THz-TDS) setup with the TELBE free electron laser source at HZDR. Our results show that the nonlinear absorption and refractive indices of the FUS protein solution differ from that of water, indicating a perturbed hydrogen bonding network.

The free-electron laser (FEL) is an ideal source of high-power coherent THz radiation for many applications. The FEL provides continuously tunable THz radiation, typically in ultrashort transform limited pulses with very high peak power. One limitation though is that the carrier envelope phase (CEP) of the FEL pulses is not fixed, making measurements of coherent THz-driven processes extremely difficult, if not impossible. We present here, a novel technique that enables shot-to-shot measurement of the CEP of every FEL pulse up to very high repetition rates. This powerful technique enables phase-resolved measurements of the FEL pulses, which opens the door for the study of coherent THz-driven phenomena as well as the advanced FEL diagnostics needed in the pursuit of CEP stable operation of an FEL.

2H-NbSe2 is an archetypal system in which superconductivity and charge density wave (CDW) coexist and compete macroscopically with each other. In particular, this interplay also manifests in their dynamical fluctuations. As a result, the superconducting amplitude fluctuation (i.e., Higgs mode) is pushed below the quasiparticle continuum, allowing it to become a coherent excitation observable by Raman scattering. In the present study, we coherently drive the collective oscillations of the two orders and visualize their interplay in the time domain. We find that both collective modes contribute to terahertz third-harmonic generation (THG) and their THG signals interfere below Tc, leading to an antiresonance of the integrated THG signal. The dynamical Ginzburg-Landau model suggests that around the antiresonance a periodic energy transfer between the driven Higgs oscillations and the driven CDW oscillations is possible. Our results illustrate the roles of collective modes in the terahertz THG process, revealing a close connection of this technique to Raman scattering. In systems where the different collective modes are coupled, our experimental scheme also illustrates a paradigm for realizing coherent control via such couplings.

We investigate ultrafast harmonic generation (HG) in Si: B, driven by intense pump pulses with fields reaching∼ 100 kV cm− 1 and a carrier frequency of 300 GHz, at 4 K and 300 K, both experimentally and theoretically. We report several findings concerning the nonlinear charge carrier dynamics in intense sub-THz fields:(i) Harmonics of order up to n= 9 are observed at room temperature, while at low temperature we can resolve harmonics reaching at least n= 11. The susceptibility per charge carrier at moderate field strength is as high as for charge carriers in graphene, considered to be one of the materials with the strongest sub-THz nonlinear response.(ii) For T= 300 K, where the charge carriers bound to acceptors are fully thermally ionized into the valence subbands, the susceptibility values decrease with increasing field strength. Simulations incorporating multi-valence-band Monte Carlo and finite-difference-time-domain (FDTD) propagation show that here, the HG process becomes increasingly dominated by energy-dependent scattering rates over the contribution from band nonparabolicity, due to the onset of optical-phonon emission, which ultimately leads to the saturation at high fields. (iii) At T=4K, where the majority of charges are bound to acceptors, we observe a drastic rise of the HG yields for internal pump fields of ∼30kVcm−1, as one reaches the threshold for tunnel ionization. We disentangle the HG nonlinear response into contributions associated with the initial photoionization and subsequent motion in the bands, and show that intracycle scattering seriously degrades any contribution to HG emission from coherent recollision of the holes with their parent ions.

The coherent infrared and THz sources driven by the superconducting electron accelerator ELBE are described. The present status of the facility is summarized and a few scientific highlights are mentioned. Finally plans for a successor facility (Dresden Advanced Light Infrastructure, DALI) are outlined along with the most important scientific and technological challenges.

Der Terahertz-Frequenzbereich umfasst ein technisch wenig erschlossenes Grenzgebiet im elektromagnetischen Spektrum. Er ist aber besonders interessant, weil er viele Eigenfrequenzen verschiedener, komplexer Quantenphänomene enthält. Dafür stehen neuerdings intensive Terahertz-Pulse aus spezialisierten Elektronenbeschleunigerquellen zur Verfügung. Sie bieten nun eine einzigartige Möglichkeit, solch fundamentale Quantenprozesse im Nichtgleichgewicht zu untersuchen

Non-linear materials are cornerstones of modern optics and electronics. Strong dependence on the intrinsic properties of particular materials, however, inhibits the at-will extension of demanding non-linear effects, especially those second-order ones, to widely adopted centrosymmetric materials (for example, silicon) and technologically important burgeoning spectral domains (for example, terahertz frequencies). Here we introduce a universal route to efficient non-linear responses enabled by exciting non-linear Thomson scattering, a fundamental process in electrodynamics that was known to occur only in relativistic electrons in metamaterial composed of linear materials. Such a mechanism modulates the trajectory of charges, either intrinsically or extrinsically provided in solids, at twice the driving frequency, allowing second-harmonic generation at terahertz frequencies on crystalline silicon with extremely large non-linear susceptibility in our proof-of-concept experiments. By offering a substantially material-and frequency-independent platform, our approach opens new possibilities in the fields of on-demand non-linear optics, terahertz sources, strong field light-solid interactions and integrated photonic circuits

We study the third harmonic generation (THG) of graphite layers on paper substrate upon excitation with intense (up to 100 kV/cm) narrowband terahertz (THz) pulses. Highest THG efficiencies are comparable with those of CVD-grown single-layer graphene. Samples were hand-drawn, using commercially available pencils. The THG response showed a high sensitivity regarding the hatching direction relative to the THz polarization orientation. Using Raman spectroscopy, we confirmed the occurrence of graphene-like structures in the samples. Our findings demonstrate the feasibility of virtually no cost and easy to fabricate materials for THz nonlinear optics.

In spectroscopy studies of solids, interaction between a discrete mode and a continuum of excitations sometimes leads to an interference effect known as the Fano resonance, characterized by the asymmetric scattering amplitude of the discrete mode as a function of electromagnetic driving frequency. Cuprate high-Tc superconductors are known for its intertwined interactions and the coexistence of competing orders. In this study, we report a new type of Fano resonance manifested by the collective amplitude oscillations of the superconducting order, i.e. the Higgs mode, in cuprate high-Tc superconductors, where we resolve both the amplitude and phase signatures of the Fano resonance. Our observation suggests that the heavily damped Higgs mode is coupled to another collective mode in the system. Based on the results of an extensive hole-doping and magnetic field dependent investigation, we speculate charge density wave fluctuations as the coupled mode. Our study highlights the possibility of a dynamical interaction between superconductivity and charge density wave in cuprate high-Tc superconductors, which demonstrates the scientific prospect of Higgs spectroscopy as a new type of spectroscopy method.

Efficient generation and control of spin currents launched by terahertz (THz) radiation with subsequent ultrafast spin-to-charge conversion is the current challenge for the next-generation of high-speed communication and data processing units. Here, we demonstrate that THz light can efficiently drive coherent angular momentum transfer in nanometer-thick ferromagnet/heavy-metal heterostructures. This process is non-resonant and does neither require external magnetic fields nor cryogenics. The efficiency of this process is more than one order of magnitude higher as compared to the recently observed THz induced spin-pumping in MnF2 antiferromagnet. The coherently driven spin currents originate from the ultrafast spin Seebeck effect, caused by a THz-induced temperature imbalance in electronic and magnonic temperatures and fast relaxation of the electron-phonon system. Owing to the fact that the electron-phonon relaxation time is comparable with the period of a THz wave, the induced spin current results in THz second harmonic generation and THz optical rectification, providing a spintronic basis for THz frequency mixing and rectifying components.

Several technologies, including photodetection, imaging and data communication, could greatly benefit from the availability of fast and controllable conversion of terahertz (THz) light to visible light. Here, we demonstrate that the exceptional properties and dynamics of electronic heat in graphene allow for THz-to-visible conversion, which is switchable at a sub-nanosecond timescale. We show a tunable on/off ratio of more than 30 for the emitted visible light, achieved through electrical gating using a gate voltage on the order of one Volt. We also demonstrate that a grating-graphene metamaterial leads to an increase in THz-induced emitted power in the visible range by two orders of magnitude. The experimental results are in agreement with a thermodynamic model that describes black-body radiation from the electron system heated through intraband Drude absorption of THz light. These results provide a promising route towards novel functionalities of optoelectronic technologies in the THz regime.

Spin-based technologies can operate at terahertz frequencies but require manipulation techniques that work at ultrafast timescales to become practical. For instance, devices based on spin waves, also known as magnons, require efficient generation of high-energy exchange spin waves at nanometre wavelengths. To achieve this, a substantial coupling is needed between the magnon modes and an electro-magnetic stimulus such as a coherent terahertz field pulse. However, it has been difficult to excite non-uniform spin waves efficiently using terahertz light because of the large momentum mismatch between the submillimetre-wave radiation and the nanometre-sized spin waves. Here we improve the light–matter interaction by engineering thin films to exploit relativistic spin–orbit torques that are confined to the interfaces of heavy metal/ferromagnet heterostructures. We are able to excite spin-wave modes with frequencies of up to 0.6 THz and wavelengths as short as 6 nm using broadband terahertz radiation. Numerical simulations demonstrate that the coupling of terahertz light to exchange-dominated magnons originates solely from interfacial spin–orbit torques. Our results are of general applicability to other magnetic multilayered structures, and offer the prospect of nanoscale control of high-frequency signals.

Der Terahertz-Frequenzbereich umfasst ein technisch wenig erschlossenes Grenzgebiet im elektromagnetischen Spektrum. Es ist aber besonders interessant, weil es viele Eigenfrequenzen verschiedener, komplexer Quantenphänomene enthält. Teil 2 widmet sich den Dirac-Materialien wie Graphen und topologischen Isolatoren, die extrem stark mit Terahertz-Feldern wechselwirken.

Water possesses strong absorption in the THz range due to intermolecular vibrational modes in a network of hydrogen-bonded water molecules. Its THz response is also sensitive to the coupling of water to other molecules, i.e. the hydration shell of a protein. Probing the nonlinear properties of hydration water can provide insight into protein solvent dynamics, and in the case of intrinsically disordered proteins, its subsequent role in the liquid-liquid phase separation (LLPS). Such characterization at low THz frequencies (< 3 THz) remains yet limited, due to the scarcity of brilliant light sources in this range. Here, we present the nonlinear characterization at 0.5 THz of water and FUS protein solution in a liquid transmission cell, using a THz time-domain spectroscopy (THz-TDS) setup with the TELBE free electron laser source at HZDR. Our results show that the nonlinear absorption and refractive indices of the FUS protein solution differ from that of water, indicating a perturbed hydrogen bonding network.

Research data and metadata that was used in the corresponding publication "Fano interference between collective modes in cuprate high-Tc superconductors" ( https://doi.org/10.1038/s41467-023-36787-4 ).

In our HELIPORT workshop, we provided insights into our project and share our results. In addition, we would like to provide a platform for the presentation of similar projects, as well as extensions or integrations from the surrounding research areas. The overall goal of the workshop is bringing together different institutions with similar challenges and establishing a community around our HELIPORT project. We therefore encouraged our community to submit an abstract for a talk or poster. The submissions are dedicated to four thematic points: • HELIPORTuse-cases, • Scientificprojectandmetadatamanagement, • Experiment-specificandoverallmetadataand • Scientificworkflows. HELIPORT (Helmholtz ScIentific Project WORkflow PlaTform) itself is a project funded by the Helmholtz Metadata Collaboration, and runs from July 2021 until June 2023. HELIPORT aims to make the entire life cycle of a scientific project findable, accessible, interoperable and reusable according to the FAIR principles. In particular, our data management solution deals with the areas from the generation of the data to the publication of primary research data, the workflows carried out and the actual research results. For this purpose, a concept was developed which shows the various essential components and their connections.

Datasets measured at the TELBE THz facility consisting of raw (time-sorted) data and binned data that was used for further analysis. The xlsx-file contains measured THz powers. Metadata can be found in labbook file zip archive. Final data analysis was performed by Jakub Vít.

Research data generated at the TELBE facility and used in the linked publication. The filenumber corresponding to the figures in the publication are as follows: Fig.1 (a): 032 (b): 032 (c)-(e): 023-033, 035-039 Fig.2 (a): 152 (b): 152 (c): 150-164 Fig. 3 (a): 023-033, 035-039, 108-120, 072, 073, 079-100. Data evaluation and figure preparation was completed externally by Chris Reinhoffer.

In this Origin project file (*.opju) we provide an access to the raw data which we obtained and analyzed. The result of our analysis are presented in the publication "Efficient ultrafast field-driven spin current generation for spintronic terahertz frequency conversion".

At the High-Field High-Repetition-Rate Terahertz facility @ ELBE (TELBE)[1], ultrafast terahertz-induced dynamics can be probed in various states of matter with highest precision. The TELBE sources offer both, stable and tunable narrowband THz radiation with pulse energies of several microjoules at high repetition rates and a synchronized coherent diffraction radiator,that provides broadband single-cycle pulses. The measurements at TELBE are data intensive, which can be as high as 20GB per experiment, that can lasts up to several minutes. As a result, the current data aquisition and data analysis stages are decoupled, where in the first step the primary data is processed and stored at HZDR and in a later step, restricted data access is made available to the user for post-processing. In this poster contribution, we present an integrated workflow for post-processing of the experimental data at TELBE with in-built exchange of metadata between the experiment control software LabView and the workflow execution engine UNICORE[2]. We also present the guidance system HELIPORT[3] which manages the metadata of the associated project proposal and job information from UNICORE, and integrates with the electronic lab notebook (MediaWiki[4]), providing a user-friendly interface for monitoring the actively running experiments at TELBE. [1] https://doi.org/10.1063/1.4978042 [2] https://doi.org/10.1109/HPCSim.2016.7568392 [3] https://doi.org/10.1145/3456287.3465477 [4] https://www.mediawiki.org/wiki/Project:About

Achieving efficient, high-power harmonic generation in the terahertz (THz) spectral domain has technological applications, for example in sixth generation (6G) communication networks [1, 2]. Massless Dirac fermions possess extremely large THz nonlinear susceptibilities and harmonic conversion efficiencies [3–7]. However, the observed maximum generated harmonic power is limited, because of saturation effects at increasing incident powers, as shown recently for graphene [8]. Here, we demonstrate room-temperature THz harmonic generation in a Bi2Se3 topological insulator (TI) and TI-grating metamaterial structures with surface-selective THz field enhancement. We obtain a third-harmonic power approaching the milliwatt range for an incident power of 75 mW – an improvement by two orders of magnitude compared to a benchmarked graphene sample. We establish a framework in which this exceptional performance is the result of thermodynamic harmonic generation by the massless topological surface states, benefiting from ultrafast dissipation of electronic heat via surface-bulk Coulomb interactions. These results are an important step towards on-chip THz (opto)electronic applications.

Radiation sources with a stable carrier-envelope phase (CEP) are highly demanded tools for field-resolved studies of light-matter interaction, providing access both to the amplitude and phase information of dynamical processes. At the same time, many coherent light sources, including those with outstanding power and spectral characteristics lack CEP stability, and so far could not be used for this type of research. In this work, we present a method enabling linear and non-linear phase-resolved terahertz (THz) -pump laser-probe experiments with CEP-unstable THz sources. THz CEP information for each pulse is extracted using a specially designed electro-optical detection scheme. The method correlates the extracted CEP value for each pulse with the THz-induced response in the parallel pump-probe experiment to obtain an absolute phase-resolved response after proper sorting and averaging. As a proof-of-concept, we demonstrate experimentally field-resolved THz time-domain spectroscopy with sub-cycle temporal resolution using the pulsed radiation of a CEP-unstable infrared free-electron laser (IR-FEL) operating at 13 MHz repetition rate. In spite of the long history of IR-FELs and their unique operational characteristics, no successful realization of CEP-stable operation has been demonstrated yet. Being CEP-unstable, IR-FEL radiation has so far only been used in non-coherent measurements without phase resolution. The technique demonstrated here is robust, operates easily at high-repetition rates and for short THz pulses, and enables common sequential field-resolved time-domain experiments. The implementation of such a technique at IR-FEL user end-stations will facilitate a new class of linear and non-linear experiments for studying coherent light-driven phenomena with increased signal-to-noise ratio.

In recent years, femtosecond extreme-ultraviolet (XUV) and X-ray pulses from free-electron lasers have developed into important probes to monitor processes and dynamics in matter on femtosecond-time and Angstroem-length-scales. With the rapid progress of versatile ultra-fast X-ray spectroscopy techniques and more sophisticated data-analysis tools, accurate single-pulse information on the arrival time, duration and shape of the probing X-ray and XUV pulses becomes essential. Here, we demonstrate for the first time that XUV pulses can be converted into terahertz electromagnetic pulses. We observe that the duration, arrival time and energy of each individual XUV pulse is encoded in the waveform of the associated terahertz pulses and can, thus, be readily deduced from single-shot terahertz time-domain detection.

A conceptually new approach to synchronizing accelerator-based light sources and external laser systems is presented. The concept is based on utilizing a sufficiently intense accelerator-based single-cycle terahertz pulse to slice a thereby intrinsically synchronized femtosecond-level part of a longer picosecond laser pulse in an electro-optic crystal. A precise synchronization of the order of 10 fs is demonstrated, allowing for real-time lock-in amplifier signal demodulation. We demonstrate successful operation of the concept with three benchmark experiments using a 4th generation accelerator-based terahertz light source, i.e. (i) far-field terahertz time-domain spectroscopy, (ii) terahertz high harmonic generation spectroscopy, and (iii) terahertz scattering-type scanning near-field optical microscopy.

We report on high-order harmonic generation in the two-band superconductor MgB 2 driven by intense terahertz electromagnetic pulses. Third- and fifth-order harmonics are resolved in time domain and investigated as a function of temperature and in applied magnetic fields crossing the superconducting phase boundary. The high-order harmonics in the superconducting phase reflects nonequilibrium dynamics of the superconducting order parameter in MgB2, which is probed via nonlinear coupling to the terahertz field. The observed temperature and field dependence of the nonlinear response allows to establish the superconducting phase diagram.

Complex frustrated magnetic structures in multiferroic hexaferrites are well tunable by temperature, magnetic field and doping. We investigated the influence of strong THz pulses generated by superradiant THz sources on magnetic structure and related electromagnons’ absorption in Y- and Z-type multiferroic hexaferrites. While in Z-type hexaferrite (Ba0.2Sr0.8)3Co2Fe24O41 polycrystal, the observed changes in transmission spectra were fully described by sample heating, a blue-shift of the electromagnon frequency observed in Y-type hexaferrite Ba0.2Sr1.8Co2(Fe0.96Al0.04)12O22 single-crystal could be possibly ascribed to the transition from the alternating longitudinal conical to the transverse conical magnetic structure. We elaborated a nonlinear model which explained absence of nonlinearity in Z-type hexaferrite (Ba0.2Sr0.8)3Co2Fe24O41. For Y-type hexaferrite Ba0.2Sr1.8Co2(Fe0.96Al0.04)12O22, we discuss possible transient or even permanent effects of both THz electric and magnetic fields on its magnetic structure.

At the High-Field High-Repetition-Rate Terahertz facility @ ELBE (TELBE)[1], ultrafast terahertz-induced dynamics can be probed in various states of matter with highest precision. The TELBE sources offer both, stable and tunable narrowband THz radiation with pulse energies of several microjoules at high repetition rates and a synchronized coherent diffraction radiator,that provides broadband single-cycle pulses. The measurements at TELBE are data intensive, which can be as high as 20GB per experiment, that can lasts up to several minutes. As a result, the current data aquisition and data analysis stages are decoupled, where in the first step the primary data is processed and stored at HZDR and in a later step, restricted data access is made available to the user for post-processing. In this poster contribution, we present an integrated workflow for post-processing of the experimental data at TELBE with in-built exchange of metadata between the experiment control software LabView and the workflow execution engine UNICORE[2]. We also present the guidance system HELIPORT[3] which manages the metadata of the associated project proposal and job information from UNICORE, and integrates with the electronic lab notebook (MediaWiki[4]), providing a user-friendly interface for monitoring the actively running experiments at TELBE. [1] https://doi.org/10.1063/1.4978042 [2] https://doi.org/10.1109/HPCSim.2016.7568392 [3] https://doi.org/10.1145/3456287.3465477 [4] https://www.mediawiki.org/wiki/Project:About

Research data measured during the TELBE beamtime in March 2022 for the proposal 21202600 (THz-induced structural phase transition in hybrid perovskites). PI: Heejae Kim, experimental team: Jaco Geuchies, Sheng Qu, and the TELBE team

This repository entry contains the research data used for generating the publication "Terahertz-wave decoding of femtosecond extreme-ultraviolet light pulses".

At the ELBE high power radiation facility, the second version of a superconducting radio frequency (SRF) photoinjector has been put into operation and is now routinely applied for user operation at the ELBE electron accelerator. SRF guns are suitable for generating continuous wave (CW) electron beam with high average currents and high beam brightness. The SRF gun at ELBE has the goal to generate short electron pulses with bunch charges of 200-300 pC at typical repetition rates of 100 kHz for the production of super radiant, coherent terahertz radiation. The SRF gun includes a 3.5-cell, 1.3 GHz niobium cavity and a superconducting solenoid. A support system with liquid nitrogen (LN2) cooling allows the operation of normal-conducting, high quantum efficiency photo cathodes. In the paper we present the design and performance of the SRF gun as well as beam measurements for the operation with Mg photocathodes and an acceleration gradient of 8 MV/m (4 MeV kinetic energy). Finally, we discuss the SRF gun application for production of coherent terahertz radiation at the ELBE facility.

Graphene is conceivably the most nonlinear optoelectronic material. Its nonlinear optical coefficients in the terahertz (THz) frequency range surpass those of other materials by many orders of magnitude. This, in particular, allows one to use graphene for extremely efficient up-conversion of sub-THz electronic input signals into the THz frequency range at room temperature and under ambient conditions, thus paving the way for practical graphene-based ultrahigh-frequency electronic technology. Here, we show that the THz nonlinearity of graphene can be efficiently controlled using electrical gating, with gating voltages as low as a few volts. For example, optimal electrical gating enhances the power conversion efficiency in THz third-harmonic generation in graphene by about two orders of magnitude. We demonstrate gating control of THz nonlinearity of graphene for both ultrashort single-cycle and quasi-monochromatic multi-cycle input signals. Our experimental results are in quantitative agreement with a physical model of graphene nonlinearity, describing the time-dependent thermodynamic balance maintained within the electronic population of graphene during interaction with ultrafast electric fields. Our results can serve as a basis for straightforward and accurate design of devices and applications for efficient electronic signal processing in graphene at ultra-high frequencies.

Nonlinear optics is an increasingly important field for scientific and technological applications, owing to its relevance and potential for optical and optoelectronic technologies. Currently, there is an active search for suitable nonlinear material systems with efficient conversion and small material footprint. Ideally, the material system should allow for chip-integration and room-temperature operation. Two-dimensional materials are highly interesting in this regard. Particularly promising is graphene, which has demonstrated an exceptionally large nonlinearity in the terahertz regime. Yet, the light-matter interaction length in two-dimensional materials is inherently minimal, thus limiting the overall nonlinear-optical conversion efficiency. Here we overcome this challenge using a metamaterial platform that combines graphene with a photonic grating structure providing field enhancement. We measure terahertz third-harmonic generation in this metamaterial and obtain an effective third-order nonlinear susceptibility with a magnitude as large as 3·10−⁸ m² /V² , or 21 esu, for a fundamental frequencyof 0.7 THz. This nonlinearity is 50 times larger than what we obtain for graphene without grating. Such an enhancement corresponds to third-harmonic signal with an intensity that is three orders of magnitude larger due to the grating. Moreover, we demonstrate a field conversion efficiency for the third harmonic of up to ∼1% using a moderate field strength of ∼30 kV/cm. Finally we show that harmonics beyond the third are enhanced even more strongly, allowing us to observe signatures of up to the 9th harmonic. Grating-graphene metamaterials thus constitute an outstanding platform for commercially viable, CMOS compatible, room temperature, chip-integrated,THz nonlinear conversion applications.

The understanding of how spins move at pico- and femtosecond time scales is the goal of much of modern research in condensed matter physics, with implications for ultrafast and more energy-efficient data storage. However, the limited comprehension of the physics behind this phenomenon has hampered the possibility of realising a commercial technology based on it. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast time scales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report the first direct experimental evidence of inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetisation at a frequency of approximately 0.6 THz. This allows us to evince that the angular momentum relaxation time in ferromagnets is on the order of 10 ps.

The understanding of how spins move at pico- and femtosecond time scales is the goal of much of modern research in condensed matter physics, with implications for ultrafast and more energy-efficient data storage. However, the limited comprehension of the physics behind this phenomenon has hampered the possibility of realising a commercial technology based on it. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast time scales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report the first direct experimental evidence of inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetisation at a frequency of approximately 0.6 THz. This allows us to evince that the angular momentum relaxation time in ferromagnets is on the order of 10 ps.

Topologically-protected surface states present rich physics and promising spintronic, optoelectronic and photonic applications that require a proper understanding of their ultrafast carrier dynamics. Here, we investigate these dynamics in topological insulators (TIs) of the bismuth and antimony chalcogenide family, where we isolate the response of Dirac fermions at the surface from the response of bulk carriers by combining photoexcitation with below-bandgap terahertz (THz) photons with TI samples with vary- ing Fermi level, including one sample with the Fermi level located within the bandgap. We identify distinctly faster relaxation of charge carriers in the topologically-protected Dirac surface states (few hundred femtosec- onds), compared to bulk carriers (few picoseconds). In agreement with such fast cooling dynamics, we observe THz harmonic generation without any saturation effects for increasing incident fields, unlike graphene which exhibits strong saturation. This opens up promising avenues for increased THz nonlinear conversion effciencies, and high-bandwidth optoelectronic and spintronic information and communication applications.

This research data publication contains: - Experimental datasets which were evaluated and presented in the corresponding article. - Origin software file that contains the raw data as well as the different steps of the data analysis, the results of which are presented in the article.

This research data publications contains the sorted pulse-resolved data and metadata corresponding to the linked publication: Electrical tunability of terahertz nonlinearity in graphene. The final data evaluation and preparation of figures was done externally by Dr. Hassan Hafez, who should be contacted in terms of assigning raw data to data shown in publication.

In high energy physics, the Higgs field couples to gauge bosons and fermions and gives mass to their elementary excitations. Experimentally, such couplings can be verified from the decay product of the Higgs boson, the scalar (amplitude) excitation of the Higgs field. In superconductors, Cooper pairs bear a certain analogy to the Higgs field. Coulomb interactions between the Cooper pairs give mass to the electromagnetic field, which leads to the Meissner effect. Additional coupling with other types of interactions or collective modes is foreseeable, and even highly probable for high-Tc superconductors, where multiple degrees of freedom are intertwined. The superconducting Higgs mode may reveal such couplings spectroscopically and uncover interactions directly relevant to Cooper pairing. To this end, we investigate the Higgs mode of several cuprate thin films using phase-resolved terahertz third harmonic generation (THG) to. In addition to the heavily damped Higgs mode itself, we observe a universal jump in the phase of the driven Higgs oscillation as well as a non-vanishing THG above Tc. These findings indicate coupling of the Higgs mode to other collective modes and a nonzero pairing amplitude above Tc. Our study demonstrates a new approach for investigating unconventional superconductivity. We foresee a fruitful future for phase-resolved spectroscopy in various superconducting systems.

Research data for the May 2020 beamtime on "THz-driven structural phase transition in a hybrid perovskite". PI: Heejae Kim, MPI for polymer research, Mainz.

Reserach data for Publication: Non-perturbative high-harmonic generation in the three-dimensional Dirac semimetal Cd₃As₂ DOI: 10.1038/s41467-020-16133-8

Research data for used for the publication: "Grating-graphene metamaterial as a platform for terahertz nonlinear photonics". Datasets measured at the TELBE accelerator-based THz source are measured using a pulse-resolved detection scheme. The data points are sorted according to the absolute arrival time measurement. The four columns hold the following data: 1) absolute time in picoseconds 2) Signal of the emitted THz measured by electro-optic sampling. 3) Relative THz intensity measured using a pyroelectric detector. THz intensity is proportional to absolute power of the signal. 4) Data corresponding to the relative timing of each pulse. Not used for further analysis of the data. The filenumbers of the measurements used for the figures are as follows: Fig. 1a: File 003 Fig. 1b-c: File 043 Fig. 1d-e: File 086 Fig. 2a: Files 080..088 (bare graphene) and 031..049 (grating) Fig. 2b: same Fig. 3a: Files 050..057 Fig. 3c: Files 076..079 Fig. 4. Table top measurements; no file numbers Supp. Fig. 2: File 030 Supp. Fig. 4: File 024..025 Supp. Fig. 7a: Files 031..034 and 036..041 Supp. Fig. 7b: Files 080..083 Supp. Fig. 7d: Files 031..049 and 080..086 Supp. Fig. 9a: Files 031..046 Supp. Fig. 9b: Files 080..085 and 087..088 The datasets measured using a table-top laser source contain two columns. The first one is the position of the optical delay stage in mm that has to be multiplied by 6.667 ps/mm to define the time axis. The second column contains the THz signal as measured using electro-optic sampling.

Research data from the June 2021 TELBE beamtime for scientific exchange.

The complexity of competing interactions in high-temperature superconductors provides a fertile ground for collective modes of different origins. Their coupling to the superconducting order parameter may give important insight into the microscopic pairing mechanism. One prominent example in cuprates is the magnetic resonant mode, whose experimental observation spawned theoretical investigations of pairing scenarios mediated by antiferromagnetic fluctuations. Now, phase-resolved nonlinear terahertz spectroscopy of the superconducting Higgs mode offers a new way to reveal the coupling between the collective modes and the superconducting order parameter. Using this technique, we discover a new collective mode distinct from the heavily damped Higgs mode in different families of cuprates. We discuss the origin of this mode and characterize its interplay with the Higgs mode. Our results demonstrate Higgs spectroscopy as a new approach to uncover interactions directly relevant to superconductivity. This technique opens up entirely new avenues for understanding unconventional superconductivity and calls for supporting theoretical work to unlock its full power.

Harmonic generation is a general characteristic of driven nonlinear systems, and serves as an efficient tool for investigating the fundamental principles that govern the ultrafast nonlinear dynamics. In atomic gases, high-harmonic radiation is produced via a three-step process of ionization, acceleration, and recollision by strong-field infrared laser. This mechanism has been intensively investigated in the extreme ultraviolet and soft X-ray regions, forming the basis of attosecond research, e.g. real-time observation of electron dynamics and sub-atomic tomography of molecular orbitals. In solid-state materials, which are characterized by crystalline symmetry and strong interactions, yielding of harmonics has just recently been reported. The observed high-harmonic generation was interpreted with fundamentally different mechanisms, such as interband tunneling combined with dynamical Bloch oscillations, intraband thermodynamics and nonlinear dynamics, and many-body electronic interactions. Here, in a distinctly different context of three-dimensional Dirac semimetal, we report on experimental observation of high-harmonic generation up to the seventh order driven by a strong-field terahertz pulse. The observed non-perturbative high-harmonic generation is interpreted as a generic feature of terahertz-field driven nonlinear intraband kinetics of Dirac fermions. We anticipate that our results will trigger great interest in detection, manipulation, and coherent control of the nonlinear response in the vast family of three-dimensional Dirac and Weyl materials.

In high energy physics, the Higgs field couples to gauge bosons and fermions and gives mass to their elementary excitations. Experimentally, such couplings can be verified from the decay product of the Higgs boson, the scalar (amplitude) excitation of the Higgs field. In superconductors, Cooper pairs bear a certain analogy to the Higgs field. Coulomb interactions between the Cooper pairs give mass to the electromagnetic field, which leads to the Meissner effect. Additional coupling with other types of interactions or collective modes is foreseeable, and even highly probable for high-Tc superconductors, where multiple degrees of freedom are intertwined4. The superconducting Higgs mode may reveal such couplings spectroscopically and uncover interactions directly relevant to Cooper pairing. To this end, we investigate the Higgs mode of several cuprate thin films using phase-resolved terahertz third harmonic generation (THG) to. In addition to the heavily damped Higgs mode itself, we observe a universal jump in the phase of the driven Higgs oscillation as well as a non-vanishing THG above Tc. These findings indicate coupling of the Higgs mode to other collective modes and a nonzero pairing amplitude above Tc. Our study demonstrates a new approach for investigating unconventional superconductivity. We foresee a fruitful future for phase-resolved spectroscopy in various superconducting systems.

In this study, a conceptually different approach for investigating magnetic phase transitions in ultra-thin films is presented. THz emission from a laser-excited material is used to monitor the magnetization dynamics during the laser-driven antiferromagnetic to ferromagnetic transition in FeRh. The emitted THz signal is calibrated against static magnetometry data measurements, giving a direct measure of the absolute magnetic moment of the sample on the sub-picosecond timescale. The technique is, therefore, highly complementary to conventional time-resolved experiments such as time resolved magneto-optic Kerr effect (MOKE) or x-ray magnetic circular dichroism.

The conversion of optical and electrical energies in novel materials is key to modern optoelectronic and light-harvesting applications. Here, we investigate the equilibration dynamics of photoexcited 2,7-bis(biphenyl-4-yl)-2′,7′-ditertbutyl-9,9′-spirobifluorene (SP6) molecules adsorbed on ZnO(10-10) using femtosecond time-resolved two-photon photoelectron and optical spectroscopies. We find that, after initial ultrafast relaxation on femtosecond and picosecond time scales, an optically dark state is populated, likely the SP6 triplet (T) state, that undergoes Dexter-type energy transfer (rDex = 1.3 nm) and exhibits a long decay time of 0.1 s. Because of this long lifetime, a photostationary state with average T–T distances below 2 nm is established at excitation densities in the 1020 cm−2 s−1 range. This large density enables decay by T–T annihilation (TTA) mediating autoionization despite an extremely low TTA rate of kTTA = 4.5 ⋅ 10−26 m3 s−1. The large external quantum efficiency of the autoionization process (up to 15%) and photocurrent densities in the mA cm−2 range offer great potential for light-harvesting applications.

Raw files from the TELBE beamtime August 2020 for exchange.