Nonlinear phenomena in the terahertz (THz) spectral domain are essential for advancing our understanding of the optoelectronic properties of quantum materials and form the basis for emerging signal processing technologies. We investigate highly efficient third-order nonlinear processes in HgTe-based heterostructures, with a focus on third-harmonic generation (THG) and four-wave mixing (FWM). The key enabling factor is a high-mobility HgTe structure with band inversion, resulting in one of the strongest χ(3) nonlinearities reported in the THz range. Its linear Dirac-like dispersion allows efficient mixing of broadband fields, resulting in frequency-converted output characteristic of third-order nonlinear processes. To further investigate the underlying dynamics, we performed time-resolved pump-probe measurements to find the energy and momentum relaxation times. Our results establish HgTe-based Dirac materials as promising platforms for nonlinear THz photonics and ultrafast signal conversion.

High harmonic generation (HHG) in the terahertz (THz) regime is an emerging field, which has so far been
focusing on Dirac materials and high-TC superconductors. Here, we demonstrate THz harmonic generation
across the Mott insulator-metal transition in rare-earth nickelates (RNiO3, R = rare-earth atom). The THz har-
monic signal shows distinct characteristics in all the three different phases: the intensity of harmonics increases
upon cooling in both the low-temperature antiferromagnetic (AFM) insulating and high-temperature paramag-
netic (PM) metallic phases, while this trend is reversed in the intermediate PM insulating phase. Using single-
and two-band Hubbard models, we find different dominant origins of THz harmonics in different phases: strong
spin-charge and orbital-charge couplings in the AFM insulating phase, intraband currents from renormalized
quasi-particles with frequency-dependent scattering rate in the PM metallic phase, and the reduction of the
charge carrier density due to the opening of the Mott gap in the PM insulating phase. These results and mecha-
nisms significantly differ from those observed in the optical regime. Our study provides the basis for THz HHG
physics in Mott and other strongly correlated systems, developing strategies for efficient THz HHG from these
systems and using THz HHG to gain insights into their complex physics

In the past years, there is an active research of materials displaying the non-linear Hall effect with time-reversal symmetry [1-5]. From a fundamental point of view, this quantum transport effect provides a direct way to detect in nonmagnetic materials the Berry curvature – a quantity in which the geometry of the electronic wavefunctions is encoded. The nonlinear Hall effect is also at the basis of terahertz optoelectronic applications of interest for instance for sixth generation (6G) communication networks.

An appropriate material platform for such applications should satisfy a number of criteria: i) the nonlinear Hall effect should survive up to room temperature; ii) the effect should be tunable; iii) the material fabrication should be technologically relevant (simple chemical composition of the material and low-cost microstructure); iv) ideally the material should not contain toxic heavy rare-earth elements. So far, candidate materials address only partially these requirements.

Here, we discover the first material addressing all the requirements at the same time: polycrystalline bismuth thin films [6]. We demonstrate that in this elemental green (semi)metal, the room-temperature nonlinear Hall effect is generated by surface states that are characterized by a Berry curvature triple: a quantity governing a skew scattering effect that generates non-linear transverse currents. Furthermore, we also show that the strength of nonlinear Hall effect can be controlled on demand using an extrinsic classical shape effect: the geometric nonlinear Hall effect. We demonstrate this by fabricating arc-shaped bismuth Hall bars. This endows the nonlinear Hall effect of Bismuth with the tunability encountered only in low-dimensional materials at low temperatures.

To show the potential of polycrystalline Bi thin films for optoelectronic applications in the terahertz (THz) spectral domain, we have performed high harmonic generation experiments. Polycrystalline Bi thin films reveal a high efficiency of THz third-harmonic generation (THG) that reaches levels >1% at room temperature. Moreover, our material possesses a non-saturating trend of the efficiency of the THz THG. This enables the use of Bi thin films for high- and wide- THz bandwidth electronics which works at high peak power and long pulses.

[1] Z. Z. Du et al., Nonlinear Hall effects. Nature Reviews Physics 3, 744 (2021).
[2] I. Sodemann et al., Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials. Phys. Rev. Lett. 115, 216806 (2015).
[3] Q. Ma et al., Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565, 337 (2019).
[4] K. Kang et al., Nonlinear anomalous Hall effect in few-layer WTe2. Nature Mater. 18, 324 (2019).
[5] P. He et al., Quantum frequency doubling in the topological insulator Bi2Se3. Nature Communications 12, 698 (2021).
[6] P. Makushko et al., A tunable room-temperature nonlinear Hall effect in elemental bismuth thin films. Nature Electronics 7, 207 (2024).

We demonstrate a highly efficient method for upconverting broadband sub-terahertz (sub-THz) signals to multiple terahertz (THz) bands using a photoconductive antenna coupled with the TELBE radiation source, leveraging the unique properties of HgTe-based Dirac materials. HgTe heterostructures known for their robust third-order nonlinearities, enhance frequency mixing and signal amplification across THz bands. We achieved a field conversion efficiency over 2% for room temperature.

Frequency mixing in the terahertz (THz) range holds promise for bridging the sub-THz and multi-THz spectral domains, critical for next-generation wireless communication and ultrafast signal processing [1]. We demonstrate room-temperature upconversion of broadband sub-THz signals (0.1–0.5 THz) into higher THz bands using a 70 nm-thick HgTe-based Dirac semimetal, leveraging its strong third-order nonlinear response without requiring resonant enhancement. The process relies on four-wave mixing (FWM), driven by the high χ(3) of HgTe, which arises from its gapless Dirac-like dispersion and long carrier relaxation times [2]. Our dual-source excitation scheme combines broadband pulses from a photoconductive antenna (PCA) with narrowband superradiant pulses from the TELBE source [3]. When coherently overlapped in the HgTe film, the input fields generate distinct frequency sidebands at f_{\mathrm{high}}=2f_T+f_a and f_{\mathrm{low}}=2f_T-f_a, as expected for third-order FWM. A field conversion efficiency exceeding 2% was achieved—among the highest reported for solid-state THz nonlinear processes at ambient conditions [2]. The efficiency scaling with field strengths and polarization confirms the coherent and χ⁽³⁾-driven nature of the process. These results establish HgTe Dirac semimetals as highly promising platforms for THz photonics, with further enhancement anticipated from multilayer or metamaterial integration [4].

Reference:

[1] Hafez et al., Nature 561, 507 (2018)
[2] Svetikova et al., ACS Photonics 10, 3708 (2023)
[3] Helm et al., Eur. Phys. J. Plus 138, 158 (2023)
[4] Giorgianni et al., Nat. Commun. 7, 11421 (2016)

The use of the THz frequency domain in future network generations offers an unparalleled level of capacity, which can enhance innovative applications in wireless communication, analytics, and imaging. Communication technologies rely on frequency mixing, enabling signals to be converted from one frequency to another and transmitted from a sender to a receiver. Technically, this process is implemented using nonlinear components such as diodes or transistors. However, the highest operation frequency of this approach is limited to sub-THz bands. Here, we demonstrate the upconversion of a weak sub-THz signal from a photoconductive antenna to multiple THz bands. The key element is a high-mobility HgTe-based heterostructure with electronic band inversion, leading to one of the strongest third-order nonlinearities among all materials in the THz range. Due to the Dirac character of electron dispersion, the highly intense sub-THz radiation is efficiently mixed with the antenna signal, resulting in a THz response at linear combinations of their frequencies. The field conversion efficiency above 2% is provided by a bare tensile-strained HgTe layer with a thickness below 100 nm at room temperature under ambient conditions. Devices based on Dirac materials allow for high degree of integration, with field-enhancing metamaterial structures, making them very promising for THz communication with unprecedented data transfer rate.

Spintronic terahertz (THz) frequency conversion in ferromagnet/heavy metal (FM/HM) heterostructures has the potential to enhance high-speed data communication and advance ultrafast magnetic memory applications. By leveraging ultrafast spin currents and spin-orbit interactions in FM/HM systems, broadband THz generation can be achieved, with recent studies demonstrating spintronic THz second harmonic generation (TSHG) and optical rectification. We introduce concepts for controlling the frequency conversion and temporal characteristics of TSHG through active manipulation of FM magnetization, providing flexibility in second harmonic emission and waveform shaping. The TSHG valve is realized by employing THz metamaterials, consisting of hybrid FM/HM structures combined with subwavelength gold periodic arrays. Additionally, using microstructured gold periodic arrays, we investigate the TSHG field enhancement capability as a function of grating filling factor and explore the potential for TSHG cavity enhancement.

Curvilinear magnetism is a framework, which helps understanding the impact of geometric curvature on complex magnetic responses of curved 1D wires and 2D shells. This approach provides means to modify conventional or to launch novel functionalities by tailoring curvature and 3D shape of ferro- and antiferromagnetic thin films and nanowires. In this talk, we will address fundamentals of curvature-induced effects in magnetism and review envisioned application scenarios. In particular, we will demonstrate that curvature allows tailoring fundamental anisotropic and chiral magnetic interactions and enables fundamentally new nonlocal chiral symmetry breaking effect. The topology of the geometry of 3D shaped magnetic objects allows stabilizing multiple solitons within a confined nanoarchitecture. Those are relevant for numerous research and technology fields ranging from non-conventional computing and spin-wave splitters for low-energy magnonics. The application potential of geometrically curved magnetic architectures is being explored as mechanically reshapeable magnetic field sensors for automotive applications, spin-wave filters, high-speed racetrack memory devices, magnetic soft robots as well as on-skin interactive electronics relying on thin films as well as printed magnetic composites with appealing self-healing performance. This opens perspectives for magnetoelectronics in smart wearables, interactive printed electronics and motivates further explorations towards the realization of eco-sustainable magnetic field sensing relying on biocompatible and biodegradable materials.

Terahertz (THz) spintronics, operating on picosecond timescales, involves the generation and control of non-equilibrium electron spin states within the THz frequency regime. Efficient generation and control of spin currents launched by 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. Recent studies have shown that THz light can efficiently drive coherent spin currents in nanometer-thick ferromagnet (FM)/heavy-metal (HM) heterostructures, primarily due to demagnetization process of FM and the ultrafast spin Seebeck effect arising from a THz-induced temperature imbalance between electronic and magnonic systems and rapid electron-phonon relaxation. Owing to the fact that the electron-phonon relaxation time is comparable (or smaller) to the period of a THz wave, the induced spin current from each half cycle of the THz wave results in THz second harmonic generation (TSHG) and THz optical rectification. In this study, we explore the potential of utilizing subwavelength-sized gold periodic arrays with a grating period smaller than the THz wavelength to enhance local spin currents, thereby improving the efficiency of THz frequency conversion. By fabricating different gratings with varying widths of Au stripes and spacing between them, we aim to achieve efficient spintronic THz frequency conversion in the near-field regime. Our findings indicate that power efficiency increases as the gap size decreases, resulting in a nine-fold enhancement at a 2 μm gap size.

Terahertz (THz) spintronics, operating on picosecond timescales, involves the generation and control of non equilibrium electron spin states within the THz frequency regime. Recent studies have shown that THz light can efficiently drive coherent spin currents in nanometer-thick ferromagnet (FM)/heavy-metal (HM) heterostructures, primarily due to demagnetization process of FM and the ultrafast spin Seebeck effect. Owing to the fact that the electronphonon relaxation time is comparable (or smaller) to the period of a THz wave, the induced spin current from each half cycle of the THz wave results in THz second harmonic generation (TSHG) and THz optical rectification. In this study, we explore the potential of utilizing subwavelength-sized gold periodic arrays with a grating period smaller than the THz wavelength to enhance local spin currents, thereby improving the efficiency of THz frequency conversion.

All data that were used to generate the figures in the related publication are currently stored in the Springer Nature Figshare repository.

The THz frequency domain offers unique capabilities for applications in wireless communication, spectroscopy, and imaging. Communication technologies rely on frequency mixing, but traditional methods using nonlinear components such as diodes and transistors are limited to sub-THz bands.

This presentation will discuss our demonstration of THz upconversion using a high-mobility HgTe-based topological insulator, characterized by its exceptional third-order nonlinearity. We employ intense sub-THz radiation, facilitating efficient nonlinear mixing with signals from a photoconductive antenna. This method results in a strong THz response at the sum and difference frequencies, achieving a field conversion efficiency of approximately 2% with a tensile-strained HgTe nanolayer at room temperature.

The interplay of electronic charge, spin, and orbital currents, coherently driven by picosecond long oscillations of light fields in spin-orbit coupled systems, is the foundation of emerging terahertz lightwave spintronics and orbitronics. The essential rules for how terahertz fields interact with these systems in a nonlinear way are still not understood. In this work, we demonstrate a universally applicable electronic nonlinearity originating from spin-orbit interactions in conducting materials, wherein the interplay of light-induced spin and orbital textures manifests. We utilized terahertz harmonic generation spectroscopy to investigate the nonlinear dynamics over picosecond timescales in various transition metal films. We found that the terahertz harmonic generation efficiency scales with the spin Hall conductivity in the studied films, while the phase takes two possible values (shifted by π), depending on the d-shell filling. These findings elucidate the fundamental mechanisms governing nonequilibrium spin and orbital polarization dynamics at terahertz frequencies, which is relevant for potential applications of terahertz spin- and orbital-based devices.

Nonlinear THz transmission is utilized to investigate the solvation dynamics of proteins. Protein structure and function are inherently dependent on their solvation shell, and an understanding of the underlying solvation dynamics provides valuable insight into how solute-solvent interactions impact biophysical processes. Here, the results of concentration dependent z-scan experiments are reported.

In this manuscript we demonstrate the successful implementation of reconfigurable field-programmable gate array (FPGA) technology into a pulse-resolved data acquisition (DAQ) system to achieve a femtosecond temporal resolution in ultrafast pump-probe experiments in real-time at large scale facilities. As a proof of a concept, electro-optic sampling (EOS) of terahertz waveforms radiated by a superradiant emitter of a quasi-cw accelerator operating at 50 kHz repetition rate and probed by external laser system is performed. Options for up-scaling the developed technique to a MHz range repetition rates are discussed.

In this Letter, we demonstrate terahertz (THz) magnetic field detection in fused silica with sensitivity that can be easily controlled by sample tilting (for both amplitude and polarization). The proposed technique remains in the linear regime at magnetic fields exceeding 0.3 T (0.9 MV/cm of equivalent electric field) and allows the use of low-cost amorphous materials. Furthermore, the demonstrated effects should be present in a wide variety of materials used as substrates in different THz-pump laser–probe experiments and need to be considered in order to disentangle different contributions to the measured signals.

Electric fields operating at THz frequencies hold significant promise for inducing ultrafast coherent excitations in magnetic heterostructures. Through the utilization of ferromagnetic/heavy metal (FM/HM) heterostructures, we have demonstrated that THz radiation (0.1 – 30 THz) exhibits combined functionality of microwaves and visible light. 1) Similar to microwaves, THz fields can effectively generate spin currents through the spin-Hall effect (SHE), resulting in an excitation of THz-frequency magnon modes. 2) Akin to visible light excitation, THz fields deposit heat, leading to the demagnetization of FM layers. Harnessing the THz-induced demagnetization as a spin current source within FM/HM heterostructures, we exploit the half-cycle THz electric field to incite spin currents, which subsequently transformed into picosecond charge currents through the inverse SHE within the HM layer. This conversion process results in the emission of a THz second harmonic signal, offering the THz spintronic frequency conversion.

The ultrafast control of magnetisation states in magnetically ordered systems poses significant technological challenges yet is vital for the development of memory devices that operate at picosecond timescales or terahertz (THz) frequencies. Despite considerable efforts achieving convenient ultrafast readout of magnetic states remains an area of active investigation. For practical applications, energy-efficient and cost-effective electrical detection is highly desirable. In this context, unidirectional spin-Hall magnetoresistance (USMR) has been proposed as a straightforward two-terminal geometry for the electrical detection of magnetisation states in magnetic heterostructures. In this work, we demonstrate that USMR is effective at THz frequencies, enabling picosecond time readouts initiated by light fields. We observe ultrafast USMR in various ferromagnet/heavy metal thin film heterostructures via THz second-harmonic generation. Our findings, along with temperature-dependent measurements of USMR, reveal a substantial contribution from electron-magnon spin-flip scattering, highlighting the potential for all-electrical detection of THz magnon modes.

Current communication technologies are constrained to sub-THz bands due to the frequency limits of traditional nonlinear components. We introduce a new approach to upconverting weak sub-THz signals into multiple THz bands using a high-mobility HgTe-based heterostructure with Dirac electronic state dispersion. Building on our previous success in achieving record third harmonic generation in this material, we anticipated efficient frequency mixing and a strong THz response across various input frequency combinations. With a field conversion efficiency exceeding 2% in a sub-100 nm HgTe layer at room temperature, we hope to open the door to highly integrated THz communication devices with very high data transfer rates.

High harmonic generation (HHG) is a nonlinear optical process that has a range of applications in various fields, including ultrashort pulse measurements, material characterization, and imaging microscopy. Recently, there has been increasing interest in studying the THz nonlinearity and efficient third harmonic generation (THG) in Dirac materials such as graphene [1]. It is natural to assume that other Dirac materials, such as topological insulators (TI), could also exhibit similar effects [2,3]. In particular, topological states can be found in HgTe quantum wells with a thickness of more than 6.3 nm [4].

High harmonic generation (HHG) is a nonlinear optical process that has a range of applications in various fields, including ultrashort pulse measurements, material characterization, and imaging microscopy. Recently, there has been increasing interest in studying the THz nonlinearity and efficient third harmonic generation (THG) in Dirac materials such as graphene [1]. It is natural to assume that other Dirac materials, such as topological insulators (TI), could also exhibit similar effects [2,3]. In particular,
topological states can be found in HgTe quantum wells with a thickness of more than 6.3 nm [4].
1. Hafez, H. A. et al., Nature 561, 507-511 (2018).
2. Kovalev, S. et al. Quantum Materials 6, 84 (2021)
3. Tielrooij, K.-J. et al. Light Sci. Appl. 11, 315 (2022).
4. Bernevig, B. A. et al. Science 314, 1757-1761 (2006).

Understanding spin-lattice interactions in antiferromagnets is a critical element of the fields of antiferromagnetic spintronics and magnonics. Recently, coherent nonlinear phonon dynamics mediated by a magnon state were discovered in an antiferromagnet. Here, we suggest that a strongly coupled two-magnon-one phonon state in this prototypical system opens a novel pathway to coherently control magnon-phonon dynamics. Utilizing intense narrow-band terahertz (THz) pulses and tunable magnetic fields up to μ_0 H_ext = 7 T, we experimentally realize the conditions of magnon-phonon Fermi resonance in antiferromagnetic CoF2. These conditions imply that both the spin and the lattice anharmonicities harvest energy from the transfer between the subsystems if the magnon eigenfrequency f_m is half the frequency of the phonon 2f_m = f_ph. Performing THz pump-infrared probe spectroscopy in conjunction with simulations, we explore the coupled magnon-phonon dynamics in the vicinity of the Fermi-resonance and reveal the corresponding fingerprints of nonlinear interaction facilitating energy exchange between these subsystems.

Extending 2D structures into 3D space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics, superconductivity and magnetism [1,2]. This approach provides means to modify conventional or to launch novel functionalities by tailoring curvature and 3D shape of magnetic thin films and nanowires [2,3]. In this talk, we will address fundamentals of curvature-induced effects in magnetism and review the envisioned application scenarios. In particular, we will demonstrate that curvature allows tailoring fundamental anisotropic and chiral magnetic interactions [4] and enables fundamentally new non-local chiral symmetry breaking effect [5,6]. Application potential of geometrically curved magnetic architectures is currently being explored as mechanically reshapeable magnetic field sensors for automotive applications, memory, spin-wave filters, high-speed racetrack memory devices, magnetic soft robotics [7] as well as on-skin interactive electronics relying on thin films [8,9,10] as well as printed magnetic composites [11,12] with appealing self-healing performance [13].

[1] P. Gentile et al., Electronic materials with nanoscale curved geometries. Nature Electronics (Review) 5, 551 (2022).
[2] D. Makarov et al., New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures. Advanced Materials (Review) 34, 2101758 (2022).
[3] D. Makarov et al., Curvilinear micromagnetism: from fundamentals to applications (Springer, Zurich, 2022).
[4] O. Volkov et al., Experimental observation of exchange-driven chiral effects in curvilinear magnetism. Physical Review Letters 123, 077201 (2019).
[5] D. D. Sheka et al., Nonlocal chiral symmetry breaking in curvilinear magnetic shells. Communications Physics 3, 128 (2020).
[6] O. M. Volkov et al., Chirality coupling in topological magnetic textures with multiple magnetochiral parameters. Nature Communications 14, 1491 (2023).
[7] M. Ha et al., Reconfigurable Magnetic Origami Actuators with On-Board Sensing for Guided Assembly. Advanced Materials 33, 2008751 (2021).
[8] G. S. Canon Bermudez et al., Magnetosensitive e-skins for interactive devices. Advanced Functional Materials (Review) 31, 2007788 (2021).
[9] J. Ge et al., A bimodal soft electronic skin for tactile and touchless interaction in real time. Nature Communications 10, 4405 (2019).
[10] G. S. Canon Bermudez et al., Electronic-skin compasses for geomagnetic field driven artificial magnetoception and interactive electronics. Nature Electronics 1, 589 (2018).
[11] M. Ha et al., Printable and Stretchable Giant Magnetoresistive Sensors for Highly Compliant and Skin-Conformal Electronics. Advanced Materials 33, 2005521 (2021).
[12] E. S. Oliveros Mata et al., Dispenser printed bismuth-based magnetic field sensors with non-saturating large magnetoresistance for touchless interactive surfaces. Adv. Mater. Technol. 7, 2200227 (2022).
[13] R. Xu et al., Self-healable printed magnetic field sensors using alternating magnetic fields. Nature Communications 13, 6587 (2022).

The folded structure and stability of proteins emanates from their interaction with the water solvent. Water at the protein surface is strongly impacted, resulting in a region with a perturbed hydrogen bonding network. This region, the solvation shell, has distinct properties from that of bulk water, including retarded dynamics and fewer hydrogen bonds. Changes in the structure and dynamics of solvation water can be both perturbed and reported on by Terahertz radiation. Yet, some fundamental properties of solvation water, such as energy transfer within the hydrogen bonding network, remain largely unexplored.
Here, we utilize the TELBE free electron laser source to investigate the nonlinear transmission of lysozyme protein solutions. Z-scan experiments were performed at 0.5 THz, revealing a large nonlinear transmission of water. The nonlinear transmission of lysozyme solutions had a concentration dependent effect, showing that the amount of available water has a role. For the largest protein concentration measured, an inversion in the sign of the nonlinear transmission was observed. These results indicate that the nonlinear properties of protein solutions depend on the fraction of bulk and solvation water, and suggest that the mechanism of energy transfer changes at a threshold value. This work has implications for the study of nonlinear properties in biological systems.

Biomolecular condensates are membrane-less organelles formed via liquid-liquid phase separation of intrinsically disordered proteins. Here, THz spectroscopy is utilized to reveal the structure and dynamics of hydration water in these liquid-like protein environments.

In the past years, there is an active research of materials displaying the non-linear Hall effect with time-reversal symmetry [1-5]. From a fundamental point of view, this quantum transport effect provides a direct way to detect in nonmagnetic materials the Berry curvature – a quantity in which the geometry of the electronic wavefunctions is encoded. The nonlinear Hall effect is also at the basis of terahertz optoelectronic applications of interest for instance for sixth generation (6G) communication networks.

An appropriate material platform for such applications should satisfy a number of criteria: i) the nonlinear Hall effect should survive up to room temperature; ii) the effect should be tunable; iii) the material fabrication should be technologically relevant (simple chemical composition of the material and low-cost microstructure); iv) ideally the material should not contain toxic heavy rare-earth elements. So far, candidate materials address only partially these requirements.

Here, we discover the first material addressing all the requirements at the same time: polycrystalline bismuth thin films [6]. We demonstrate that in this elemental green (semi)metal, the room-temperature nonlinear Hall effect is generated by surface states that are characterized by a Berry curvature triple: a quantity governing a skew scattering effect that generates non-linear transverse currents. Furthermore, we also show that the strength of nonlinear Hall effect can be controlled on demand using an extrinsic classical shape effect: the geometric nonlinear Hall effect. We demonstrate this by fabricating arc-shaped bismuth Hall bars. This endows the nonlinear Hall effect of Bismuth with the tunability encountered only in low-dimensional materials at low temperatures.

To show the potential of polycrystalline Bi thin films for optoelectronic applications in the terahertz (THz) spectral domain, we have performed high harmonic generation experiments. Polycrystalline Bi thin films reveal a high efficiency of THz third-harmonic generation (THG) that reaches levels >1% at room temperature. Moreover, our material possesses a non-saturating trend of the efficiency of the THz THG. This enables the use of Bi thin films for high- and wide- THz bandwidth electronics which works at high peak power and long pulses.

[1] Z. Z. Du et al., Nonlinear Hall effects. Nature Reviews Physics 3, 744 (2021).
[2] I. Sodemann et al., Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials. Phys. Rev. Lett. 115, 216806 (2015).
[3] Q. Ma et al., Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565, 337 (2019).
[4] K. Kang et al., Nonlinear anomalous Hall effect in few-layer WTe2. Nature Mater. 18, 324 (2019).
[5] P. He et al., Quantum frequency doubling in the topological insulator Bi2Se3. Nature Communications 12, 698 (2021).
[6] P. Makushko et al., A tunable room-temperature nonlinear Hall effect in elemental bismuth thin films. Nature Electronics 7, 207 (2024).

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.

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 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.

In this presentation I will describe our recent experiments with polycrystalline Bi thin films, where we observed non-linear Hall effect.

Nonlinear phenomena in the THz spectral domain are important for the understanding of optoelectronic properties of quantum systems and provide a basis for modern information technologies. Here, we report a giant THz nonlinearity in high-mobility 2D topological insulators based on HgTe quantum wells, which manifests itself in a highly efficient third harmonic generation. We observe a third harmonic THz susceptibility several times higher than in bare graphene and many orders of magnitude higher than in trivial quantum well structures based on other materials. To explain the strong nonlinearity of HgTe-based heterostructures at the THz frequencies, we consider the acceleration of free carriers with high mobility and variable dispersion. This acceleration model, for which the non-parabolicity of the band dispersion is key, in combination with independently measured scattering time and conductivity is in good agreement with our experimental data in a wide temperature range for THz fields below the saturation. Our approach provides a route to material engineering for THz applications based on frequency conversion.

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.

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

The continuous evolution of photon sources and their instrumentation enables more and new scientific endeavors at ever increasing pace. This technological evolution is accompanied by an exponential growth of data volumes of increasing complexity, which must be addressed by maximizing efficiency of scientific experiments and automation of workflows covering the entire data lifecycle, aiming to reduce data volumes while producing FAIR and open data of highest reliability. This papers briefly outlines the strategy of the league of European accelerator-based photon sources user facilities to achieve these goals collaboratively in an efficient and sustainable way which will ultimately lead to an increase in the number of publications.

This presentation will provide an overview of the coherent THz sources and the user activities at the ELBE Radiation Source. Ideas for new types of measurements and materials to study will be discussed, followed by a look toward DALI, the concept for a new facility at HZDR for advanced accelerator-based THz sources.

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.

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.

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.

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.

The heart of the ELBE Center for High Power Radiation Sources is a superconducting RF (SRF) linac, which accelerates electrons up to 35 MeV for driving a diverse set of secondary radiation sources. The ELBE linac is particularly unique in the capability of accelerating a continuous beam of ultrashort bunches of electrons at very high repetition rates (up to 26 MHz). This extremely high-power electron beam is selectively directed into specially designed beamlines to drive secondary radiation sources for THz/IR photons (FELBE and TELBE), positrons (pELBE), neutrons (nELBE), and gamma radiation (ELBE), each with dedicated laboratories and instrumentation. Users from all over the world utilize the advanced radiation sources at ELBE for a wide array of both fundamental and applied studies of matter, health, energy, and technology.
The ELBE accelerator was first commissioned in 2001 in the form of a grid-pulsed 250 kV thermionic gun followed by two stages of RF bunching to inject beam into a linac comprised of two SRF cryomodules, each containing two 9-cell DESY TTF-type niobium accelerating cavities. Through continuous development and research, the ELBE facility has achieved many major advancements in accelerator technology, the most important being the ELBE SRF Gun program, which has designed, built, and commissioned several prototype SRF electron guns for high bunch charge, high average current, and low emittance. The ELBE SRF Gun-II is the first and only electron source of its type to deliver electron beam to a user experiment, and is now in routine operation for the TELBE and pELBE beamlines.
An overview of the performance parameters of the ELBE accelerator and secondary sources will be presented in this talk along with a summary of the experimental capabilities available to users. Highlights of recent user results will also be presented to help illustrate the great potential ELBE provides for a diverse scientific community. Beamtime proposals are accepted and reviewed by an external scientific advisory committee twice per year.
https://www.hzdr.de/db/Cms?pNid=1732

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.

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.

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.

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.

Nonvolatile and energy-efficient spin-based technologies call for new prospects to realize computation and communication devices that are able to operate at terahertz (THz) frequencies. In particular, the coupling of electro-magnetic radiation to a spin system is a general requirement for future communication units and sensors. Here we propose a layered metallic system, based on a ferromagnetic film sandwiched in between two heavy metals that allows a highly effective coupling of millimeter wavelength THz light to nanometer-wavelength magnon modes. Using single-cycle broadband THz radiation we are able to excite spin-wave modes with a frequency of up to 0.6 THz and a wavelength as short as 6 nm. Our experimental and theoretical studies demonstrate that the coupling originates solely from interfacial spin-orbit torques. These results are of general applicability to magnetic multilayered structures, and offer the perspective of coherent THz excitation of exchange-dominated nanoscopic magnon modes.

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

I will discuss some developments related to two types of THz sources: on the one hand photoconductive antennas, including recent results using the material germanium, and on the other hand I will give an overview on the accelerator based coherent infrared and THz sources operating at HZDR, and discuss plans for a successor facility.

Free-electron lasers: past, present, and future challenges

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.

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 time-resolved linear and nonlinear terahertz spectroscopy of the two-band superconductor MgB2
with a superconducting transition temperature Tc ≈ 36 K. Third-harmonic generation (THG) is observed below
Tc by driving the system with intense narrow-band THz pulses. For the pump-pulse frequencies f = 0.3, 0.4,
and 0.5 THz, the temperature-dependent evolution of the THG signals exhibits a resonance maximum at the
temperatures with the resonance conditions 2 f = 2Delta π (T ) fulfilled, for the dirty-limit superconducting gap
2Delta π . In contrast, for f = 0.6 and 0.7 THz with 2 f > 2Delta π (T → 0) = 1.03 THz, the THG intensity increases
monotonically with decreasing temperature. Moreover, for 2 f < 2Delta π (T → 0) the THG is found nearly isotropic
with respect to the pump-pulse polarization. These results suggest a predominant contribution of the driven
Higgs amplitude mode of the dirty-limit π -band superconducting gap, pointing to the importance of scattering
for observation of the Higgs mode in superconductors.

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.

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.

Graphene has long been predicted to show exceptional nonlinear optical properties, especially in the technologically important terahertz (THz) frequency range. Recent experiments demonstrated that this atomically-thin material indeed exhibits possibly the largest nonlinear coefficients of any material known to date. These findings in particular pave ways for practical graphene-based applications in ultrafast electronics and optoelectronics operating at THz rates. Here we report on the advances in the booming field of nonlinear THz optics of graphene, and describe the state-of-the-art understanding of the nature of the nonlinear interaction of electrons in graphene with intense THz fields based on the thermodynamic model of electron transport in graphene. We also provide a comparison between different mechanisms of nonlinear interaction of graphene with light fields in THz, infrared and visible frequency ranges.
We conclude the report with the perspectives for the expected technological applications of graphene based on its extraordinary THz nonlinear properties. This report covers the evolution of the field of THz nonlinear optics of graphene from the very pioneering to the state-of-the-art works. It also serves as a concise overview of the current understanding of THz nonlinear optics of graphene, and as a compact reference for researchers entering the field, as well as for the technology developers.

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.

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.

Multi-color pump-probe techniques utilizing modern accelerator-based 4th generation light sources such as X-ray free electron lasers or superradiant THz facilities have become important science drivers over the past 10 years. In this type of experiments the precise knowledge of the properties of the involved accelerator-based light pulses crucially determines the achievable sensitivity and temporal resolution. In this work we demonstrate and discuss the powerful role pulse- and field-resolved- detection of superradiant THz pulses can play for improving the precision of THz pump - femtosecond laser probe experiments at superradiant THz facilities in particular and at 4th generation light sources in general. The developed diagnostic scheme provides real-time information on the properties of individual pulses from multiple accelerator based THz sources and opens a robust way for sub femtosecond timing. Correlations between amplitude and phase of the pulses emitted from different superradiant THz sources furthermore provide insides into the properties of the driving electron bunches and is of general interest for the ultra-fast diagnostics at 4th generation light sources.

Multiple optical harmonics generation—the multiplication of photon energy as a result of nonlinear interaction between light and matter—has become one of the key technologies in modern electronics and optoelectronics. Owing to its unique electronic band structure featuring massless Dirac fermions, graphene has been repeatedly predicted to have high efficiency of optical harmonics generation in the technologically important terahertz frequency range. So far, experiments have failed to confirm these predictions under technologically relevant operation conditions. Here we report the generation of terahertz harmonics up to the seventh order in single-layer graphene at room temperature and under ambient conditions, driven by terahertz fields of only tens of kilovolts per centimetre, and with field conversion efficiencies in excess of 10⁻³, 10⁻⁴ and 10⁻⁵ for the third, fifth and seventh terahertz harmonics, respectively. The key to such highly efficient harmonics generation in graphene is the collective thermal response of its background Dirac electrons to the driving terahertz fields. The generated terahertz harmonics were observed directly in the time domain as electromagnetic field oscillations at these newly synthesized frequencies. The effective nonlinear optical coefficients of graphene for the third, fifth and seventh harmonics exceed the respective nonlinear coefficients of typical solids by 7–18 orders of magnitude. Our results provide a direct pathway to highly efficient terahertz frequency synthesis that is within the capabilities of the present generation of graphene electronics operating at fundamental frequencies of only a few hundreds of gigahertz.

In this letter we present the layout and demonstrate the performance for an integrated millimeter-scale on-chip THz spectrometer. The device is based on eight Schottky-Diode detectors which are combined with narrow-band THz antennas, thereby enabling the simultaneous detection of eight frequencies in the THz range on one chip. The size of the active detector area matches the focal spot size of superradiant THz radiation utilized in bunch compression monitors of modern linear electron accelerators. The 3 dB bandwidth of the on-chip Schottky-Diode detectors is less than 10% of the center frequency and allows pulse-resolved detection at up to 5 GHz repetition rates. The performance of a first prototype device is demonstrated at a repetition rate of 100 kHz at the quasi-cw SRF linear accelerator ELBE operated with electron bunch charges between few pC and 100 pC.

We report on measurements of magnetic field and temperature dependence of antiferromagnetic resonances in the prototypical antiferromagnet NiO. The frequencies of the magnetic resonances in the vicinity of 1 THz have been determined in the time-domain via time-resolved Faraday measurements after selective excitation by narrow-band superradiant terahertz (THz) pulses at temperatures down to 3 K and in magnetic fields up to 10 T. The measurements reveal two antiferromagnetic resonance modes, which can be distinguished by their characteristic magnetic field dependencies. The nature of the two modes is discussed by comparison to an eight-sublattice antiferromagnetic model, which includes superexchange between the next-nearest-neighbor Ni spins, magnetic dipolar interactions, cubic magneto-crystalline anisotropy, and Zeeman interaction with the external magnetic field. Our study indicates that a two-sublattice model is insufficient for the description of spin dynamics in NiO, while the magnetic-dipolar interactions and magneto-crystalline anisotropy play important roles.

In this Letter, the proof of principle for a scheme providing intrinsic femtosecond-level synchronization between an external laser system and fourth generation light sources is presented. The scheme is applicable at any accelerator-based light source that is based on the generation of coherent radiation from ultrashort electron bunches such as superradiant terahertz (THz) facilities or X-FELs. It makes use of a superradiant THz pulse generated by the accelerator as an intrinsically synchronized gate signal for electro-optical slicing. We demonstrate that the scheme enables a reduction of the timing instability by more than 2 orders of magnitude. This demonstration experiment thereby proves that intrinsically synchronized time-resolved experiments utilizing laser and accelerator-based radiation pulses on few tens of femtosecond (fs) to few fs timescales are feasible.

Recent advancements of accelerator technology enable the generation of carrier-envelope-phase stable THz pulses with high-fields at adjustably high repetition rates. The appropriate choice of THz radiator allows generating narrow-band, spectrally dense, multicycle THz transients of tunable THz frequency which are ideally suited to selectively excite low-energy excitations such as magnons or phonons. They also allow one to study the frequency dependence of nonresonant THz-field interactions with various order parameters with high dynamic range. In this paper we discuss the future prospects of this new type of THz light sources for studying the coherent control of magnetic order based on recent results.

Understanding dynamics on ultrafast timescales enables unique and new insights into important processes in the materials and life sciences. In this respect, the fundamental pump-probe approach based on ultra-short photon pulses aims at the creation of stroboscopic movies. Performing such experiments at one of the many recently established accelerator-based 4th-generation light sources such as free-electron lasers (FELs) or superradiant THz sources allows an enormous widening of the accessible parameter space for the excitation and/or probing light pulses. Compared to table-top devices, critical issues of this type of experiment are fluctuations of the timing between the accelerator and external laser systems and intensity instabilities of the accelerator-based photon sources. Existing solutions have so far been only demonstrated at low repetition rates and/or achieved a limited dynamic range in comparison to table-top experiments, while the 4th generation of accelerator-based light sources is based on superconducting radio-frequency (SRF) technology which enables operation at MHz or even GHz repetition rates. In this article, we present the successful demonstration of ultra-fast accelerator-laser pump-probe experiments performed at an unprecedentedly high repetition rate in the few-hundred-kHz regime and with a currently achievable optimal time resolution of 13 femtoseconds (fs) (rms). Our scheme, based on the pulse-resolved detection of multiple beam parameters relevant for the experiment, allows us to achieve an excellent sensitivity in real-world ultra-fast experiments, as demonstrated for the example of THz-field-driven coherent spin precession.

Narrow-band terahertz emission from coherently excited spin precession in metallic Mn3-xGa Heusler alloy nanofilms has been observed. The efficiency of the emission, per nanometer film thickness, is comparable or higher than that of classical laser-driven terahertz sources based on optical rectification. The center frequency of the emission from the films can be tuned precisely via the film composition making this type of metallic films a candidate for efficient on-chip terahertz emitters. Terahertz emission spectroscopy is potentially a sensitive probe of magnetic properties of ultra-thin films.

Ultra-short flashes of THz light with low quantum energies of a few meV, but strong electric or magnetic field transients have recently been employed to prepare various fascinating nonequilibrium states in matter. Here we present a new class of sources based on superradiant enhancement of radiation from relativistic ultra-short electron bunches in a compact electron accelerator that we believe will revolutionize experiments in this field. Our prototype source generates high-field THz pulses at unprecedented repetition rates up to the MHz regime. We demonstrate parameters that already exceed state of the art laser-based sources by more than 2 orders of magnitude. The parameters are scalable and once operational at their design parameters this type of sources will provide 1 MV/cm electric fields and magnetic fields in the few 100 mT regime at repetition rates of few 100 kHz.