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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.

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 ).

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.

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.

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.

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.

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.

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.

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.

The exploration of nonlinear optical phenomena has not only deepened the understanding of light-matter interaction, but it also enabled novel technologies that make use of the resulting synthesis of electromagnetic radiation at new frequencies. Whereas the nonlinear responses of matter in the microwave and optical regimes are well explored, research addressing the intermediate Terahertz (THz) regime is still largely in its infancy, despite its high technological relevance, e.g. for novel high-speed (opto-)electronics. For these future applications in the THz range, graphene is a highly promising material, because of the unique optical properties originating from its prototypical Dirac-type electronic structure. Soon after its discovery, there have multiple predictions of efficient harmonic generation in the THz range [1, 2], but experimental evidence has remained incomplete. Recently, we experimentally demonstrated the highly efficient THz harmonics generation (HG) in a single layer graphene sample (up to 7th order) at ambient conditions upon excitation with a moderate THz field of only 85 kV/cm (see Fig. 1) [3]. Our observations have been successfully described by a thermodynamic model, which clearly explains the experimentally observed crucial role of the graphene doping level for THz HG [3, 4]. By using gated graphene samples and multilayer structures, we are able to predictably modify the HG efficiency and thereby corroborate the thermodynamic model. In addition, we employed the same experimental scheme to other Dirac materials, such as topological insulators and Dirac/Weyl semimetals, showing that THz HG is a rather universal phenomenon based on the linear band dispersion in the vicinity of the Dirac point. [1] S. Mikhailov et al., Microelectron. J. 40 (2009) 712. [2] I. Al-Naib, Phys. Rev. B, 90 (2014) 245423 [3] H. Hafez, S. Kovalev et al., Nature, 561 (2018) 507 [4] Z. Mics et al., Nat. Commun., 6 (2015) 7655

The control of magnetic order by intense THz radiation is an emerging area in today’s ultra-fast Science community. Many different studies have investigated the interaction between THz fields and magnetic order on sub-picosecond timescales and have demonstrated different mechanisms for THz control. In this contribution, we discuss the opportunities to control the magnetic order of the material using spectrally dense, high repetition rate, narrow band THz pulses at TELBE. The THz facility at ELBE (TELBE) is one of only a few superradiant THz light sources operated at an SRF accelerator and the only facility worldwide that provides: high THz fields at quasi-CW repetition rates. TELBE is operated in early-stage user operation since 08/2016.

The control of magnetic order by intense THz radiation is an emerging area in today’s ultra-fast Science community. Many different studies have investigated the interaction between THz fields and magnetic order on sub-picosecond timescales and have demonstrated different mechanisms for THz control. In this contribution, we discuss the opportunities to control the magnetic order of the material using spectrally dense, high repetition rate, narrow band THz pulses at TELBE.

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.

The control of magnetic order by intense THz radiation is an emerging area in today’s ultra-fast Science community. Many different studies have investigated the interaction between THz fields and magnetic order on sub-picosecond timescales and have demonstrated different mechanisms for THz control. In this contribution, we discuss the opportunities to control the magnetic order of the material using spectrally dense, high repetition rate, narrow band THz pulses at TELBE. The THz facility at ELBE (TELBE) is one of only a few superradiant THz light sources operated at an SRF accelerator and the only facility worldwide that provides: high THz fields at quasi-CW repetition rates. TELBE is operated in early-stage user operation since 08/2016.

As a new electron source with higher brilliance, the second superconducting RF photoinjector (SRF Gun II) has been built at the ELBE radiation center for high power radiation sources. One of the main goals of SRF gun II is to achieve a higher bunch charge (>200 pC) and lower emittance (3 mm mrad) than the present ELBE thermionic DC gun. SRF Gun II features a 3.5-cell niobium cavity as well as a superconducting solenoid in the same cryomodule. With Mg photocathodes the gun is able to provide medium current beam with bunch charge of more than 200 pC and sub-ps bunch length at 100 kHz repetition rate. With this contribution we present convincing results from long-term user operation of SRF gun II in combination with the bunching concept of the ELBE accelerator in order to produce THz radiation with much higher stability and power than available using the existing thermionic gun.

The control of magnetic order by intense THz radiation is an emerging area in today’s ultra-fast Science community. Many different studies have investigated the interaction between THz fields and magnetic order on sub-picosecond timescales and have demonstrated different mechanisms for THz control. In this contribution, we discuss the opportunities to control the magnetic order of the material using spectrally dense, high repetition rate, narrow band THz pulses at TELBE.

Terahertz (THz) frequency range contains wave-lengths between 3 mm to 30 µm that corresponds to the energies between 0.4 meV to 40 meV. Spectroscopy in this range plays very important role in an understanding the solid state physics as there are multiple low energy excitations (phonons, magnons, Higgs mode etc.) that determine numerous physical parameters of the matter. Not only to perform THz spectroscopy but to coherently manipulate the phase of matter through these excitations it is required to develop high field narrow band THz radi-ation sources with very sensitive probing techniques. THz user facility TELBE at Helmholtz-Zentrum Dresden-Rossendorf provides quasi CW SRF accelerator based narrowband THz radiation at high repetition rates. The source is based on superradiant principle that ena-bles high degree of CEP stability, operation in deep THz frequencies tunable between 100 GHz to 3 THz and rep-etition rates up to MHz range [1]. The bandwidth of radi-ation is 10-15 % with pulse energies up to 2-3 µJ in a fundamental band (up to 100 µJ as design parameter) that results in few 100 kV/cm peak field strength. Using pulse-resolved technique we can reach few femto-second synchronization with ultra-fast laser system that is crucial for studying ultrafast dynamics [2]. The listed above parameters outperform state of the art high repeti-tion rates laser based THz sources and are important for observing novel high field THz phenomena. In this con-tribution we present concept of superradiant THz sources and our recent results on observing novel high field te-rahertz phenomena making use of such sources. Among the experimental results we will present THz high har-monic generation in Dirac materials, Higgs spectroscopy of high TC superconductors and spintronic based THz oscillators.

The TELBE Terahertz (THz) facility at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) offers narrowband high-field high-repetition rate THz radiation for driving low-energy excitations in matter in the spectral region between 0.1 THz and 1.5 THz [1]. In combination with our pulse-resolved data acquisition and the numerous available probing techniques based on table-top laser systems, we can resolve THz-driven dynamics with few 10 fs time resolution and high dynamic range of up to 120 dB [2]. This makes TELBE a unique facility for exploring low-energy THz excitations offering (resonant) access to a multitude of fundamental modes, e.g., lattice vibrations, molecular rotations, spin precession and the motion of free electrons [3]. Recently, we demonstrated THz high harmonic generation (HHG) in the model 2D material graphene [4]. Here, the ultrafast collective thermal response of free background electrons near the Dirac point [5] enables very efficient generation of harmonics in the technologically relevant THz frequency range. We further show that the underlying principle of the collective response can be generalized to other 2D and 3D Dirac materials, such as CdAs. The crucial role of doping in graphene can be exploited by, e.g. electrochemical gating, which allows tuning of the HHG efficiency by almost two orders of magnitude. The corresponding setup for phase-resolved nonlinear THz spectroscopy further enables a novel technique: Higgs spectroscopy, which offers new ways for understanding unconventional superconductivity. Using this technique, we recently discovered a new collective mode distinct from the heavily damped Higgs mode in different families of cuprates [6]. Our results establish Higgs spectroscopy as a new approach to uncover interactions directly relevant to superconductivity. In this contribution, I will also discuss experiments on the selective THz control of magnetic properties in a number of different materials [7], which is enabled by probing techniques

The exploration of nonlinear optical phenomena has not only deepened the understanding of light-matter interaction, but it also enabled novel technologies that make use of the resulting synthesis of electromagnetic radiation at new frequencies. Whereas the nonlinear responses of matter in the microwave and optical regimes are well explored, research addressing the intermediate Terahertz (THz) regime is still largely in its infancy, despite its high technological relevance, e.g. for novel high-speed (opto-)electronics. For these future applications in the THz range, graphene is a highly promising material, because of the unique optical properties originating from its prototypical Dirac-type electronic structure. Soon after its discovery, there have multiple predictions of efficient harmonic generation in the THz range [1, 2], but experimental evidence has remained incomplete. Recently, we experimentally demonstrated the highly efficient THz harmonics generation (HG) in a single layer graphene sample (up to 7th order) at ambient conditions upon excitation with a moderate THz field of only 85 kV/cm (see Fig. 1) [3]. Our observations have been successfully described by a thermodynamic model, which clearly explains the experimentally observed crucial role of the graphene doping level for THz HG [3, 4]. By using gated graphene samples and multilayer structures, we are able to predictably modify the HG efficiency and thereby corroborate the thermodynamic model. In addition, we employed the same experimental scheme to other Dirac materials, such as topological insulators and Dirac/Weyl semimetals, showing that THz HG is a rather universal phenomenon based on the linear band dispersion in the vicinity of the Dirac point. [1] S. Mikhailov et al., Microelectron. J. 40 (2009) 712. [2] I. Al-Naib, Phys. Rev. B, 90 (2014) 245423 [3] H. Hafez, S. Kovalev et al., Nature, 561 (2018) 507 [4] Z. Mics et al., Nat. Commun., 6 (2015) 7655

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.

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.

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.