Multiple optical harmonic generation-the multiplication of photon energy as a result of nonlinear interaction between light and matter-is a key technology in modern electronics and optoelectronics, because it allows the conversion of optical or electronic signals into signals with much higher frequency, and the generation of frequency combs. Owing to the unique electronic band structure of graphene, which features massless Dirac fermions, it has been repeatedly predicted that optical harmonic generation in graphene should be particularly efficient at the technologically important terahertz frequencies. However, these predictions have yet to be confirmed experimentally 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, 10 and 10 for the third, fifth and seventh terahertz harmonics, respectively. These conversion efficiencies are remarkably high, given that the electromagnetic interaction occurs in a single atomic layer. The key to such extremely efficient generation of terahertz high harmonics in graphene is the collective thermal response of its background Dirac electrons to the driving terahertz fields. The terahertz harmonics, generated via hot Dirac fermion dynamics, were observed directly in the time domain as electromagnetic field oscillations at these newly synthesized higher 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 using the present generation of graphene electronics, which operate at much lower fundamental frequencies of only a few hundreds of gigahertz.

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 inferred from the decay product of the Higgs boson, i.e., the scalar (amplitude) excitation of the Higgs field. In superconductors, Cooper pairs bear a close analogy to the Higgs field. Interaction between the Cooper pairs and other degrees of freedom provides dissipation channels for the amplitude mode, which may reveal important information about the microscopic pairing mechanism. To this end, we investigate the Higgs (amplitude) mode of several cuprate thin films using phase-resolved terahertz third harmonic generation (THG). 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 T c. These findings indicate coupling of the Higgs mode to other collective modes and potentially a nonzero pairing amplitude above T c .

The understanding of how spins move and can be manipulated 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 processing and storage applications. 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 intrinsic inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetisation at a frequency of approximately 0.5 THz. This allows us to reveal that the angular momentum relaxation time in ferromagnets is on the order of 10 ps.

Ultrashort flashes of THz light with low photon 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 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 quasi-continuous-wave repetition rates up to the MHz regime. We demonstrate parameters that exceed state-of-the-art laser-based sources by more than 2 orders of magnitude. The peak fields and the repetition rates are highly scalable and once fully operational this type of sources will routinely provide 1 MV/cm electric fields and 0.3 T magnetic fields at repetition rates of few 100 kHz. We benchmark the unique properties by performing a resonant coherent THz control experiment with few 10 fs resolution.

visible light frequencies, corresponding to interband transitions leading to electron-hole pair generation. [5,6,12] In the case of doped graphene, that is, graphene containing a certain concentration of free electrons or holes, Drude-like conductivity was observed at far-infrared and terahertz (THz) frequencies, corresponding to intraband free-carrier absorption. [8,9,[12][13][14][15] Further, theoretical studies predicted strong nonlinear interaction of graphene with intense light fields, in particular at the technologically important THz frequencies (typically, in the range 0.1-10 THz), [16][17][18][19][20][21][22][23][24][25] as originating from both interband and intraband electron dynamics. These predictions were inspired by the unique band structure of graphene: absence of a bandgap and linear energy-momentum dispersion for its electrons. [2,3,[26][27][28] A plethora of strong nonlinear effects in graphene in the IR and optical frequency ranges, originating from interband electron dynamics, was successfully demonstrated, including saturable absorption and nonlinear refraction, [29][30][31][32][33][34][35][36][37][38][39] higherharmonic generation, [40][41][42][43][44][45][46][47] and wave-mixing processes [48][49][50] (see also reviews [51][52][53] ). At THz frequencies, however, until recently only saturable absorption effects in doped graphene, [54][55][56][57][58][59][60][61] and induced multiphoton-like absorption in multilayer near-intrinsic graphene were successfully demonstrated. [62] At the same time, the observation of the long sought-after effect of THz higher-order harmonics generation, Graphene has long been predicted to show exceptional nonlinear optical properties, especially in the technologically important terahertz (THz) frequency range. Recent experiments have shown that this atomically thin material indeed exhibits possibly the largest nonlinear coefficients of any material known to date, paving the way for practical graphene-based applications in ultrafast (opto-)electronics operating at THz rates. Here the advances in the booming field of nonlinear THz optics of graphene are reported, and the state-of-the-art understanding of the nature of the nonlinear interaction of graphene with the THz fields based on the thermodynamic model of electron transport in graphene is described. A comparison between different mechanisms of nonlinear interaction of graphene with light fields in THz, infrared, and visible frequency ranges is also provided. Finally, the perspectives for the expected technological applications of graphene based on its extraordinary THz nonlinear properties are summarized. 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.