Electrical tunability of terahertz nonlinearity in graphene.

Graphene is conceivably the most nonlinear optoelectronic material we know. Its nonlinear optical coefficients in the terahertz frequency range surpass those of other materials by many orders of magnitude. Here, we show that the terahertz nonlinearity of graphene, both for ultrashort single-cycle and quasi-monochromatic multicycle input terahertz signals, 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 terahertz third-harmonic generation in graphene by about two orders of magnitude. Our experimental results are in quantitative agreement with a physical model of the 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 ultrahigh frequencies.

Non-perturbative terahertz high-harmonic generation in the three-dimensional Dirac semimetal Cd3As2.

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. Here, we report on terahertz-field driven high-harmonic generation in the three-dimensional Dirac semimetal Cd3As2 at room temperature. Excited by linearly-polarized multi-cycle terahertz pulses, the third-, fifth-, and seventh-order harmonic generation is very efficient and detected via time-resolved spectroscopic techniques. The observed harmonic radiation is further studied as a function of pump-pulse fluence. Their fluence dependence is found to deviate evidently from the expected power-law dependence in the perturbative regime. The observed highly non-perturbative behavior is reproduced based on our analysis of the intraband kinetics of the terahertz-field driven nonequilibrium state using the Boltzmann transport theory. Our results indicate that the driven nonlinear kinetics of the Dirac electrons plays the central role for the observed highly nonlinear response.

Phase-resolved Higgs response in superconducting cuprates.

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 Tc. These findings indicate coupling of the Higgs mode to other collective modes and potentially a nonzero pairing amplitude above Tc.

Photon diagnostics at the FLASH THz beamline.

The THz beamline at FLASH, DESY, provides both tunable (1-300 THz) narrow-bandwidth (∼10%) and broad-bandwidth intense (up to 150 uJ) THz pulses delivered in 1 MHz bursts and naturally synchronized with free-electron laser X-ray pulses. Combination of these pulses, along with the auxiliary NIR and VIS ultrashort lasers, supports a plethora of dynamic investigations in physics, material science and biology. The unique features of the FLASH THz pulses and the accelerator source, however, bring along a set of challenges in the diagnostics of their key parameters: pulse energy, spectral, temporal and spatial profiles. Here, these challenges are discussed and the pulse diagnostic tools developed at FLASH are presented. In particular, a radiometric power measurement is presented that enables the derivation of the average pulse energy within a pulse burst across the spectral range, jitter-corrected electro-optical sampling for the full spectro-temporal pulse characterization, spatial beam profiling along the beam transport line and at the sample, and a lamellar grating based Fourier transform infrared spectrometer for the on-line assessment of the average THz pulse spectra. Corresponding measurement results provide a comprehensive insight into the THz beamline capabilities.

Extremely efficient terahertz high-harmonic generation in graphene by hot Dirac fermions.

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 fermions1-3, it has been repeatedly predicted that optical harmonic generation in graphene should be particularly efficient at the technologically important terahertz frequencies4-6. 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 10-3, 10-4 and 10-5 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 magnitude7-9. 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.

Terahertz field control of in-plane orbital order in La(0.5)Sr(1.5)MnO4.

In-plane anisotropic ground states are ubiquitous in correlated solids such as pnictides, cuprates and manganites. They can arise from doping Mott insulators and compete with phases such as superconductivity; however, their origins are debated. Strong coupling between lattice, charge, orbital and spin degrees of freedom results in simultaneous ordering of multiple parameters, masking the mechanism that drives the transition. Here we demonstrate that the orbital domains in a manganite can be oriented by the polarization of a pulsed THz light field. Through the application of a Hubbard model, we show that domain control can be achieved by enhancing the local Coulomb interactions, which drive domain reorientation. Our results highlight the key role played by the Coulomb interaction in the control and manipulation of orbital order in the manganites and demonstrate a new way to use THz to understand and manipulate anisotropic phases in a potentially broad range of correlated materials.