Search

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.

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.

The electron linear accelerators driving modern X-ray free-electron lasers can emit intense, tunable, quasi-monochromatic terahertz (THz) transients with peak electric fields of V Å−1 and peak magnetic fields in excess of 10 T when a purpose-built, compact, superconducting THz undulator is implemented. New research avenues such as X-ray movies of THz-driven mode-selective chemistry come into reach by making dual use of the ultra-short GeV electron bunches, possible by a rather minor extension of the infrastructure.

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

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

The 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.

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.

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.