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Symmetries essentially provide conservation rules in nonlinear light-matter interactions, that facilitate control and understanding of photon conversion processes or electron dynamics. Since anisotropic solids have rich symmetries, they are strong candidate to control both optical micro- and macroscale structures, namely spin (circular polarization) and orbital angular momentum (spiral wavefront), respectively. Here, we show structured high harmonic generation linked to the anisotropic symmetry of a solid. By strategically preserving a dynamical symmetry arising from the spin-orbit interaction of light, we generate multiple orbital angular momentum states in high-order harmonics. The experimental results exhibit the total angular momentum conservation rule of light even in the extreme nonlinear region, which is evidence that the mechanism originates from a dynamical symmetry. Our study provides a deeper understanding of multiscale nonlinear optical phenomena and a general guideline for using electronic structure to control structured light, such as through Floquet engineering.

We show that high-harmonic generation (HHG) in carbon nanotubes (CNTs) can be efficiently controlled using the Aharanov-Bohm (AB) effect. When a static magnetic field (B) is applied along the tube, electronic wave functions acquire complex phases along the circumferential direction (AB effect), which modifies the band structure. In particular, when the magnetic field is applied to metallic CNTs, which can be regarded as one-dimensional massless Dirac systems, realistic values of B lead to a nonzero gap in the THz regime. We demonstrate that such change from gapless to gapped Dirac systems drastically increases the HHG intensity in the THz regime. In the gapless Dirac system, the velocity of each electron never changes under the electric field, and thus there is no HHG. On the other hand, the gap opening activates both the interband and itraband currents, which strongly contribute to HHG. Our work demonstrates a unique way to manipulate HHG in nanotubes by tuning electronic wave functions using the magnetic field and the tube structure., Comment: 7 pages, 4 figures + 8 pages, 6 figures

We consider high-harmonic generation (HHG) in the Rice-Mele model to study the role of the intraband current originating from the change of the intraband dipole via interband transition. This contribution, which has been often neglected in previous works, is necessary for the consistent theoretical formulation of the light-matter coupling. We demonstrate that the contribution becomes crucial when the gap is smaller than or comparable to the excitation frequency and the system is close to the half filling., Comment: 6 pages, 2 figures

Floquet engineering of electronic systems is a promising way of controlling quantum material properties on an ultrafast time scale. So far, the energy structure of Floquet states in solids has been observed through time and angle-resolved photoelectron spectroscopy or pump-probe measurement techniques. However, the dynamical aspects of the photon-dressed states under ultrashort pulse driving have not been explored yet. Their dynamics become highly sensitive to the envelope of the driving field when the light-matter interaction enters non-perturbative regime, and thus, understanding of them is crucial for ultrafast manipulation of quantum state. Here, we observed coherent exciton emissions under intense and non-resonant mid-infrared fields in monolayer WSe2 at room temperature, which is unexpected in perturbative nonlinear optics. Together with numerical calculations, our measurements revealed that the coherent exciton emission reflects the diabatic and adiabatic dynamics of Floquet states. Our results provide a new approach to probing the dynamics of the Floquet state and lead to control of quantum materials through pulse shaping of the driving field.

High harmonic generation (HHG) in solids reflects the underlying nonperturbative nonlinear dynamics of electrons in a strong light field and is a powerful tool for ultrafast spectroscopy of electronic structures. Photo-carrier doping allows us to understand the carrier dynamics and the correlations between the carriers in the HHG process. Here, we study the effect of incoherent electron-hole pairs on HHG in an atomically thin semiconductor. The experimentally observed response to photo-carrier doping is successfully reproduced in numerical simulations incorporating the photo-excited carrier distribution, excitonic Coulomb interaction and electron-electron scattering effects. The simulation results reveal that the presence of photo-carriers enhances the intraband current that contributes to high harmonics below the absorption edge. We also clarify that the excitation-induced dephasing process rather than the phase-space filling effect is the dominant mechanism reducing the higher order harmonics above the absorption edge. Our work provides a deeper understanding of high harmonic spectroscopy and the optimum conditions for generating extreme ultraviolet light from solids.

High-harmonic generation (HHG), which is generation of multiple optical harmonic light, is an unconventional nonlinear optical phenomenon beyond perturbation regime. HHG, which was initially observed in gaseous media, has recently been demonstrated in solid state materials. How to control the extreme nonlinear optical phenomena is a challenging subject. Compared to atomic gases, solid state materials have advantages in controlling electronic structures and carrier injection. Here, we demonstrate control of HHG by tuning electronic structure and carrier injection using single-walled carbon nanotubes (SWCNTs). We reveal systematic changes in the high-harmonic spectra of SWCNTs with a series of electronic structures from a metal to a semiconductor. We demonstrate enhancement or reduction of harmonic generation by more than one order of magnitude by tuning electron and hole injection into the semiconductor SWCNTs through electrolyte gating. These results open a way to control HHG within the concept of field effect transistor devices.

The Floquet state, which is a periodically and intensely light driven quantum state in solids, has been attracting attention as a novel state that is coherently controllable on an ultrafast time scale. An important issue has been to demonstrate experimentally novel electronic properties in the Floquet state. One technique to demonstrate them is the light scattering spectroscopy, which offers an important clue to clarifying the symmetries and energy structures of the states through symmetry analysis of the polarization selection rules. Here, we determine circular and linear polarization selection rules of light scattering in a mid-infrared-driven Floquet system in monolayer MoS2 and provide a comprehensive understanding in terms of the "dynamical symmetry" of the Floquet state.

Coherent manipulation of quasi-particles is a crucial method to realize ultrafast switching of the relating macroscopic order. In this letter, we studied coherent phonon generation under strong light field which allows to induce non-perturbative nonlinear optical phenomena in solids. The efficiency of coherent phonon generation starts to saturate and deviate from the pronounced linear power dependence when the light intensity goes into the non-perturbative regime. We propose a novel theoretical model based on Floquet picture and show that the saturation is due to a limitation of the driving force inherent in non-resonant driving of the electronic system in the non-perturbative regime.

We demonstrated nonperturbative high harmonics induced by intense mid-infrared light up to 18th order that well exceed the material bandgap in monolayer transition metal dichalcogenides. The intensities of the even-order high-harmonic radiation did not monotonically decrease as the harmonic order increased. By comparing the high harmonic spectra with the optical absorption spectra, we found that the enhancement in the even-order high harmonics could be attributed to the resonance to the band nesting energy. The symmetry analysis shows that the valley polarization and anisotropic band structure lead to polarization of the high-harmonic radiation under excitation with the polarization along the zigzag direction. We also examined the possible recombination pathways of electrons and holes by calculating their dynamics in real and momentum spaces based on three-step model in solids. It revealed that, by considering the electrons and holes generated at neighboring lattice sites, the electron-hole polarization driven to the band nesting region should contribute to the high harmonic radiation. Our findings open the way for attosecond science with monolayer materials having widely tunable electronic structures.