The terahertz (THz) response of the ferroelectric prototype material lithium niobate (LiNbO3) is studied in the nonperturbative regime of light-matter interaction. Applying two-dimensional THz spectroscopy with few-cycle pulses of an amplitude E≈100  kV/cm and a center frequency of 2 THz, we dissect the overall nonlinear response into different orders in the electric field. The underlying nonlinear current is of interband character and consists of a strong low-frequency shift current (SC) and higher harmonics of the THz fundamental. The SC component originates from the lack of inversion symmetry and the strong interband decoherence for long electron trajectories in k space as shown by theoretical calculations.

We present the first two-dimensional (2D) terahertz (THz) experiment with three phase-locked THz pulses and a fully phase-resolved detection of the nonlinearly emitted field by electrooptic sampling. In a prototype experiment we study the ultrafast dynamics of nonlinear two-phonon and two-photon interband coherences in the narrow-gap semiconductor InSb. Due to the extraordinarily large optical interband dipole of InSb the experiments were performed in the strongly nonperturbative regime of light-matter interaction allowing for impulsive off-resonant excitation of both two-phonon coherences and two-photon interband coherences, the ultrafast dynamics of which is experimentally observed as a function of the waiting time in the three-pulse 2D experiment. Our novel three-pulse 2D THz spectroscopy paves the way for the detailed investigation of nonlinear quantum coherences in solids and holds potential for an extension to other systems.

We report the first observation of two-phonon quantum coherences in a semiconductor. Two-dimensional terahertz (THz) spectra recorded with a sequence of three THz pulses display strong two-phonon signals, clearly distinguished from signals due to interband two-photon absorption and electron tunneling. The two-phonon coherences originate from impulsive off-resonant excitation in the nonperturbative regime of light-matter interaction. A theoretical analysis provides the relevant Liouville pathways, showing that nonlinear interactions using the large interband dipole moment generate stronger two-phonon excitations than linear interactions.

Electric-field transients covering the extremely wide frequency range from 0.5 to 26 THz are generated in the organic nonlinear crystal 4-N,N-dimethylamino-4'-N'-methylstilbazolium 2,4,6-trimethylbenzenesulfonate (DSTMS). Parametric difference frequency mixing within the spectrum of 25-fs amplified pulses centered at 800 nm provides a highly stable broadband output with an electric-field amplitude of up to several hundred kilovolts/cm. The high stability of the terahertz pulse parameters allows for sensitive phase-resolved broadband spectroscopy of optically thick crystalline samples.

We demonstrate amplification of longitudinal optical (LO) phonons by polar-optical interaction with an electron plasma in a GaAs structure coupled to a metallic metasurface using two-color two-dimensional spectroscopy. In a novel scheme, the metamaterial resonator enhances broadband terahertz fields, which generate coherent LO phonons and drive free electrons in the conduction band of GaAs. The time evolution of the LO phonon amplitude is monitored with mid-infrared pulses via the LO-phonon-induced Kerr nonlinearity of the sample, showing an amplification of the LO phonon amplitude by up to a factor of 10, in agreement with a theoretical estimate.