The nonlinear optical response of bismuth (Bi) in the nonperturbative regime is studied by phase-resolved two-dimensional terahertz (THz) spectroscopy. A (111)-oriented rhombohedral Bi film of 45-nm thickness is excited by a pair of THz pulses with center frequencies of 1.1 THz, electric field amplitudes of 300 and 600 kV/cm, and pulse durations of 1 ps. The phase-resolved nonlinear signal field, emitted by the sample and recorded in a transmission geometry, allows for a separation of different components of the total nonlinear response, including higher harmonics of the THz pulses and pump-probe signals with few-picosecond decay times. The pump-probe signals originate from irreversible electron-hole pair generation and display a sixfold amplitude pattern in the azimuthal sample orientation. The linearly polarized pump pulses generate an unequal transient carrier population in the six L valleys of the band structure, resulting in a reduction of symmetry of the excited crystal and a backfolding of phonons from the X to the Gamma point. Wave packets of back-folded acoustic phonons, which are displacively excited by the THz pump pulse, give rise to coherent pump-probe signals oscillating with a frequency of 0.8 THz.

The nonlinear polaronic response of electrons solvated in liquid 2-propanol is studied by two-dimensional terahertz spectroscopy. Solvated electrons with a concentration of c_{e}≈800  μM are generated by femtosecond photoionization of alcohol molecules. Electron relaxation to a localized ground state impulsively excites coherent polaron oscillations with a frequency of 3.9 THz. Off-resonant perturbation of the terahertz coherence by a pulse centered at 1.5 THz modifies the polaron oscillation phase. This nonlinear change of electron polarizability is reproduced by theoretical calculations.

Quantum pathways inducing coherent lattice dynamics are studied in bismuth (Bi). A crystalline Bi film is excited by femtosecond midinfrared pulses and transient intensity changes on the (111) Bragg reflection are probed by hard x-ray pulses. A fast decrease and coherent oscillations of the diffracted intensity display up to 50% and 10% intensity change, respectively. The oscillation frequency of 2.6 THz is independent of pump intensity. Midinfrared excitation opens different quantum pathways for electron-hole generation, such as field-driven carrier tunneling at the L points, which reduces the crystal symmetry and leads to optical phonon excitation at the X point with the strongest electron-phonon coupling.

We present femtosecond x-ray diffraction experiments performed on single crystal bismuth excited by 5 µm laser pulses, and nonlinear THz experiments. Our results point to a new excitation quantum pathway at longer excitation wavelengths allowing for coherent phonon excitation at the X point in the Brillouin zone.

The semimetal bismuth is studied by two-dimensional terahertz (2D-THz) spectroscopy in the nonperturbative regime. We observe and separate different components of the nonlinear THz response, including high harmonic generation and pump-probe signals pointing to anisotropic transient carrier distributions and phonon backfolding at reduced symmetry.

An electron solvated in a polar liquid is an elementary quantum system with properties governed by electric interactions with a fluctuating molecular environment. In the prevailing single particle picture, the quantum ground and excited states are determined by a self-consistent potential, as defined by the particular local configuration of the solvation shell. This description neglects collective many-body excitations, which arise from the coupling of electronic degrees of freedom and nuclear motions of the environment. While recent experiments have demonstrated collective nonequilbrium electronic-nuclear motion, i.e. polaron excitations in liquid water, their relevance in the broader context of polar liquids has remained unexplored. Here, we study the nonequilibrium dielectric response of the, compared to water, less polar alcohols isopropanol, and ethylene glycol, that also display a different hydrogen bond pattern. We demonstrate that ultrafast relaxation of photogenerated electrons impulsively induces coherent charge oscillations, which persist for some 10 ps. They emit electric waves in a frequency range from 0.1 to 2 THz, depending on electron concentration. Oscillation frequencies and line shapes are reproduced by a unified polaron picture for alcohols and water, which is based on a Clausius-Mossotti local field approach for the THz dielectric function. The analysis suggests a longitudinal character of many-body polaron excitations and a weak coupling to transverse excitations, supported by the underdamped character of charge oscillations. Polaron dynamics are governed by the long-range Coulomb interaction between an excess electron and several thousands of polar solvent molecules, while local electron solvation geometries play a minor role.

Femtosecond generation of solvated electrons in alcohols of varying polarity leads to coherent polaron oscillations of longitudinal character which modulate the terahertz (THz) dielectric properties of the liquids and give rise to THz emission.

We present ultrafast x-ray diffraction experiments of the underdamped soft mode in paraelectric KDP. Charge density maps derived from the x-ray data reveal oscillatory electronic charge relocations over interatomic distances, much larger than the sub-picometer nuclear displacements, a hallmark of soft-mode behavior.

The impact of coherent phonon excitations on the valence charge distribution in cubic boron nitride is mapped by femtosecond x-ray powder diffraction. Zone-edge transverse acoustic (TA) two-phonon excitations generated by an impulsive Raman process induce a steplike increase of diffracted x-ray intensity. Charge density maps derived from transient diffraction patterns reveal a spatial transfer of valence charge from the interstitial region onto boron and nitrogen atoms. This transfer is modulated with a frequency of 250 GHz due to a coherent superposition of TA phonons related to the 10B and 11B isotopes. Nuclear and electronic degrees of freedom couple through many-body Coulomb interactions.

Nonequilibrium dynamics of transverse optical (TO) phonons in few-layer hexagonal boron nitride is studied in mid-infrared pump-probe experiments. TO phonons display a 1.2 ps lifetime and a transient redshift due to anharmonic coupling with low-frequency interlayer modes.

Soft modes in crystals are lattice vibrations with frequencies that decrease and eventually vanish as the temperature approaches a critical point, e.g., a structural change due to a phase transition. In ionic para- or ferroelectric materials, the frequency decrease is connected with a diverging electric susceptibility and, for infrared active modes, a strong increase in oscillator strength. The traditional picture describes soft modes as overdamped transverse optical phonons of a hybrid vibrational-electronic character. In this context, potassium dihydrogen phosphate (KH2PO4, KDP) has been studied for decades as a prototypical material with, however, inconclusive results regarding the soft modes in its para- and ferroelectric phase. There are conflicting assignments of soft-mode frequencies and damping parameters. We report the first observation of a longitudinal underdamped soft mode in paraelectric KDP. Upon impulsive femtosecond Raman excitation of coherent low-frequency phonons in the electronic ground state of KDP crystallites, transient powder diffraction patterns are recorded with femtosecond hard x-ray pulses. Electron density maps derived from the x-ray data reveal oscillatory charge relocations over interatomic distances, much larger than the sub-picometer nuclear displacements, a direct hallmark of soft-mode behavior. The strongly underdamped character of the soft mode manifests in charge oscillations persisting for more than 10 ps. The soft-mode frequency decreases from 0.55 THz at T = 295 K to 0.39 THz at T = 175 K. An analysis of the Raman excitation conditions in crystallites and the weak damping demonstrate a longitudinal character. Our results extend soft-mode physics well beyond the traditional picture and pave the way for an atomic-level characterization of soft modes.

Plasmon resonances in semiconductors at microwave frequencies offer the possibility for many functionalities and integration schemes. Semiconductor materials, such as germanium, gallium arsenide, and silicon, have the further advantage of being able to be integrated with standard electronics technology. Here, we probe the bulk plasmon modes in silicon in the vicinity of a copper plate perforated by a single aperture at frequencies between 10 and 60 GHz. Sharp transmission minima are observed at discrete frequencies. The observed frequencies depend on the size of the aperture and the carrier concentration in the silicon; they are well reproduced by the dispersion relation for bulk plasmons. Our results show that one can excite plasmons in silicon in the millimeter-wave region, opening a route to microwave plasmonics for large-scale applications, using low-cost technology.

Nonequilibrium dynamics of transverse-optical (TO) phonons and low-frequency interlayer shear and breathing modes are mapped in femtosecond midinfrared pump-probe experiments. Time-resolved changes of TO phonon absorption reveal a TO phonon lifetime of 1.2 ps, while low-frequency excitations decay with a time constant of 22 ps. The coupling of intralayer TO and interlayer motions manifests in a quasi-instantaneous redshift of the TO phonon resonance by some 10 cm(-1). Theoretical calculations account for the coupling scenario and underline the relevance of interphonon interactions for the nonlinear phonon response.

Both second-order frequency mixing in nonlinear optical media and photoconductive antennas have provided terahertz (THz) transients in a wide parameter range. Here, we demonstrate a novel type of ultrafast nonlinear optical response in asymmetric semiconductor quantum wells, originating from electron shift currents. Resonant intersubband excitation by a femtosecond mid-infrared pulse induces a transient spatial shift of electronic charge, which leads to the emission of a mono-cycle THz pulse. This mechanism is characterized and separated from conventional difference frequency mixing by nonlinear two-dimensional THz spectroscopy. The amplitude of the THz electric field emitted by the shift current reaches several percent of the mid-infrared driving field, significantly higher than in difference frequency mixing. Changes in time structure of the THz pulse upon nonlinear saturation of intersubband absorption allow for generating tailored THz transients. The present concept can be implemented in highly compact devices driven by mid-infrared pulses at megahertz repetition rates to provide versatile THz pulses for spectroscopy and optoelectronics.

Free electrons generated via high THz or near-infrared excitation of water have pronounced poloranic character which manifests in coherent oscillations of the terahertz dielectric function. The oscillation frequency scales with the electron concentration.

Nonlinear two-dimensional terahertz (2D-THz) spectroscopy at frequencies of the emitted THz signal different from the driving frequencies allows for exploring the regime of (off-)resonant even-order nonlinearities in condensed matter. To demonstrate the potential of this method, we study two phenomena in the nonlinear THz response of bulk GaAs: (i) The nonlinear THz response to a pair of femtosecond near-infrared pulses unravels novel fourth- and sixth-order contributions involving interband shift currents, Raman-like excitations of transverse-optical phonon and intervalence-band coherences. (ii) Transient interband tunneling of electrons driven by ultrashort mid-infrared pulses can be effectively controlled by a low-frequency THz field with amplitudes below 50 kV/cm. The THz field controls the electron-hole separation modifying decoherence and the irreversibility of carrier generation.

Nonlinear terahertz (THz) spectroscopy relies on the interaction of matter with few-cycle THz pulses of electric field amplitudes up to megavolts/centimeter (MV/cm). In condensed-phase molecular systems, both resonant interactions with elementary excitations at low frequencies such as intra- and intermolecular vibrations and nonresonant field-driven processes are relevant. Two-dimensional THz (2D-THz) spectroscopy is a key method for following nonequilibrium processes and dynamics of excitations to decipher the underlying interactions and molecular couplings. This article addresses the state of the art in 2D-THz spectroscopy by discussing the main concepts and illustrating them with recent results. The latter include the response of vibrational excitations in molecular crystals up to the nonperturbative regime of light-matter interaction and field-driven ionization processes and electron transport in liquid water.

The terahertz (THz) response of solvated electrons in liquid water is studied in nonlinear ultrafast pump-probe experiments. Free electrons with concentrations from c_{e}=4 to 140×10^{-6} moles/liter are generated by high-field THz or near-infrared multiphoton excitation. The time-resolved change of the dielectric function as mapped by broadband THz pulses exhibits pronounced oscillations persisting up to 30 ps. Their frequency increases with electron concentration from 0.2 to 1.5 THz. The oscillatory response is assigned to impulsively excited coherent polarons involving coupled electron and water shell motions with a frequency set by the local electric field.