Nonlinear Terahertz Polarizability of Electrons Solvated in a Polar Liquid.

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.

Phonon-Induced Relocation of Valence Charge in Boron Nitride Observed by Ultrafast X-Ray Diffraction.

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 ^{10}B and ^{11}B isotopes. Nuclear and electronic degrees of freedom couple through many-body Coulomb interactions.

Underdamped longitudinal soft modes in ionic crystallites-lattice and charge motions observed by ultrafast x-ray diffraction.

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.

Coherent polaron dynamics of electrons solvated in polar liquids.

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.

Two-color two-dimensional terahertz spectroscopy: A new approach for exploring even-order nonlinearities in the nonperturbative regime.

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.

Two-dimensional terahertz spectroscopy of condensed-phase molecular systems.

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.

Terahertz Polaron Oscillations of Electrons Solvated 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.

Spatial distribution of electric-field enhancement across the gap of terahertz bow-tie antennas.

The electric-field enhancement in terahertz (THz) antennas designed for nonlinear THz spectroscopy of soft matter is characterized by spatially resolved electrooptic sampling. To mimic the relevant interaction geometry, metallic, resonant bow-tie antennas are deposited on a thin zinc telluride crystal of 10 µm thickness. The THz electric field transmitted through the antenna gap is recorded by electrooptic sampling. By focusing the 800 nm, sub-20 fs sampling pulses, we achieve a spatial resolution of some 3 µm, which is 1/3 to 1/8 of the antenna-gap width. The THz field in the gap displays an enhancement by a factor of up to 4.5 with a pronounced spectral variation, depending sensitively on the antenna-arm length and the gap width. By scanning the 800 nm probe spot laterally through the antenna gap, the spatial variation of the enhancement is determined, reaching the highest values at the edges of the gap. The results are in agreement with simulations of the electric-field distributions by finite-element calculations.

Field-Induced Tunneling Ionization and Terahertz-Driven Electron Dynamics in Liquid Water.

Liquid water at ambient temperature displays ultrafast molecular motions and concomitant fluctuations of very strong electric fields originating from the dipolar H2O molecules. We show that such random intermolecular fields induce the tunnel ionization of water molecules, which becomes irreversible if an external terahertz (THz) pulse imposes an additional directed electric field on the liquid. Time-resolved nonlinear THz spectroscopy maps charge separation, transport, and localization of the released electrons on a few-picosecond time scale. The highly polarizable localized electrons modify the THz absorption spectrum and refractive index of water, a manifestation of a highly nonlinear response. Our results demonstrate how the interplay of local electric field fluctuations and external electric fields allows for steering charge dynamics and dielectric properties in aqueous systems.

Frequency Upshift of the Transverse Optical Phonon Resonance in GaAs by Femtosecond Electron-Hole Excitation.

The impact of transient electric currents on the transverse optical (TO) phonon resonance is studied after excitation by two femtosecond near-infrared pulses via the fourth-order nonlinear terahertz emission. Nonlinear signals due to interband shift currents and heavy-hole-light-hole polarizations are separated from Raman-induced TO phonon coherences. The latter display a frequency upshift by some 100 GHz upon interband excitation of an electron-hole plasma. The frequency shift is caused by transverse electronic shift currents, which modify the dielectric function. A local-field model based on microscopic current densities reproduces the observed frequency upshift.

A Mechanistic Perspective on Plastically Flexible Coordination Polymers.

Mechanical flexibility in single crystals of covalently bound materials is a fascinating and poorly understood phenomenon. We present here the first example of a plastically flexible one-dimensional (1D) coordination polymer. The compound [Zn(µ-Cl)2 (3,5-dichloropyridine)2 ]n is flexible over two crystallographic faces. Remarkably, the single crystal remains intact when bent to 180°. A combination of microscopy, diffraction, and spectroscopic studies have been used to probe the structural response of the crystal lattice to mechanical bending. Deformation of the covalent polymer chains does not appear to be responsible for the observed macroscopic bending. Instead, our results suggest that mechanical bending occurs by displacement of the coordination polymer chains. Based on experimental and theoretical evidence, we propose a new model for mechanical flexibility in 1D coordination polymers. Moreover, our calculations propose a cause of the different mechanical properties of this compound and a structurally similar elastic material.

Terahertz Driven Amplification of Coherent Optical Phonons in GaAs Coupled to a Metasurface.

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 midinfrared 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.

Resonant Second-Order Nonlinear Terahertz Response of Gallium Arsenide.

The second-order nonlinear response of bulk GaAs in the terahertz (THz) range is mapped via the THz field emitted after near-infrared interband excitation. Phase-resolved THz detection reveals three nonlinear processes occurring in parallel, the Raman excitation of transverse optical phonons, the creation of coherent polarizations on heavy-hole-light-hole transitions, and the generation of displacive shift currents with a THz spectrum controlled by the near-infrared optical phase. Theoretical calculations reproduce the data and demonstrate the interband character of shift currents.

Mid-infrared beam splitter for ultrashort pulses.

A design is presented for a beam splitter suitable for ultrashort pulses in the mid-infrared and terahertz spectral range consisting of a structured metal layer on a diamond substrate. Both the theory and experiment show that this beam splitter does not distort the temporal pulse shape.

Strong Local-Field Enhancement of the Nonlinear Soft-Mode Response in a Molecular Crystal.

The nonlinear response of soft-mode excitations in polycrystalline acetylsalicylic acid (aspirin) is studied with two-dimensional terahertz spectroscopy. We demonstrate that the correlation of CH_{3} rotational modes with collective oscillations of π electrons drives the system into the nonperturbative regime of light-matter interaction, even for a moderate strength of the THz driving field on the order of 50 kV/cm. Nonlinear absorption around 1.1 THz leads to a blueshifted coherent emission at 1.7 THz, revealing the dynamic breakup of the strong electron-phonon correlations. The observed behavior is reproduced by theoretical calculations including dynamic local-field correlations.

Phase-resolved two-dimensional terahertz spectroscopy including off-resonant interactions beyond the χ((3)) limit.

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.

Two-Phonon Quantum Coherences in Indium Antimonide Studied by Nonlinear Two-Dimensional Terahertz Spectroscopy.

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.

Strong Amplification of Coherent Acoustic Phonons by Intraminiband Currents in a Semiconductor Superlattice.

Sound amplification in an electrically biased superlattice (SL) is studied in optical experiments with 100 fs time resolution. Coherent SL phonons with frequencies of 40, 375, and 410 GHz give rise to oscillatory reflectivity changes. With currents from 0.5 to 1.3 A, the Fourier amplitude of the 410 GHz phonon increases by more than a factor of 2 over a 200 ps period. This amplification is due to stimulated Cerenkov phonon emission by electrons undergoing intraminiband transport. The gain coefficient of 8×10^{3} cm^{-1} is reproduced by theoretical calculations and holds potential for novel sub-THz phonon emitters.

Ultra-broadband terahertz pulses generated in the organic crystal DSTMS.

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.

Focus: Phase-resolved nonlinear terahertz spectroscopy--From charge dynamics in solids to molecular excitations in liquids.

Intense terahertz (THz) electric field transients with amplitudes up to several megavolts/centimeter and novel multidimensional techniques are the key ingredients of nonlinear THz spectroscopy, a new area of basic research. Both nonlinear light-matter interactions including the non-perturbative regime and THz driven charge transport give new insight into the character and dynamics of low-energy excitations of condensed matter and into quantum kinetic phenomena. This article provides an overview of recent progress in this field, combining an account of technological developments with selected prototype results for liquids and solids. The potential of nonlinear THz methods for future studies of low-frequency excitations of condensed-phase molecular systems is discussed as well.