Sum-Frequency Signals in 2D-Terahertz-Terahertz-Raman Spectroscopy

Discovery of enhanced lattice dynamics in a single-layered hybrid perovskite

Layered hybrid perovskites exhibit emergent physical properties and exceptional functional performances, but the coexistence of lattice order and structural disorder severely hinders our understanding of these materials. One unsolved problem regards how the lattice dynamics are affected by the dimensional engineering of the inorganic frameworks and their interaction with the molecular moieties. Here, we address this question by using a combination of spontaneous Raman scattering, terahertz spectroscopy, and molecular dynamics simulations. This approach reveals the structural dynamics in and out of equilibrium and provides unexpected observables that differentiate single- and double-layered perovskites. While no distinct vibrational coherence is observed in double-layered perovskites, an off-resonant terahertz pulse can drive a long-lived coherent phonon mode in the single-layered system. This difference highlights the dramatic change in the lattice environment as the dimension is reduced, and the findings pave the way for ultrafast structural engineering and high-speed optical modulators based on layered perovskites.

Two-dimensional infrared-Raman spectroscopy as a probe of water's tetrahedrality

Two-dimensional spectroscopic techniques combining terahertz (THz), infrared (IR), and visible pulses offer a wealth of information about coupling among vibrational modes in molecular liquids, thus providing a promising probe of their local structure. However, the capabilities of these spectroscopies are still largely unexplored due to experimental limitations and inherently weak nonlinear signals. Here, through a combination of equilibrium-nonequilibrium molecular dynamics (MD) and a tailored spectrum decomposition scheme, we identify a relationship between the tetrahedral order of liquid water and its two-dimensional IR-IR-Raman (IIR) spectrum. The structure-spectrum relationship can explain the temperature dependence of the spectral features corresponding to the anharmonic coupling between low-frequency intermolecular and high-frequency intramolecular vibrational modes of water. In light of these results, we propose new experiments and discuss the implications for the study of tetrahedrality of liquid water.

Low-frequency anharmonic couplings in crystalline bromoform: Theory

Theoretical calculations of the low-frequency anharmonic couplings of the β-phase of crystalline bromoform are presented based on density functional theory quantum chemistry calculations. The electrical and mechanical anharmonicities between intra- and intermolecular modes are calculated, revealing that the electrical anharmonicity dominates the cross-peak intensities in the 2D Raman-THz response and crystalline, as well as liquid, bromoform. Furthermore, the experimentally observed difference in relative cross-peak intensities between the two intramolecular modes of bromoform and the intermolecular modes can be explained by the C_3v-symmetry of bromoform in combination with orientational averaging. The good agreement with the experimental results provides further evidence for our interpretation that the 2D Raman-THz response of bromoform is, indeed, related to the anharmonic coupling between the intra- and intermolecular modes.

Mapping LiNbO_{3} Phonon-Polariton Nonlinearities with 2D THz-THz-Raman Spectroscopy

Two-dimensional terahertz-terahertz-Raman spectroscopy can provide insight into the anharmonicities of low-energy phonon modes-knowledge of which can help develop strategies for coherent control of material properties. Measurements on LiNbO_{3} reveal THz and Raman nonlinear transitions between the E(TO_{1}) and E(TO_{3}) phonon polaritons. Distinct coherence pathways are observed with different THz polarizations. The observed pathways suggest that the origin of the third-order nonlinear responses is due to mechanical anharmonicities, as opposed to electronic anharmonicities. Further, we confirm that the E(TO_{1}) and E(TO_{3}) phonon polaritons are excited through resonant one-photon THz excitation.

Low-frequency anharmonic couplings in bromoform revealed from 2D Raman-THz spectroscopy: from the liquid to the crystalline phase

Two-dimensional (2D) Raman-THz spectroscopy in the frequency up to 7 THz has been applied to study the crystalline beta-phase of bromoform (CHBr3). As for liquid CHBr3, cross peaks are observed, which however sharpen up in the crystalline sample and split into assignable sub-contributions. In the Raman dimension, the frequency positions of these cross peaks coincide with the intramolecular bending modes of the CHBr3 molecules, and in the THz dimension with the IR active lattice modes of the crystal. This work expands the applicability of this new 2D spectroscopic technique to solid samples at cryogenic temperatures. Furthermore, it provides new experimental evidence that the cross peaks indeed originate from the coupling between intra- and intermolecular vibrational modes.

Equilibrium-nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy

Two-dimensional Raman and hybrid terahertz-Raman spectroscopic techniques provide invaluable insight into molecular structures and dynamics of condensed-phase systems. However, corroborating experimental results with theory is difficult due to the high computational cost of incorporating quantum-mechanical effects in the simulations. Here, we present the equilibrium-nonequilibrium ring-polymer molecular dynamics (RPMD), a practical computational method that can account for nuclear quantum effects on the two-time response function of nonlinear optical spectroscopy. Unlike a recently developed approach based on the double Kubo transformed (DKT) correlation function, our method is exact in the classical limit, where it reduces to the established equilibrium-nonequilibrium classical molecular dynamics method. Using benchmark model calculations, we demonstrate the advantages of the equilibrium-nonequilibrium RPMD over classical and DKT-based approaches. Importantly, its derivation, which is based on the nonequilibrium RPMD, obviates the need for identifying an appropriate Kubo transformed correlation function and paves the way for applying real-time path-integral techniques to multidimensional spectroscopy.

Distinguishing different excitation pathways in two-dimensional terahertz-infrared-visible spectroscopy

In condensed molecular matter, low-frequency modes (LFMs) associated with specific molecular motions are excited at room temperature and determine essential physical and chemical properties of materials. LFMs, with typical mode energies of up to ∼500 cm^-1 (62 meV), contribute significantly to thermodynamic parameters and functions (e.g., heat capacity and entropy) and constitute the basis for room temperature molecular dynamics (e.g., conformational fluctuations and change). LFMs are often analyzed indirectly by the measurement of their effect on specific high-frequency modes (HFMs); the LFM-HFM coupling is reflected in the lineshape, as well as in the spectral and angular diffusion of the HFM. Two-dimensional terahertz-infrared-visible (2D TIRV) spectroscopy allows measuring the LFM-HFM coupling directly and can thereby provide new insights into the strength and nature of the coupling and the character of LFMs. However, the interference between the different signals generated by different excitation pathways can complicate 2D TIRV spectra, preventing a straightforward analysis. Here, we develop an experimental method to distinguish different excitation pathways in 2D TIRV spectroscopy and plot them separately in different quadrants of a 2D spectrum. We validate this method by measuring the spectra of CaF₂ and nitrogen gas. For CaF₂, only sum-frequency mixing between infrared and terahertz fields generates the signal. In contrast, for N₂, only difference-frequency mixing is observed. We then use this method to separate sum- and difference-frequency pathways in the 2D TIRV spectrum of liquid water, verifying the previous interpretation of the lineshape of the 2D TIRV spectrum of water.

Full molecular dynamics simulations of molecular liquids for single-beam spectrally controlled two-dimensional Raman spectroscopy

Single-beam spectrally controlled (SBSC) two-dimensional (2D) Raman spectroscopy is a unique 2D vibrational measurement technique utilizing trains of short pulses that are generated from a single broadband pulse by pulse shaping. This approach overcomes the difficulty of 2D Raman spectroscopy in dealing with small-signal extraction and avoids complicated low-order cascading effects, thus providing a new possibility for measuring the intramolecular and intermolecular modes of molecular liquids using fifth-order 2D Raman spectroscopy. Recently, for quantitatively investigating the mode-mode coupling mechanism, Hurwitz et al. [Opt. Express 28, 3803 (2020)] have developed a new pulse design for this measurement to separate the contributions of the fifth- and third-order polarizations, which are often overlapped in the original single-beam measurements. Here, we describe a method for simulating these original measurements and the new 2D Raman measurements on the basis of a second-order response function approach. We carry out full molecular dynamics simulations for carbon tetrachloride and liquid water using an equilibrium-nonequilibrium hybrid algorithm, with the aim of explaining the key features of the SBSC 2D Raman spectroscopic method from a theoretical point of view. The predicted signal profiles and intensities provide valuable information that can be applied to 2D spectroscopy experiments, allowing them to be carried out more efficiently.

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.