Ultrafast Nonequilibrium Dynamics Research Articles

Terahertz Nanoscopy on Low-Dimensional Materials: Toward Ultrafast Physical Phenomena.

Low-dimensional materials (LDMs) with unique electromagnetic properties and diverse local phenomena have garnered significant interest, particularly for their low-energy responses within the terahertz (THz) range. Achieving deep subwavelength resolution, THz nanoscopy offers a promising route to investigate LDMs at the nanoscale. Steady-state THz nanoscopy has been demonstrated as a powerful tool for investigating light-matter interactions across boundaries and interfaces, enabling insights into physical phenomena such as localized collective oscillations, quantum confinement of quasiparticles, and metal-to-insulator phase transitions (MITs). However, tracking the ultrafast nonequilibrium dynamics of LDMs remains challenging. Ultrafast THz nanoscopy, with femtosecond temporal resolution, provides a direct pathway to investigate and manipulate the motion of, for example, charges, currents, and carriers at ultrashort time scales. In this review, we focus on recent advances in THz nanoscopy of LDMs, with particular emphasis on the ultrafast dynamics of light-matter interaction. We provide a concise overview of recent advances and suggest future research directions in this impactful field of interdisciplinary science.

(Invited) Exciton Transport in Strained 2D Semiconductors

Being atomically thin, flexible, and exhibiting considerable light emission and ultrafast non-equilibrium dynamics, semiconducting transition metal dichalcogenides (TMDs) have been considered as promising candidates for next-generation optoelectronic devices. The optical and electronic properties of TMDs are governed by a rich landscape of tightly bound excitons, including regular bright excitons, as well as optically inaccessible dark exciton states. Recently, strain engineering of monolayer TMDs has been introduced to tune their optical properties, such as the exciton transition energy, exciton-phonon coupling, or the Stokes shift [1-3].Transport of charge carriers is crucial for nanoelectronics. In conventional materials, electronic transport can be conveniently controlled by external electric fields. However, the tightly bound excitons, being neutral particles, are only weakly affected by electrical fields. We demonstrate that mechanical strain can also be used to manipulate the transport of excitons in TMDs. To this end, we apply homogeneous tensile strain to a WS2 monolayer by bending the substrate [1], which causes a redshift of the X0 exciton photoluminescence. By measuring the spatiotemporal photoluminescence after near-resonant excitation with femtosecond laser pulses, we map the spread of excitons and extract the strain-dependent diffusion coefficient [4].Furthermore, we demonstrate the propagation of excitons in an inhomogeneous strain landscape. We create inhomogeneous tensile strain in TMD monolayers by transferring them onto patterned substrates with nanopillars or by a nanoimprint technique [5]. Due to the redshift of the exciton resonances with applied strain, excitons are expected to move towards high-strain regions in an inhomogeneous strain field - the so-called "funneling" effect. We verify this behavior for the "bright" TMD material monolayer MoSe2. In the case of the "dark" monolayer WS2, we observe exactly the opposite effect. Here, the excitons are expelled from the high-strain regions ("anti-funneling") [6]. By comparing our experimental results with a microscopic theory, we explain this observation by the drift of momentum-dark KΛ excitons, which, in contrast to bright excitons, shift to higher energies with strain.Our joint experiment-theory study highlights the dominant role of momentum-dark excitons for the dynamics in monolayer TMDs and provides crucial design guidelines for TMD devices based on exciton transport.

Ultrafast Nonequilibrium Dynamics of Vibrationally Hot Electron Transfer in Flavodoxin.

The understanding of ultrafast short-range electron transfer (ET) in proteins remains challenging, and thorough studies on well-defined biological systems are demanding. Here, we utilized two types of flavodoxins and designed a series of mutants on two positions to systematically characterize the complete photoinduced redox cycles. We identified one position with a favorable orientation and distance for ultrafast ET in a few femtoseconds and the other position is relatively flexible with a longer ET time scale. We found that all forward and back ET dynamics are ultrafast nonequilibrium processes, occurring through highly vibronic states and ending in vibrationally hot ground states with subsequent cooling relaxation to efficiently dissipate photon energy into the protein environment.

Ultrafast dynamics in photo-excited Mott insulator Sr3Ir2O7 at high pressure

High-pressure ultrafast dynamics, as a new crossed research direction, are sensitive to subtle non-equilibrium state changes that might be unresolved by equilibrium states measurements, providing crucial information for studying delicate phase transitions caused by complex interactions in Mott insulators. With time-resolved transient reflectivity measurements, we identified the new phases in the spin–orbit Mott insulator Sr3Ir2O7 at 300 K that was previously unidentified using conventional approaches such as x-ray diffraction. Significant pressure-dependent variation of the amplitude and lifetime obtained by fitting the reflectivity ΔR/R reveal the changes of electronic structure caused by lattice distortions, and reflect the critical phenomena of phase transitions. Our findings demonstrate the importance of ultrafast nonequilibrium dynamics under extreme conditions for understanding the phase transition of Mott insulators.

Ultrafast nonequilibrium dynamics and high-harmonic generation in two-dimensional quantum spin Hall materials

We develop the theoretical framework of nonequilibrium ultrafast photonics in monolayer quantum spin Hall insulators supporting a multitude of topological states. In these materials, ubiquitous strong light-matter interactions in the femtosecond scale lead to nonadiabatic quantum dynamics, resulting in topology-dependent nonlinear optoelectronic transport phenomena. We investigate the mechanism driving topological Dirac fermions interacting with strong ultrashort light pulses and uncover various experimentally accessible physical quantities that encode fingerprints of the quantum material's topological electronic state from the high-harmonic generated spectrum. Our work sets the theoretical cornerstones to realize the full potential of time-resolved harmonic spectroscopy for understanding nonequilibrium processes in quantum topological systems and identifying topological invariants in two-dimensional quantum spin Hall solid state systems.

Few-cycle 65-µJ pulses at 11.4 µm for ultrafast nonlinear longwave-infrared spectroscopy

Low-energy excitations can provide insight into the basic ultrafast nonequilibrium dynamics of condensed matter. High-energy femtosecond pulses in the long-wavelength infrared are required to induce such processes, and can be generated in an optical parametric chirped pulse amplification (OPCPA) system comprising three GaSe stages. A femtosecond Cr:ZnS laser serves as the front-end, providing the seed for the 2.0-µm pump and the 2.4-µm signal pulses without nonlinear conversion processes. The OPCPA system is pumped at 2.05 µm by a picosecond Ho:YLF regenerative amplifier at a 1-kHz repetition rate. The recompressed idler pulses at 11.4 µm have a duration of 185 fs and an unprecedented energy of 65 µJ, corresponding to a pump-to-idler conversion efficiency of 1.2%. Nonlinear transmission experiments in the range of the L2 infrared band of liquid water demonstrate the potential of the pulses for nonlinear vibrational spectroscopy of liquids and solids.

Subcycle Mid-Infrared Electric-Field-Driven Scanning Tunneling Microscopy with a Time Resolution Higher Than 30 fs

Electric-field-driven scanning tunneling microscopy (STM) that uses carrier envelope phase-controlled pulses in the THz region (THz-STM) has been attracting considerable attention because of its capability of probing ultrafast dynamics in materials. However, since the electric field is in the THz region, its time resolution of about 1 ps limits the range of measurable targets. Therefore, to pave the way for studying the local dynamics of non-equilibrium states such as elementary excitations and phase transitions in condensed materials, it is desirable to develop an STM system with a higher time resolution. Here, we report a mid-infrared (MIR) electric-field-driven STM system enabling an atomic-scale pump–probe method to be used over a wide range of time with a time resolution higher than 30 fs. We demonstrate the high potential of the new MIR-STM system by visualizing the photo-induced ultrafast non-equilibrium dynamics in MoTe2. We succeeded in measuring ultrafast carrier dynamics in the time range of 0 to over 1 ps, which were well explained by the change in band structure associated with the carrier dynamics. In addition to time-resolved signal measurement, atomically resolved MIR-STM imaging was also realized.

Far-from-Equilibrium Electron-Phonon Interactions in Optically Excited Graphene.

Comprehending far-from-equilibrium many-body interactions is one of the major goals of current ultrafast condensed matter physics research. Here, a particularly interesting but barely understood situation occurs during a strong optical excitation, where the electron and phonon systems can be significantly perturbed and the quasiparticle distributions cannot be described with equilibrium functions. In this work, we use time- and angle-resolved photoelectron spectroscopy to study such far-from-equilibrium many-body interactions for the prototypical material graphene. In accordance with theoretical simulations, we find remarkable transient renormalizations of the quasiparticle self-energy caused by the photoinduced nonequilibrium conditions. These observations can be understood by ultrafast scatterings between nonequilibrium electrons and strongly coupled optical phonons, which signify the crucial role of ultrafast nonequilibrium dynamics on many-body interactions. Our results advance the understanding of many-body physics in extreme conditions, which is important for any endeavor to optically manipulate or create non-equilibrium states of matter.

Ultrafast nonequilibrium dynamics of short-range protein electron transfer in flavodoxin.

Short-range protein electron transfer (ET) is ubiquitous in biology and is often observed in photosynthesis, photoreceptors and photoenzymes. These ET processes occur on an ultrafast timescale from femtoseconds to picoseconds at a short donor-acceptor distance within 10 Å, and thus couple with local environmental fluctuations. Here, we use oxidized Anabaena flavodoxin as a model system and have systematically studied the photoinduced redox cycle of the wild type and seven mutant proteins by femtosecond spectroscopy. We observed a series of ultrafast dynamics from the initial charge separation in 100-200 fs, subsequent charge recombination in 1-2 ps and final vibrational cooling process of the products in 3-6 ps. We further characterized the active-site solvation and observed the relaxations in 1-200 ps, indicating a nonergodic ET dynamics. With our new ET model, we uncovered a minor outer (solvent) reorganization energy and a large inner (donor and acceptor) reorganization energy, suggesting a frozen active site in the initial ultrafast ET while the back ET couples with the environment relaxations. The vibronically coupled back ET dynamics was first reported in D. vulgaris flavodoxin and here is observed in Anabaena flavodoxin again, completely due to the faster ET dynamics than the cooling relaxations. We also compared the two flavodoxin structures, revealing a stronger coupling with the donor tyrosine in Anabaena. All ultrafast ET dynamics are from the large donor-acceptor couplings and the minor activation barriers due to the reaction free energies being close to the inner reorganization energies. These observations should be general to many redox reactions in flavoproteins.

Ultrafast excitation and topological soliton formation in incommensurate charge density wave states

Topological soliton is a nonperturbative excitation in commensurate density wave states and connects degenerate ground states. In incommensurate density wave states, ground states are continuously degenerate and topological soliton is reckoned to be smoothly connected to the perturbative phason excitation. We study the ultrafast nonequilibrium dynamics due to photoexcited electron-hole pair in a one-dimensional chain with an incommensurate charge density wave ground state. Time-resolved evolution reveals both perturbative excitation of collective modes and nonperturbative topological phase transition due to creating novel topological solitons, where the continuous complex order parameter with amplitude and phase is essential. We identify the nontrivial phase-winding solitons in the complex plane unique to this nonequilibrium state and capture it by a low-energy effective model. The perturbative temporal gap oscillation and the solitonic in-gap states enter the optical conductivity absorption edge and the spectral density related to spectroscopic measurement, providing concrete connections to real experiments.

An explicit modal discontinuous Galerkin method for Boltzmann transport equation under electronic nonequilibrium conditions

The present paper deals with the development of a numerical scheme for the solution of two-dimensional Boltzmann transport equation (BTE) under electronic nonequilibrium conditions. A two-dimensional explicit modal discontinuous Galerkin (DG) method with uniform meshes is developed for solving the BTE in conjunction with the relaxation time approximation. The spatial discretization is carried out using a high-order DG method, where the polynomial solutions are represented using scaled Legendre basis functions. A third-order explicit SSP-RK scheme is applied for temporal discretization to the resulting semi-discrete ordinary differential equation. The analytic steady state solution of BTE at low electromagnetic field is considered as the validation study. The numerical scheme is applied to the description of electron transport in non-linear dynamic conductivity based on static electric field. The electrical and Hall conductivities with nonequilibrium conditions is estimated for the BTE solution in presence of the electromagnetic field. These transport coefficients are also examined with the dependence of temperature and chemical potential. It is observed that the electrical and Hall conductivity decreases in the presence of a magnetic field. Numerical results demonstrate the potential advantages of the high-order scheme in treating ultrafast nonequilibrium dynamics.

Floquet dynamics in light-driven solids

We demonstrate how the properties of light-induced electronic Floquet states in solids impact natural physical observables, such as transport properties, by capturing the environmental influence on the electrons. We include the environment as dissipative processes, such as inter-band decay and dephasing, often ignored in Floquet predictions. These dissipative processes determine the Floquet band occupations of the emergent steady state, by balancing out the optical driving force. In order to benchmark and illustrate our framework for Floquet physics in a realistic solid, we consider the light-induced Hall conductivity in graphene recently reported by J.~W.~McIver, et al., Nature Physics (2020). We show that the Hall conductivity is estimated by the Berry flux of the occupied states of the light-induced Floquet bands, in addition to the kinetic contribution given by the average band velocity. Hence, Floquet theory provides an interpretation of this Hall conductivity as a geometric-dissipative effect. We demonstrate this mechanism within a master equation formalism, and obtain good quantitative agreement with the experimentally measured Hall conductivity, underscoring the validity of this approach which establishes a broadly applicable framework for the understanding of ultrafast non-equilibrium dynamics in solids.

DETERMINATION OF THE MECHANISM OF PHENOMENAXY OF BENZOPHENONES WITH PHENOLS WITH THE HELP OF CNP EFFECTS

The study of elementary acts of charge transfer occurring in conjugated systems under photoirradiation conditions is the most important task of chemical physics. Such studies allow us to obtain new ideas about the directions of generation of radical and ion-radical structures and to form approaches to the transformation of photoenergy into other types of energy. The currently developed general theoretical framework for proton-electron transfer reactions (PETR) is applicable to a wide range of experimentally studied reactions in solutions, proteins and electrochemistry, which play a crucial role in various chemical and biological processes, including photosynthesis, various enzyme reactions and energy devices. Currently, there is a methodology for simulating mixed quantum and classical molecular dynamics for PETR reactions; moreover, non-adiabatic dynamics methods have been developed for modeling ultrafast nonequilibrium dynamics of photoinduced PETR reactions for model systems. This paper discusses the results of the study of elementary stages and a detailed analysis of the internal mechanisms of stable generation of radio emission in photochemical reactions using the effects of chemical polarization of nuclei using the example of phototransformations of benzophenones with various electron donors. According to the results of studies conducted in a modified sensor of a multi-core NMR spectrometer with simultaneous recording of the spectrum, detailed mechanisms and elementary acts of photoreduction of benzophenones with triethylamine, N, N-diethyl-p-toluidine and N, N-dimethylaniline, as well as phenols and aniline, were established. It was found that the benzophenone photoreduced in two stages (first electron transfer, then proton) or one (transfer of a hydrogen atom only).

Short-Range Electron Transfer in Reduced Flavodoxin: Ultrafast Nonequilibrium Dynamics Coupled with Protein Fluctuations.

Short-range electron transfer (ET) in proteins is an ultrafast process on the similar time scales as local protein-solvent fluctuation, and thus the two dynamics are coupled. Here we use semiquinone flavodoxin and systematically characterized the photoinduced redox cycle with 11 mutations of different aromatic electron donors (tryptophan and tyrosine) and local residues to change redox properties. We observed the forward and backward ET dynamics in a few picoseconds, strongly following a stretched behavior resulting from a coupling between local environment relaxations and these ET processes. We further observed the hot vibrational-state formation through charge recombination and the subsequent cooling dynamics also in a few picoseconds. Combined with the ET studies in oxidized flavodoxin, these results coherently reveal the evolution of the ET dynamics from single to stretched exponential behaviors and thus elucidate critical time scales for the coupling. The observed hot vibration-state formation is robust and should be considered in all photoinduced back ET processes in flavoproteins.

Experimental methods for warm dense matter research

The study of structure, thermodynamic state, equation of state (EOS) and transport properties of warm dense matter (WDM) has become one of the key aspects of laboratory astrophysics. This field has demonstrated its importance not only concerning the internal structure of planets, but also other astrophysical bodies such as brown dwarfs, crusts of old stars or white dwarf stars. There has been a rapid increase in interest and activity in this field over the last two decades owing to many technological advances including not only the commissioning of high energy optical laser systems, z-pinches and X-ray free electron lasers, but also short-pulse laser facilities capable of generation of novel particle and X-ray sources. Many new diagnostic methods have been developed recently to study WDM in its full complexity. Even ultrafast nonequilibrium dynamics has been accessed for the first time thanks to subpicosecond laser pulses achieved at new facilities. Recent years saw a number of major discoveries with direct implications to astrophysics such as the formation of diamond at pressures relevant to interiors of frozen giant planets like Neptune, metallic hydrogen under conditions such as those found inside Jupiter’s dynamo or formation of lonsdaleite crystals under extreme pressures during asteroid impacts on celestial bodies. This paper provides a broad review of the most recent experimental work carried out in this field with a special focus on the methods used. All typical schemes used to produce WDM are discussed in detail. Most of the diagnostic techniques recently established to probe WDM are also described. This paper also provides an overview of the most prominent examples of these methods used in experiments. Even though the main emphasis of the publication is experimental work focused on laboratory astrophysics primarily at laser facilities, a brief outline of other methods such as dynamic compression with z-pinches and static compression using diamond anvil cells (DAC) is also included. Some relevant theoretical and computational efforts related to WDM and astrophysics are mentioned in this review.

Probing ultrafast nonequilibrium dynamics in single-crystal SiC through surface nanostructures induced by femtosecond laser pulses

Ultrafast non-equilibrium dynamics on the surface of a 4H-SiC crystal is experimentally investigated with time-delayed copropagating two femtosecond laser pulse trains of different linear polarizations. Rippled nanostructures are produced by this irradiation, and the alignment “slant” angle of the ripples is related to the polarizations. With varying time delays between the two laser pulses, this slant angle is found to change. In the first 10 ps, the slant quickly rotates in the direction associated with the polarization of the second incident laser pulse, but then abruptly freezes to a steady offset angle. A physical model is proposed to explain the underlying mechanisms. The first laser pulse produces a transient grating-like modulation of the dielectric constant on the surface, with which the second laser pulse interacts. Because competing fast (Auger) and slow (thermal) relaxation processes reduce the initially induced grating's dielectric constant difference, the vector sum of this partially evolved grating with the second laser pulse's interaction results in the observed slant rotation time dependence. This experiment is straightforward, conceptually simple, and utilizes commercial equipment. The time-resolved slanting of the ripple orientation provides an alternative description of the spatiotemporal evolution of a superheated semiconductor surface.

Nonlinear terahertz spectroscopy of Higgs mode in s-wave superconductors

We review our recent experiments of ultrafast dynamics in s-wave superconductors Nb1-xTixN by using nonlinear terahertz (THz) spectroscopy. The free oscillation of the Higgs mode, i.e. the amplitude mode of the superconducting order parameter, is observed after instantaneous injection of quasiparticles at the superconducting gap edge by an intense monocycle THz pulse. The ultrafast nonequilibrium dynamics of the order parameter under the strong AC driving field with the photon energy tuned below the superconducting gap is also investigated. A resonant nonlinear interaction between the Higgs mode and the electromagnetic field is revealed, as manifested by an efficient THz third-harmonic generation from the superconductor.

Condensed phase electron transfer beyond the Condon approximation.

Condensed phase electron transfer problems are often simplified by making the Condon approximation: the approximation that the coupling connecting two charge-transfer diabatic states is a constant. Unfortunately, the Condon approximation does not predict the existence of conical intersections, which are ubiquitous in both gas-phase and condensed-phase photochemical dynamics. In this paper, we develop a formalism to treat condensed-phase dynamics beyond the Condon approximation. We show that even for an extremely simple test system, hexaaquairon(ii)/hexaaquairon(iii) self-exchange in water, the electronic coupling is expected to fluctuate rapidly and non-Condon effects must be considered to obtain quantitatively accurate ultrafast nonequilibrium dynamics. As diabatic couplings are expected to fluctuate substantially in many condensed-phase electron transfer systems, non-Condon effects may be essential to quantitatively capture accurate short-time dynamics.

Excitation and relaxation dynamics in dielectrics irradiated by an intense ultrashort laser pulse

When transparent dielectrics are irradiated by an intense, ultrashort laser pulse, the electron density in the conduction band is increased tremendously. Simultaneously, valence band states become unoccupied and the electron–phonon coupling strength is increased. In this paper, we present our work on modeling the ultrafast nonequilibrium dynamics of laser-excited transparent dielectrics with Boltzmann collision integrals. We track the distribution function of conduction and valence band electrons and discuss the effects of Auger recombination in relation to impact ionization and multiphoton/tunnel ionization on the femtosecond timescale. Finally, we investigate the electron–phonon coupling strength in highly excited dielectrics and calculate the electron–phonon coupling parameter for silicon dioxide-like material.

Intraband conductivity response in graphene observed using ultrafast infrared-pump visible-probe spectroscopy

Graphene, a truly two-dimensional material with a unique linear energy-momentum dispersion, demonstrates novel photonic properties such as universal absorption and conductivity, with applications including terahertz lasing, broadband midinfrared detectors, and tunable ultrafast lasers. Understanding the ultrafast nonequilibrium dynamics of photocarriers in graphene's unique relativistic band structure is important for the development of such high-speed, graphene-based photonic devices, as well as from a fundamental point of view. Here, our experiments indicate the relativistic nature of a nonequilibrium gas of electrons and holes photogenerated in a graphene monolayer as early as 100 fs after photoexcitation. We observe a nonlinear scaling in the Drude-like optical conductivity of the photocarriers with respect to their density, in striking contrast to the linear scaling expected from conventional materials with parabolic dispersion relations. Our measurements also indicate that hot photocarriers cool on a sub-100-fs time scale via interactions with optical phonons. These results elucidate the unique nature of the ultrafast dynamics of photocarriers in a relativistic material, in contrast to conventional materials, and provide a way to manipulate graphene's optical conductivity for applications in photonics and plasmonics.