Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit

Non-thermal phonon dynamics and a quenched exciton condensate probed by surface-sensitive electron diffraction

Interactions among and between electrons and phonons steer the energy flow in photo-excited materials and govern the emergence of correlated phases. The strength of electron-phonon interactions, decay channels of strongly coupled modes and the evolution of three-dimensional order are revealed by electron or X-ray pulses tracking non-equilibrium structural dynamics. Despite such capabilities, the growing relevance of inherently anisotropic two-dimensional materials and functional heterostructures still calls for techniques with monolayer sensitivity and, specifically, access to out-of-plane phonon polarizations. Here, we resolve non-equilibrium phonon dynamics and quantify the excitonic contribution to the structural order parameter in 1T-TiSe2. To this end, we introduce ultrafast low-energy electron diffuse scattering and trace strongly momentum- and fluence-dependent phonon populations. Mediated by phonon-phonon scattering, a few-picosecond build-up near the zone boundary precedes a far slower generation of zone-centre acoustic modes. These weakly coupled phonons are shown to substantially delay overall equilibration in layered materials. Moreover, we record the surface structural response to a quench of the material's widely investigated exciton condensate, identifying an approximate 30:70 ratio of excitonic versus Peierls contributions to the total lattice distortion in the charge density wave phase. The surface-sensitive approach complements the ultrafast structural toolbox and may further elucidate the impact of phonon scattering in numerous other phenomena within two-dimensional materials, such as the formation of interlayer excitons in twisted bilayers.

Inverted nucleation for photoinduced nonequilibrium melting

Ultrafast photoinduced melting provides an essential platform for studying nonequilibrium phase transitions by linking the kinetics of electron dynamics to ionic motions. Knowledge of dynamic balance in their energetics is essential to understanding how the ionic reaction is influenced by femtosecond photoexcited electrons with notable time lag depending on reaction mechanisms. Here, by directly imaging fluctuating density distributions and evaluating the ionic pressure and Gibbs free energy from two-temperature molecular dynamics that verified experimental results, we uncovered that transient ionic pressure, triggered by photoexcited electrons, controls the overall melting kinetics. In particular, ultrafast nonequilibrium melting can be described by the reverse nucleation process with voids as nucleation seeds. The strongly driven solid-to-liquid transition of metallic gold is successfully explained by void nucleation facilitated by photoexcited electron-initiated ionic pressure, establishing a solid knowledge base for understanding ultrafast nonequilibrium kinetics.

Quenched lattice fluctuations in optically driven SrTiO3

Crystal lattice fluctuations, which are known to influence phase transitions of quantum materials in equilibrium, are also expected to determine the dynamics of light-induced phase changes. However, they have only rarely been explored in these dynamical settings. Here we study the time evolution of lattice fluctuations in the quantum paraelectric SrTiO3, in which mid-infrared drives have been shown to induce a metastable ferroelectric state. Crucial in these physics is the competition between polar instabilities and antiferrodistortive rotations, which in equilibrium frustrate the formation of long-range ferroelectricity. We make use of high-intensity mid-infrared optical pulses to resonantly drive the Ti-O-stretching mode at 17 THz, and we measure the resulting change in lattice fluctuations using time-resolved X-ray diffuse scattering at a free-electron laser. After a prompt increase, we observe a long-lived quench in R-point antiferrodistortive lattice fluctuations. Their enhancement and reduction are theoretically explained by considering the fourth-order nonlinear phononic interactions to the driven optical phonon and third-order coupling to lattice strain, respectively. These observations provide a number of testable hypotheses for the physics of light-induced ferroelectricity.

Structural dynamics at surfaces by ultrafast reflection high-energy electron diffraction

Many fundamental processes of structural changes at surfaces occur on a pico- or femtosecond timescale. In order to study such ultrafast processes, we have combined modern surface science techniques with fs-laser pulses in a pump-probe scheme. Grazing incidence of the electrons ensures surface sensitivity in ultrafast reflection high-energy electron diffraction (URHEED). Utilizing the Debye-Waller effect, we studied the nanoscale heat transport from an ultrathin film through a hetero-interface or the damping of vibrational excitations in monolayer adsorbate systems on the lower ps-timescale. By means of spot profile analysis, the different cooling rates of epitaxial Ge nanostructures of different size and strain state were determined. The excitation and relaxation dynamics of a driven phase transition far away from thermal equilibrium is demonstrated using the In-induced (8 × 2) reconstruction on Si(111). This Peierls-distorted surface charge density wave system exhibits a discontinuous phase transition of first order at 130 K from a (8 × 2) insulating ground state to (4 × 1) metallic excited state. Upon excitation by a fs-laser pulse, this structural phase transition is non-thermally driven in only 700 fs into the excited state. A small barrier of 40 meV hinders the immediate recovery of the ground state, and the system is found in a metastable supercooled state for up to few nanoseconds.

Evidence for phonon hardening in laser-excited gold using x-ray diffraction at a hard x-ray free electron laser

Studies of laser-heated materials on femtosecond timescales have shown that the interatomic potential can be perturbed at sufficiently high laser intensities. For gold, it has been postulated to undergo a strong stiffening leading to an increase of the phonon energies, known as phonon hardening. Despite efforts to investigate this behavior, only measurements at low absorbed energy density have been performed, for which the interpretation of the experimental data remains ambiguous. By using in situ single-shot x-ray diffraction at a hard x-ray free-electron laser, the evolution of diffraction line intensities of laser-excited Au to a higher energy density provides evidence for phonon hardening.

A modular table-top setup for ultrafast x-ray diffraction

We present a table-top setup for femtosecond time-resolved x-ray diffraction based on a Cu Kα (8.05 keV) laser driven plasma x-ray source. Due to its modular design, it provides high accessibility to its individual components (e.g., x-ray optics and sample environment). The Kα-yield of the source is optimized using a pre-pulse scheme. A magnifying multilayer x-ray mirror with Montel-Helios geometry is used to collect the emitted radiation, resulting in a quasi-collimated flux of more than 105 Cu Kα photons/pulse impinging on the sample under investigation at a repetition rate of 10 Hz. A gas ionization chamber detector is placed right after the x-ray mirror and used for the normalization of the diffraction signals, enabling the measurement of relative signal changes of less than 1% even at the given low repetition rate. Time-resolved diffraction experiments on laser-excited epitaxial Bi films serve as an example to demonstrate the capabilities of the setup. The setup can also be used for Debye-Scherrer type measurements on poly-crystalline samples.

Strain and atomic stacking of bismuth thin film in its quasi-van der Waals epitaxy on (111) Si substrate

We report on the structural properties of Bi thin films grown on (111) Si substrates with a thickness of 22-30 BL. HRXRD and EBSD measurements show that these Bi films are mainly composed of twinning grains in the (0003) direction. The grain size can be as large as tens of microns. From a double-peak (01[Formula: see text]4) φ-scan, we found two pairs of twinning phases coexisting with a rotation angle of ~ 3.6°. We proposed a coincidence site lattice model based on preferential close-packed sites for Bi atoms on Si (111) surface to explain the coexistence of the rotation phases in the quasi-van der Waals epitaxy. From the measured lattice constants c and a of our samples, along with the data from the literature, we derived a c-a relation: (c-c0) = - 2.038(a-a0), where c0 and a0 are the values of bulk Bi. The normalized position of the second basis atom in the unit cell x, in these strained Bi films is found very close to that of bulk Bi, indicating that the strain does not disturb the Peierls distortion of the lattice. The fixed ratio of bilayer thickness to lattice constant c, reveals that the elastic properties of covalent-bonded bilayer dominate those of Bi crystal.

Nonequilibrium warm dense matter investigated with laser-plasma-based XANES down to the femtosecond

The use of laser-plasma-based x-ray sources is discussed, with a view to carrying out time-resolved x-ray absorption spectroscopy measurements, down to the femtosecond timescale. A review of recent experiments performed by our team is presented. They concern the study of the nonequilibrium transition of metals from solid to the warm dense regime, which imposes specific constraints (the sample being destroyed after each shot). Particular attention is paid to the description of experimental devices and methodologies. Two main types of x-ray sources are compared, respectively, based on the emission of a hot plasma, and on the betatron radiation from relativistic electrons accelerated by laser.

Inverse Design of Light Manipulating Structural Phase Transition in Solids

This Perspective focuses on recent advances in understanding ultrafast processes involved in photoinduced structural phase transitions and proposes a strategy for precise manipulation of such transitions. It has been demonstrated that photoexcited carriers occupying empty antibonding or bonding states generate atomic driving forces that lead to either stretching or shortening of associated bonds, which in turn induce collective and coherent motions of atoms and yield structural transitions. For instance, phase transitions in IrTe₂ and VO₂, and nonthermal melting in Si, can be explained by the occupation of specific local bonding or antibonding states during laser excitation. These cases reveal the electronic-orbital-selective nature of laser-induced structural transitions. Based on this understanding, we propose an inverse design protocol for achieving or preventing a target structural transition by controlling the related electron occupations with orbital-selective photoexcitation. Overall, this Perspective provides a comprehensive overview of recent advancements in dynamical structural control in solid materials.

Verwey transition as evolution from electronic nematicity to trimerons via electron-phonon coupling

Understanding the driving mechanisms behind metal-insulator transitions (MITs) is a critical step toward controlling material's properties. Since the proposal of charge order-induced MIT in magnetite Fe3O4 in 1939 by Verwey, the nature of the charge order and its role in the transition have remained elusive. Recently, a trimeron order was found in the low-temperature structure of Fe3O4; however, the expected transition entropy change in forming trimeron is greater than the observed value, which arises a reexamination of the ground state in the high-temperature phase. Here, we use electron diffraction to unveil that a nematic charge order on particular Fe sites emerges in the high-temperature structure of bulk Fe3O4 and that, upon cooling, a competitive intertwining of charge and lattice orders arouses the Verwey transition. Our findings discover an unconventional type of electronic nematicity in correlated materials and offer innovative insights into the transition mechanism in Fe3O4 via the electron-phonon coupling.

Concepts and use cases for picosecond ultrasonics with x-rays

This review discusses picosecond ultrasonics experiments using ultrashort hard x-ray probe pulses to extract the transient strain response of laser-excited nanoscopic structures from Bragg-peak shifts. This method provides direct, layer-specific, and quantitative information on the picosecond strain response for structures down to few-nm thickness. We model the transient strain using the elastic wave equation and express the driving stress using Grüneisen parameters stating that the laser-induced stress is proportional to energy density changes in the microscopic subsystems of the solid, i.e., electrons, phonons and spins. The laser-driven strain response can thus serve as an ultrafast proxy for local energy-density and temperature changes, but we emphasize the importance of the nanoscale morphology for an accurate interpretation due to the Poisson effect. The presented experimental use cases encompass ultrathin and opaque metal-heterostructures, continuous and granular nanolayers as well as negative thermal expansion materials, that each pose a challenge to established all-optical techniques.

Photo-induced phase-transitions in complex solids

Photo-induced phase-transitions (PIPTs) driven by highly cooperative interactions are of fundamental interest as they offer a way to tune and control material properties on ultrafast timescales. Due to strong correlations and interactions, complex quantum materials host several fascinating PIPTs such as light-induced charge density waves and ferroelectricity and have become a desirable setting for studying these PIPTs. A central issue in this field is the proper understanding of the underlying mechanisms driving the PIPTs. As these PIPTs are highly nonlinear processes and often involve multiple time and length scales, different theoretical approaches are often needed to understand the underlying mechanisms. In this review, we present a brief overview of PIPTs realized in complex materials, followed by a discussion of the available theoretical methods with selected examples of recent progress in understanding of the nonequilibrium pathways of PIPTs.

Photoinduced Ultrafast Transition of the Local Correlated Structure in Chalcogenide Phase-Change Materials

Revealing the bonding and time-evolving atomic dynamics in functional materials with complex lattice structures can update the fundamental knowledge on rich physics therein, and also help to manipulate the material properties as desired. As the most prototypical chalcogenide phase change material, Ge_{2}Sb_{2}Te_{5} has been widely used in optical data storage and nonvolatile electric memory due to the fast switching speed and the low energy consumption. However, the basic understanding of the structural dynamics on the atomic scale is still not clear. Using femtosecond electron diffraction, structure factor calculation, and time-dependent density-functional theory molecular dynamic simulation, we reveal the photoinduced ultrafast transition of the local correlated structure in the averaged rocksalt phase of Ge_{2}Sb_{2}Te_{5}. The randomly oriented Peierls distortion among unit cells in the averaged rocksalt phase of Ge_{2}Sb_{2}Te_{5} is termed as local correlated structures. The ultrafast suppression of the local Peierls distortions in the individual unit cell gives rise to a local structure change from the rhombohedral to the cubic geometry within ∼0.3  ps. In addition, the impact of the carrier relaxation and the large number of vacancies to the ultrafast structural response is quantified and discussed. Our Letter provides new microscopic insights into contributions of the local correlated structure to the transient structural and optical responses in phase change materials. Moreover, we stress the significance of femtosecond electron diffraction in revealing the local correlated structure in the subunit cell and the link between the local correlated structure and physical properties in functional materials with complex microstructures.

Ultrafast Suppression of the Ferroelectric Instability in KTaO_{3}

We use an x-ray free-electron laser to study the lattice dynamics following photoexcitation with ultrafast near-UV light (wavelength 266 nm, 50 fs pulse duration) of the incipient ferroelectric potassium tantalate, KTaO_{3}. By probing the lattice dynamics corresponding to multiple Brillouin zones through the x-ray diffuse scattering with pulses from the Linac Coherent Light Source (LCLS) (wavelength 1.3 Å and <10  fs pulse duration), we observe changes in the diffuse intensity associated with a hardening of the transverse acoustic phonon branches along Γ to X and Γ to M. Using force constants from density functional theory, we fit the quasiequilibrium intensity and obtain the instantaneous lattice temperature and density of photoexcited charge carriers. The density functional theory calculations demonstrate that photoexcitation transfers charge from oxygen 2p derived π-bonding orbitals to Ta 5d derived antibonding orbitals, further suppressing the ferroelectric instability and increasing the stability of the cubic, paraelectric structure.

Traversing Double-Well Potential Energy Surfaces: Photoinduced Concurrent Intralayer and Interlayer Structural Transitions in XTe2 (X = Mo, W)

The microscopic arrangement of atoms and molecules is the determining factor in how materials behave and perform; i.e., the structure determines the property, a traditional paradigm in materials science. Photoexcitation-driven manipulation of the crystal structure and associated electronic properties in quantum materials provides opportunities for the exploration of exotic physics and practical applications; however, a generalized mechanism for such symmetry engineering is absent. Here, by ultrafast electron diffraction, structure factor calculation, and TDDFT-MD simulations, we report the photoinduced concurrent intralayer and interlayer structural transitions in the Td and 1T' phases of XTe₂ (X = Mo, W). We discuss the modification of multiple quantum electronic states associated with the intralayer and interlayer structural transitions, such as the topological band inversion and the higher-order topological state. The twin structures and the stacking faults in XTe₂ are also identified by ultrafast structural responses. The comprehensive study of the ultrafast structural response in XTe₂ suggests the traversal of all double-well potential energy surfaces (DWPES) by laser excitation, which is expected to be an intrinsic mechanism in the field of photoexcitation-driven global/local symmetry engineering and also a critical ingredient inducing the exotic properties in the non-equilibrium state in a large number of material systems.

Ultrafast Generation of Coherent Phonons in Two-Dimensional Bismuthene

Coherent phonons generated through regulation of lattice oscillation via ultrafast laser pulses or X-rays have been desired in various fields, including optoelectronics, thermal and quantum information, and communications. Phonon coherence of two-dimensional (2D) materials is particularly attractive as it enables controllable information transmission but is challenging as the weak interplanar coupling makes phonon excitation extremely difficult. Herein we managed to generate size-dependent phonon coherence from bulk Bi to few-layer bismuthene by an ultrafast femtosecond laser pulse and made a systematic comparison thorough a combination of computation, transient absorption, and reflectance spectroscopic methods. The results witnessed the A_1g phonon excitation in all of the three Bi materials with distinct thicknesses, and the quantum size effect of 2D materials caused phonon confinement and eventual bond softening manifested as a red-shifted vibration frequency and shortened decoherence time compared with those of their bulk counterpart. This study offers new perspectives for tailoring coherent phonons in 2D materials for quantum science and technology including quantum communication, computing, and design of novel quantum devices, etc.

Ultrafast laser ablation simulator using deep neural networks

Laser-based material removal, or ablation, using ultrafast pulses enables precision micro-scale processing of almost any material for a wide range of applications and is likely to play a pivotal role in providing mass customization capabilities in future manufacturing. However, optimization of the processing parameters can currently take several weeks because of the absence of an appropriate simulator. The difficulties in realizing such a simulator lie in the multi-scale nature of the relevant processes and the high nonlinearity and irreversibility of these processes, which can differ substantially depending on the target material. Here we show that an ultrafast laser ablation simulator can be realized using deep neural networks. The simulator can calculate the three-dimensional structure after irradiation by multiple laser pulses at arbitrary positions and with arbitrary pulse energies, and we applied the simulator to a variety of materials, including dielectrics, semiconductors, and an organic polymer. The simulator successfully predicted their depth profiles after irradiation by a number of pulses, even though the neural networks were trained using single-shot datasets. Our results indicate that deep neural networks trained with single-shot experiments are able to address physics with irreversibility and chaoticity that cannot be accessed using conventional repetitive experiments.

Nonequilibrium band occupation and optical response of gold after ultrafast XUV excitation

Free electron lasers offer unique properties to study matter in states far from equilibrium as they combine short pulses with a large range of photon energies. In particular, the possibility to excite core states drives new relaxation pathways that, in turn, also change the properties of the optically and chemically active electrons. Here, we present a theoretical model for the dynamics of the nonequilibrium occupation of the different energy bands in solid gold driven by exciting deep core states. The resulting optical response is in excellent agreement with recent measurements and, combined with our model, provides a quantitative benchmark for the description of electron–phonon coupling in strongly driven gold. Focusing on sub-picosecond time scales, we find essential differences between the dynamics induced by XUV and visible light.

Toward fully automated UED operation using two-stage machine learning model

To demonstrate the feasibility of automating UED operation and diagnosing the machine performance in real time, a two-stage machine learning (ML) model based on self-consistent start-to-end simulations has been implemented. This model will not only provide the machine parameters with adequate precision, toward the full automation of the UED instrument, but also make real-time electron beam information available as single-shot nondestructive diagnostics. Furthermore, based on a deep understanding of the root connection between the electron beam properties and the features of Bragg-diffraction patterns, we have applied the hidden symmetry as model constraints, successfully improving the accuracy of energy spread prediction by a factor of five and making the beam divergence prediction two times faster. The capability enabled by the global optimization via ML provides us with better opportunities for discoveries using near-parallel, bright, and ultrafast electron beams for single-shot imaging. It also enables directly visualizing the dynamics of defects and nanostructured materials, which is impossible using present electron-beam technologies.

Dynamics of Ultrafast Phase Transitions in (001) Si on the Shock-Wave Front

We demonstrate an ultrafast (<0.1 ps) reversible phase transition in silicon (Si) under ultrafast pressure loading using molecular dynamics. Si changes its structure from cubic diamond to β-Sn on the shock-wave front. The phase transition occurs when the shock-wave pressure exceeds 11 GPa. Atomic volume, centrosymmetry, and the X-ray-diffraction spectrum were revealed as effective indicators of phase-transition dynamics. The latter, being registered in actual experimental conditions, constitutes a breakthrough in the path towards simple X-ray optical cross-correlation and pump-probe experiments.

Evolution of laser-induced strain in a Ge crystal for the [111] and [100] directions probed by time-resolved X-ray diffraction

Ultra-short laser-pulse-induced strain propagation in a Ge crystal is studied in the [111] and [100] directions using time-resolved X-ray diffraction (TXRD). The strain propagation velocity is derived by analysis of the TXRD signal from the strained crystal planes. Numerical integration of the Takagi–Taupin equations is performed using open source code, which provides a very simple approach to estimate the strain propagation velocity. The present method will be particularly useful for relatively broad spectral bandwidths and weak X-ray sources, where temporal oscillations in the diffracted X-ray intensity at the relevant phonon frequencies would not be visible. The two Bragg reflections of the Ge sample, viz. 111 and 400, give information on the propagation of strain for two different depths, as the X-ray extinction depths are different for these two reflections. The strain induced by femtosecond laser excitation has a propagation velocity comparable to the longitudinal acoustic velocity. The strain propagation velocity increases with increasing laser excitation fluence. This fluence dependence of the strain propagation velocity can be attributed to crystal heating by ambipolar carrier diffusion. Ge is a promising candidate for silicon-based optoelectronics, and this study will enhance the understanding of heat transport by carrier diffusion in Ge induced by ultra-fast laser pulses, which will assist in the design of optoelectronic devices.

Accurate prediction of mega-electron-volt electron beam properties from UED using machine learning

To harness the full potential of the ultrafast electron diffraction (UED) and microscopy (UEM), we must know accurately the electron beam properties, such as emittance, energy spread, spatial-pointing jitter, and shot-to-shot energy fluctuation. Owing to the inherent fluctuations in UED/UEM instruments, obtaining such detailed knowledge requires real-time characterization of the beam properties for each electron bunch. While diagnostics of these properties exist, they are often invasive, and many of them cannot operate at a high repetition rate. Here, we present a technique to overcome such limitations. Employing a machine learning (ML) strategy, we can accurately predict electron beam properties for every shot using only parameters that are easily recorded at high repetition rate by the detector while the experiments are ongoing, by training a model on a small set of fully diagnosed bunches. Applying ML as real-time noninvasive diagnostics could enable some new capabilities, e.g., online optimization of the long-term stability and fine single-shot quality of the electron beam, filtering the events and making online corrections of the data for time-resolved UED, otherwise impossible. This opens the possibility of fully realizing the potential of high repetition rate UED and UEM for life science and condensed matter physics applications.

Hybrid x-ray laser-plasma/laser-synchrotron facility for pump-probe studies of the extreme state of matter at NRC "Kurchatov Institute"

We developed a hybrid optical pump-x-ray probe facility based on the "Kurchatov's synchrotron radiation source" and terawatt (TW) femtosecond laser. The bright x-ray photon source is based on either synchrotron radiation [up to 6 × 10¹⁴ photons/(s mm² mrad² 0.1% bandwidth)] or laser-plasma generators (up to 10⁸ photons/sr/pulse). The terawatt (TW) femtosecond laser pulse initiated phase transitions and a non-stationary "extreme" state of matter, while the delayed x-ray pulse acts as a probe. The synchronization between synchrotron radiation and laser pulses is achieved at 60.3 MHz using an intelligent field-programmable gate array-based phased locked loop. The timing jitter of the system is less than 30 ps. In laser-plasma sources, the x-ray and laser pulses are automatically synchronized because they are produced by using the same laser source (TW laser system). We have reached an x-ray yield of about 10⁶ photons/sr/pulse with 6-mJ sub-ps laser pulses and using helium as a local gas medium. Under vacuum conditions, the laser energy increase up to 40 mJ leads to the enhancement of the x-ray yield of up to 10⁸ photons/sr/pulse. The developed hybrid facility paves the way for a new class of time-resolved x-ray optical pump-probe experiments in the time interval from femtoseconds to microseconds and the energy spectrum from 3 to 30 keV.

Ultrafast strain propagation and acoustic resonances in nanoscale bilayer systems

Ultrafast structural probing has greatly enhanced our understanding of the coupling of atomic motion to electronic and phononic degrees-of-freedom in quasi-bulk materials. In bi- and multilayer model systems, additionally, spatially inhomogeneous relaxation channels are accessible, often governed by pronounced interfacial couplings and local excitations in confined geometries. Here, we systematically explore the key dependencies of the low-frequency acoustic phonon spectrum in an elastically mismatched metal/semiconductor bilayer system optically excited by femtosecond laser pulses. We track the spatiotemporal strain wave propagation in the heterostructure employing a discrete numerical linear chain simulation and access acoustic wave reflections and interfacial couplings with a phonon mode description based on a continuum mechanics model. Due to the interplay of elastic properties and mass densities of the two materials, acoustic resonance frequencies of the heterostructure significantly differ from breathing modes in monolayer films. For large acoustic mismatch, the spatial localization of phonon eigenmodes is derived from analytical approximations and can be interpreted as harmonic oscillations in decoupled mechanical resonators.

Transient optical non-linearity in p-Si induced by a few cycle extreme THz field

We study the impact of a few cycle extreme terahertz (THz) radiation (the field strength E_THz ∼1-15 MV/cm is well above the DC-field breakdown threshold) on a p-doped Si wafer. Pump-probe measurements of the second harmonic of a weak infrared probe were done at different THz field strengths. The second harmonic yield has an unusual temporal behavior and does not follow the common instantaneous response, ∝ETHz2. These findings were attributed to: (i) the lattice strain by the ponderomotive force of the extreme THz pulse at the maximal THz field strength below 6 MV/cm and (ii) the modulation of the THz field-induced impact ionization rate at the optical probe frequency (due to the modulation of the free carriers' drift kinetic energy from the probe field) at the THz field strength above 6-8 MV/cm.

Toward monochromated sub-nanometer UEM and femtosecond UED

A preliminary design of a mega-electron-volt (MeV) monochromator with 10⁻⁵ energy spread for ultrafast electron diffraction (UED) and ultrafast electron microscopy (UEM) is presented. Such a narrow energy spread is advantageous in both the single shot mode, where the momentum resolution in diffraction is improved, and the accumulation mode, where shot-to-shot energy jitter is reduced. In the single-shot mode, we numerically optimized the monochromator efficiency up to 13% achieving 1.3 million electrons per pulse. In the accumulation mode, to mitigate the efficiency degradation caused by the shot-to-shot energy jitter, an optimized gun phase yields only a mild reduction of the single-shot efficiency, therefore the number of accumulated electrons nearly proportional to the repetition rate. Inspired by the recent work of Qi et al. (Phys Rev Lett 124:134803, 2020), a novel concept of applying reverse bending magnets to adjust the energy-dependent path length difference has been successfully realized in designing a MeV monochromator to achieve the minimum energy-dependent path length difference between cathode and sample. Thanks to the achromat design, the pulse length of the electron bunches and the energy-dependent timing jitter can be greatly reduced to the 10 fs level. The introduction of such a monochromator provides a major step forward, towards constructing a UEM with sub-nm resolution and a UED with ten-femtosecond temporal resolution. The one-to-one mapping between the electron beam parameter and the diffraction peak broadening enables a real-time nondestructive diagnosis of the beam energy spread and divergence. The tunable electric–magnetic monochromator allows the scanning of the electron beam energy with a 10⁻⁵ precision, enabling online energy matching for the UEM, on-momentum flux maximizing for the UED and real-time energy measuring for energy-loss spectroscopy. A combination of the monochromator and a downstream chicane enables “two-color” double pulses with femtosecond duration and the tunable delay in the range of 10 to 160 fs, which can potentially provide an unprecedented femtosecond time resolution for time resolved UED.

Coherent control of a surface structural phase transition

Active optical control over matter is desirable in many scientific disciplines, with prominent examples in all-optical magnetic switching^1,2, light-induced metastable or exotic phases of solids^3-8 and the coherent control of chemical reactions^9,10. Typically, these approaches dynamically steer a system towards states or reaction products far from equilibrium. In solids, metal-to-insulator transitions are an important target for optical manipulation, offering ultrafast changes of the electronic⁴ and lattice^11-16 properties. The impact of coherences on the efficiencies and thresholds of such transitions, however, remains a largely open subject. Here, we demonstrate coherent control over a metal-insulator structural phase transition in a quasi-one-dimensional solid-state surface system. A femtosecond double-pulse excitation scheme^17-20 is used to switch the system from the insulating to a metastable metallic state, and the corresponding structural changes are monitored by ultrafast low-energy electron diffraction^21,22. To govern the transition, we harness vibrational coherence in key structural modes connecting both phases, and observe delay-dependent oscillations in the double-pulse switching efficiency. Mode-selective coherent control of solids and surfaces could open new routes to switching chemical and physical functionalities, enabled by metastable and non-equilibrium states.

Parametric Excitation of an Optically Silent Goldstone-Like Phonon Mode

It has recently been indicated that the hexagonal manganites exhibit Higgs- and Goldstone-like phonon modes that modulate the amplitude and phase of their primary order parameter. Here, we describe a mechanism by which a silent Goldstone-like phonon mode can be coherently excited, which is based on nonlinear coupling to an infrared-active Higgs-like phonon mode. Using a combination of first-principles calculations and phenomenological modeling, we describe the coupled Higgs-Goldstone dynamics in response to the excitation with a terahertz pulse. Besides theoretically demonstrating coherent control of crystallographic Higgs and Goldstone excitations, we show that the previously inaccessible silent phonon modes can be excited coherently with this mechanism.

Time-resolved diffraction with an optimized short pulse laser plasma X-ray source

We present a setup for time-resolved X-ray diffraction based on a short pulse, laser-driven plasma X-ray source. The employed modular design provides high flexibility to adapt the setup to the specific requirements (e.g., X-ray optics and sample environment) of particular applications. The configuration discussed here has been optimized toward high angular/momentum resolution and uses K α -radiation (4.51 keV) from a Ti wire-target in combination with a toroidally bent crystal for collection, monochromatization, and focusing of the emitted radiation. 2 × 10 5 Ti-K α1 photons per pulse with10 - 4 relative bandwidth are delivered to the sample at a repetition rate of 10 Hz. This allows for the high dynamic range (104) measurements of transient changes in the rocking curves of materials as for example induced by laser-triggered strain waves.

Decelerated lattice excitation and absence of bulk phonon modes at surfaces: Ultra-fast electron diffraction from Bi(111) surface upon fs-laser excitation

Ultrafast reflection high-energy electron diffraction is employed to follow the lattice excitation of a Bi(111) surface upon irradiation with a femtosecond laser pulse. The thermal motion of the atoms is analyzed through the Debye–Waller effect. While the Bi bulk is heated on time scales of 2 to 4 ps, we observe that the excitation of vibrational motion of the surface atoms occurs much slower with a time constant of 12 ps. This transient nonequilibrium situation is attributed to the weak coupling between bulk and surface phonon modes which hampers the energy flow between the two subsystems. From the absence of a fast component in the transient diffraction intensity, it is in addition concluded that truncated bulk phonon modes are absent at the surface.

Superheating and Homogeneous Melting Dynamics of Bulk Ice

Homogeneous melting of crystals is a complex multistep process involving the formation of transient states at temperatures considerably higher than the melting point. The nature and persistence of these metastable structures are intimately connected to the melting process, and a precise definition of the temporal boundaries of these phenomena is not yet available. We set up a specifically designed experiment to probe by transient infrared absorption spectroscopy the entire dynamics, ranging from tens of picoseconds to microseconds, of superheating and melting of an ice crystal. In spite of a large excess of energy provided, only about 30% of the micrometric crystal liquefies in the first 20-25 ns because of the long persistence of the superheated metastable phase that extends for more than 100 ns. This behavior is ascribed to the population of low-energy states that trap a large amount of energy, favoring the formation of a metastable, likely plastic, ice phase.

Direct observation of picosecond melting and disintegration of metallic nanoparticles

Despite more than a century of study, the fundamental mechanisms behind solid melting remain elusive at the nanoscale. Ultrafast phenomena in materials irradiated by intense femtosecond laser pulses have revived the interest in unveiling the puzzling processes of melting transitions. However, direct experimental validation of various microscopic models is limited due to the difficulty of imaging the internal structures of materials undergoing ultrafast and irreversible transitions. Here we overcome this challenge through time-resolved single-shot diffractive imaging using X-ray free electron laser pulses. Images of single Au nanoparticles show heterogeneous melting at the surface followed by density fluctuation deep inside the particle, which is directionally correlated to the polarization of the pumping laser. Observation of this directionality links the non-thermal electronic excitation to the thermal lattice melting, which is further verified by molecular dynamics simulations. This work provides direct evidence to the understanding of irreversible melting with an unprecedented spatiotemporal resolution.

Laser-matter interaction has been intensively studied in equilibrium states, but irreversible processes in a highly nonequilibrium state at nanoscales remains elusive due to experimental challenges. Here, Ihm et al. image heterogeneous melting of gold nanoparticles with nanometer and picosecond resolution.

Measuring non-equilibrium dynamics in complex solids with ultrashort X-ray pulses

Strong interactions between electrons give rise to the complexity of quantum materials, which exhibit exotic functional properties and extreme susceptibility to external perturbations. A growing research trend involves the study of these materials away from equilibrium, especially in cases in which the stimulation with optical pulses can coherently enhance cooperative orders. Time-resolved X-ray probes are integral to this type of research, as they can be used to track atomic and electronic structures as they evolve on ultrafast timescales. Here, we review a series of recent experiments where femtosecond X-ray diffraction was used to measure dynamics of complex solids. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Ultrafast electron diffraction from a Bi(111) surface: Impulsive lattice excitation and Debye-Waller analysis at large momentum transfer

The lattice response of a Bi(111) surface upon impulsive femtosecond laser excitation is studied with time-resolved reflection high-energy electron diffraction. We employ a Debye-Waller analysis at large momentum transfer of 9.3 Å^-1 ≤ Δ k ≤ 21.8 Å^-1 in order to study the lattice excitation dynamics of the Bi surface under conditions of weak optical excitation up to 2 mJ/cm² incident pump fluence. The observed time constants τ _int of decay of diffraction spot intensity depend on the momentum transfer Δk and range from 5 to 12 ps. This large variation of τ _int is caused by the nonlinearity of the exponential function in the Debye-Waller factor and has to be taken into account for an intensity drop ΔI > 0.2. An analysis of more than 20 diffraction spots with a large variation in Δk gave a consistent value for the time constant τ_T of vibrational excitation of the surface lattice of 12 ± 1 ps independent on the excitation density. We found no evidence for a deviation from an isotropic Debye-Waller effect and conclude that the primary laser excitation leads to thermal lattice excitation, i.e., heating of the Bi surface.

Recent Advances in Ultrafast Structural Techniques

A review that summarizes the most recent technological developments in the field of ultrafast structural dynamics with focus on the use of ultrashort X-ray and electron pulses follows. Atomistic views of chemical processes and phase transformations have long been the exclusive domain of computer simulators. The advent of femtosecond (fs) hard X-ray and fs-electron diffraction techniques made it possible to bring such a level of scrutiny to the experimental area. The following review article provides a summary of the main ultrafast techniques that enabled the generation of atomically resolved movies utilizing ultrashort X-ray and electron pulses. Recent advances are discussed with emphasis on synchrotron-based methods, tabletop fs-X-ray plasma sources, ultrabright fs-electron diffractometers, and timing techniques developed to further improve the temporal resolution and fully exploit the use of intense and ultrashort X-ray free electron laser (XFEL) pulses.

Pulsed electron gun for electron diffraction at surfaces with femtosecond temporal resolution and high coherence length

We present a newly designed 30 kV pulsed electron gun for ultrafast electron diffraction suited for pump-probe setups driven by femtosecond laser pulses. The electron gun can be operated both in transmission and reflection geometry. A robust design with a back illuminated Au photocathode, extraction fields of 7.5 kV/mm, and a magnetic focus lens ensures reliable daily use. Magnetic deflectors allow for beam alignment and characterization. Focusing of the UV pulse on the photocathode results in a small source size of photoemitted electrons and thus a high transverse coherence length of more than 50 nm in diffraction. A low difference of ΔE = 0.1 eV between the work function of the 10 nm Au photocathode and photon energy of the frequency tripled UV laser pulses results in an instrumental temporal resolution of 330 fs full width at half maximum. This resolution is discussed with respect to the number of electrons per pulse.

Femtosecond phase-transition in hard x-ray excited bismuth

The evolution of bismuth crystal structure upon excitation of its A_1g phonon has been intensely studied with short pulse optical lasers. Here we present the first-time observation of a hard x-ray induced ultrafast phase transition in a bismuth single crystal at high intensities (~10¹⁴ W/cm²). The lattice evolution was followed using a recently demonstrated x-ray single-shot probing setup. The time evolution of the (111) Bragg peak intensity showed strong dependence on the excitation fluence. After exposure to a sufficiently intense x-ray pulse, the peak intensity dropped to zero within 300 fs, i.e. faster than one oscillation period of the A_1g mode at room temperature. Our analysis indicates a nonthermal origin of a lattice disordering process, and excludes interpretations based on electron-ion equilibration process, or on thermodynamic heating process leading to plasma formation.

Ultrafast tunable modulation of light polarization at terahertz frequencies

Controlling light polarization is one of the most essential routines in modern optical technology. Since the demonstration of optical pulse shaping by spatial light modulators and its potential in controlling the quantum reaction pathways, it paved the way for many applications as a coherent control of the photoionization process or as polarization shaping of terahertz (THz) pulses. Here, we evidenced efficient nonresonant and noncollinear χ⁽²⁾-type light-matter interaction in femtosecond polarization-sensitive time-resolved optical measurements. Such nonlinear optical interaction of visible light and ultrashort THz pulses leads to THz modulation of visible light polarization in bulk LiNbO₃ crystal. Theoretical simulations based on the wave propagation equation capture the physical processes underlying this nonlinear effect. Apart from the observed tunable polarization modulation of visible pulses at ultrahigh frequencies, this physical phenomenon can be envisaged in THz depth-profiling of materials.

High-order harmonic generation from a solid-surface plasma by relativistic-intensity sub-100-fs mid-infrared pulses

High-order harmonic generation (HHG) in plasmas induced by ultrashort, relativistic-intensity laser pulses on solid surfaces can provide an efficient source of attosecond pulses and opens routes toward new regimes of laser-matter interactions, x-ray generation, laser particle acceleration, and relativistic nonlinear optics. However, field intensities in the range of I_rel∼10¹⁹  W/cm² are typically needed to achieve the relativistic regime of HHG in experiments with near-infrared laser pulses. Here, we show that, in the mid-infrared range, due to the λ^-2 scaling of I_rel with the driver wavelength λ, relativistic HHG can be observed at much lower levels of laser field intensities. High-peak-power 80-fs, 3.9-μm pulses are focused in our experiments on a solid surface to provide field intensities in the range of 10¹⁷  W/cm². Remarkably, this level of field intensities, considered as low by the standards of relativistic optics in the near infrared, is shown to be sufficient for generation of high-order harmonics with signature properties of relativistic HHG-beam directionality, spectra with extended plateaus, and a high HHG yield sustained for both p- and s-polarized driver fields.

Direct Measurement of Anharmonic Decay Channels of a Coherent Phonon

We report channel-resolved measurements of the anharmonic coupling of the coherent A_{1g} phonon in photoexcited bismuth to pairs of high wave vector acoustic phonons. The decay of a coherent phonon can be understood as a parametric resonance process whereby the atomic displacement periodically modulates the frequency of a broad continuum of modes. This coupling drives temporal oscillations in the phonon mean-square displacements at the A_{1g} frequency that are observed across the Brillouin zone by femtosecond x-ray diffuse scattering. We extract anharmonic coupling constants between the A_{1g} and several representative decay channels that are within an order of magnitude of density functional perturbation theory calculations.

Non-perturbing THz generation at the Tsinghua University Accelerator Laboratory 31 MeV electron beamline

In recent experiments at Tsinghua University Accelerator Laboratory, the 31 MeV electron beam, which has been compressed to subpicosecond pulse durations, has been used to generate high peak power, narrow band Terahertz (THz) radiation by transit through different slow wave structures, specifically quartz capillaries metallized on the outside. Despite the high peak powers that have been produced, the THz pulse energy is negligible compared to the energy of the electron beam. Therefore, the THz generation process can be complementary to other beamline applications like plasma wakefield acceleration studies and Compton x-ray free electron lasers. This approach can be used at x-ray free electron laser beamlines, where THz radiation can be generated without disturbing the x-ray generation process. In the experiment reported here, a high peak current electron beam generated strong narrow band (∼1% bandwidth) THz signals in the form of a mixture of TM₀₁ and TM₀₂ modes. Each slow wave structure is completed with a mode converter at the end of the structure that allows for efficient (>90%) power extraction into free space. In the experiment, both modes in these two dielectric-loaded waveguides TM₀₁ (0.3 THz/0.5 THz) and TM₀₂ (0.9 THz/1.3 THz) were explicitly measured with an interferometer. The THz pulse energy was measured with a calibrated Golay cell at a few μJ.

Tuning and Tracking of Coherent Shear Waves in Molecular Films

We have determined the time-dependent displacement fields in molecular sub-micrometer thin films as response to femtosecond and picosecond laser pulse heating by time-resolved X-ray diffraction. This method allows a direct absolute determination of the molecular displacements induced by electron-phonon interactions, which are crucial for, for example, charge transport in organic electronic devices. We demonstrate that two different modes of coherent shear motion can be photoexcited in a thin film of organic molecules by careful tuning of the laser penetration depth relative to the thickness of the film. The measured response of the organic film to impulse heating is explained by a thermoelastic model and reveals the spatially resolved displacement in the film. Thereby, information about the profile of the energy deposition in the film as well as about the mechanical interaction with the substrate material is obtained.

Kinetics of Decelerated Melting

Melting presents one of the most prominent phenomena in condensed matter science. Its microscopic understanding, however, is still fragmented, ranging from simplistic theory to the observation of melting point depressions. Here, a multimethod experimental approach is combined with computational simulation to study the microscopic mechanism of melting between these two extremes. Crystalline structures are exploited in which melting occurs into a metastable liquid close to its glass transition temperature. The associated sluggish dynamics concur with real-time observation of homogeneous melting. In-depth information on the structural signature is obtained from various independent spectroscopic and scattering methods, revealing a step-wise nature of the transition before reaching the liquid state. A kinetic model is derived in which the first reaction step is promoted by local instability events, and the second is driven by diffusive mobility. Computational simulation provides further confirmation for the sequential reaction steps and for the details of the associated structural dynamics. The successful quantitative modeling of the low-temperature decelerated melting of zeolite crystals, reconciling homogeneous with heterogeneous processes, should serve as a platform for understanding the inherent instability of other zeolitic structures, as well as the prolific and more complex nanoporous metal-organic frameworks.

Non-equilibrium lattice dynamics of one-dimensional In chains on Si(111) upon ultrafast optical excitation

The photoinduced structural dynamics of the atomic wire system on the Si(111)-In surface has been studied by ultrafast electron diffraction in reflection geometry. Upon intense fs-laser excitation, this system can be driven in around 1 ps from the insulating [Formula: see text] reconstructed low temperature phase to a metastable metallic [Formula: see text] reconstructed high temperature phase. Subsequent to the structural transition, the surface heats up on a 6 times slower timescale as determined from a transient Debye-Waller analysis of the diffraction spots. From a comparison with the structural response of the high temperature [Formula: see text] phase, we conclude that electron-phonon coupling is responsible for the slow energy transfer from the excited electron system to the lattice. The significant difference in timescales is evidence that the photoinduced structural transition is non-thermally driven.

FemtoMAX - an X-ray beamline for structural dynamics at the short-pulse facility of MAX IV

The FemtoMAX beamline facilitates studies of the structural dynamics of materials. Such studies are of fundamental importance for key scientific problems related to programming materials using light, enabling new storage media and new manufacturing techniques, obtaining sustainable energy by mimicking photosynthesis, and gleaning insights into chemical and biological functional dynamics. The FemtoMAX beamline utilizes the MAX IV linear accelerator as an electron source. The photon bursts have a pulse length of 100 fs, which is on the timescale of molecular vibrations, and have wavelengths matching interatomic distances (Å). The uniqueness of the beamline has called for special beamline components. This paper presents the beamline design including ultrasensitive X-ray beam-position monitors based on thin Ce:YAG screens, efficient harmonic separators and novel timing tools.