Directly observing squeezed phonon states with femtosecond x-ray diffraction

Photoinduced Electronic and Spin Topological Phase Transitions in Monolayer Bismuth

Ultrathin bismuth exhibits rich physics including strong spin-orbit coupling, ferroelectricity, nontrivial topology, and light-induced structural dynamics. We use ab initio calculations to show that light can induce structural transitions to four transient phases in bismuth monolayers. These light-induced phases exhibit nontrivial topological character, which we illustrate using the recently introduced concept of spin bands and spin-resolved Wilson loops. Specifically, we find that the topology changes via the closing of the electron and spin band gaps during photoinduced structural phase transitions, leading to distinct edge states. Our study provides strategies to tailor electronic and spin topology via ultrafast control of photoexcited carriers and associated structural dynamics.

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.

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.

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.

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

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

Spiers Memorial Lecture: From Optical to THz control of materials

Advances over the past decade have presented new avenues to achieve control over material properties using intense pulses of electromagnetic radiation, with frequencies ranging from optical (approximately 1 PHz, or 10¹⁵ Hz) down to below 1 THz (10¹² Hz). Some of these new developments have arisen from new experimental methods to drive and observe transient material properties, while others have emerged from new computational techniques that have made nonequilibrium dynamics more tractable to our understanding. One common issue with most attempts to realize control using electromagnetic pulses is the dissipation of energy, which in many cases poses a limit due to uncontrolled heating and has led to strong interest in using lower frequency and/or highly specific excitations to minimize this effect. Emergent developments in experimental tools using shaped X-ray pulses may in the future offer new possibilities for material control, provided that the issue of heat dissipation can be resolved for higher frequency light.

The concept of using appropriately shaped pulses of light to control the properties of materials has a range of potential applications, and relies on an understanding of intricate couplings within the material.

New insights into correlated materials in the time domain-combining far-infrared excitation with x-ray probes at cryogenic temperatures

Modern techniques for the investigation of correlated materials in the time domain combine selective excitation in the THz frequency range with selective probing of coupled structural, electronic and magnetic degrees of freedom using x-ray scattering techniques. Cryogenic sample temperatures are commonly required to prevent thermal occupation of the low energy modes and to access relevant material ground states. Here, we present a chamber optimized for high-field THz excitation and (resonant) x-ray diffraction at sample temperatures between 5 and 500 K. Directly connected to the beamline vacuum and featuring both a Beryllium window and an in-vacuum detector, the chamber covers the full (2-12.7) keV energy range of the femtosecond x-ray pulses available at the Bernina endstation of the SwissFEL free electron laser. Successful commissioning experiments made use of the energy tunability to selectively track the dynamics of the structural, magnetic and orbital order of Ca₂RuO₄and Tb₂Ti₂O₇at the Ru (2.96 keV) and Tb (7.55 keV)L-edges, respectively. THz field amplitudes up to 1.12 MV cm^-1peak field were demonstrated and used to excite the samples at temperatures as low as 5 K.

Self-Learning Method for Construction of Analytical Interatomic Potentials to Describe Laser-Excited Materials

Large-scale simulations using interatomic potentials provide deep insight into the processes occurring in solids subject to external perturbations. The atomistic description of laser-induced ultrafast nonthermal phenomena, however, constitutes a particularly difficult case and has so far not been possible on experimentally accessible length scales and timescales because of two main reasons: (i) ab initio simulations are restricted to a very small number of atoms and ultrashort times and (ii) simulations relying on electronic temperature- (T_{e}) dependent interatomic potentials do not reach the necessary ab initio accuracy. Here we develop a self-learning method for constructing T_{e}-dependent interatomic potentials which permit ultralarge-scale atomistic simulations of systems suddenly brought to extreme nonthermal states with density-functional theory (DFT) accuracy. The method always finds the global minimum in the parameter space. We derive a highly accurate analytical T_{e}-dependent interatomic potential Φ(T_{e}) for silicon that yields a remarkably good description of laser-excited and -unexcited Si bulk and Si films. Using Φ(T_{e}) we simulate the laser excitation of Si nanoparticles and find strong damping of their breathing modes due to nonthermal melting.

Optical Control of Non-Equilibrium Phonon Dynamics

The light-induced selective population of short-lived far-from-equilibrium vibration modes is a promising approach for controlling ultrafast and irreversible structural changes in functional nanomaterials. However, this requires a detailed understanding of the dynamics and evolution of these phonon modes and their coupling to the excited-state electronic structure. Here, we combine femtosecond mega-electronvolt electron diffraction experiments on a prototypical layered material, MoTe₂, with non-adiabatic quantum molecular dynamics simulations and ab initio electronic structure calculations to show how non-radiative energy relaxation pathways for excited electrons can be tuned by controlling the optical excitation energy. We show how the dominant intravalley and intervalley scattering mechanisms for hot and band-edge electrons leads to markedly different transient phonon populations evident in electron diffraction patterns. This understanding of how tuning optical excitations affect phonon populations and atomic motion is critical for efficiently controlling light-induced structural transitions of optoelectronic devices.

Time-resolved X-ray reflection phases of the nearly forbidden Si(222) reflection under laser excitation

The covalent electron density, which makes Si(222) measurable, is subject to laser excitation. The three-wave Si(222)/(13 {\overline 1}) diffraction at 7.82 keV is used for phase measurements. It is found that laser excitation causes a relative phase change of around 4° in Si(222) in the first 100 ps of excitation and this is gradually recovered over several nanoseconds. This phase change is due to laser excitation of covalent electrons around the silicon atoms in the unit cell and makes the electron density deviate further from the centrosymmetric distribution.

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.

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.

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.

Hot electron relaxation dynamics in semiconductors: assessing the strength of the electron-phonon coupling from the theoretical and experimental viewpoints

The rapid development of the computational methods based on density functional theory, on the one hand, and of time-, energy-, and momentum-resolved spectroscopy, on the other hand, allows today an unprecedently detailed insight into the processes governing hot-electron relaxation dynamics, and, in particular, into the role of the electron-phonon coupling. Instead of focusing on the development of a particular method, theoretical or experimental, this review aims to treat the progress in the understanding of the electron-phonon coupling which can be gained from both, on the basis of recently obtained results. We start by defining several regimes of hot electron relaxation via electron-phonon coupling, with respect to the electron excitation energy. We distinguish between energy and momentum relaxation of hot electrons, and summarize, for several semiconductors of the IV and III-V groups, the orders of magnitude of different relaxation times in different regimes, on the basis of known experimental and numerical data. Momentum relaxation times of hot electrons become very short around 1 eV above the bottom of the conduction band, and such ultrafast relaxation mechanisms are measurable only in the most recent pump-probe experiments. Then, we give an overview of the recent progress in the experimental techniques allowing to obtain detailed information on the hot-electron relaxation dynamics, with the main focus on time-, energy-, and momentum-resolved photoemission experiments. The particularities of the experimental approach developed by one of us, which allows to capture time-, energy-, and momentum-resolved hot-electron distributions, as well as to measure momentum relaxation times of the order of 10 fs, are discussed. We further discuss the main advances in the calculation of the electron-phonon scattering times from first principles over the past ten years, in semiconducting materials. Ab initio techniques and efficient interpolation methods provide the possibility to calculate electron-phonon scattering times with high precision at reasonable numerical cost. We highlight the methods of analysis of the obtained numerical results, which allow to give insight into the details of the electron-phonon scattering mechanisms. Finally, we discuss the concept of hot electron ensemble which has been proposed recently to describe the hot-electron relaxation dynamics in GaAs, the applicability of this concept to other materials, and its limitations. We also mention some open problems.

Perspective: Opportunities for ultrafast science at SwissFEL

We present the main specifications of the newly constructed Swiss Free Electron Laser, SwissFEL, and explore its potential impact on ultrafast science. In light of recent achievements at current X-ray free electron lasers, we discuss the potential territory for new scientific breakthroughs offered by SwissFEL in Chemistry, Biology, and Materials Science, as well as nonlinear X-ray science.

Ultrafast isomerization in acetylene dication after carbon K-shell ionization

Ultrafast proton migration and isomerization are key processes for acetylene and its ions. However, the mechanism for ultrafast isomerization of acetylene [HCCH]²⁺ to vinylidene [H₂CC]²⁺ dication remains nebulous. Theoretical studies show a large potential barrier ( > 2 eV) for isomerization on low-lying dicationic states, implying picosecond or longer isomerization timescales. However, a recent experiment at a femtosecond X-ray free-electron laser suggests sub-100 fs isomerization. Here we address this contradiction with a complete theoretical study of the dynamics of acetylene dication produced by Auger decay after X-ray photoionization of the carbon atom K shell. We find no sub-100 fs isomerization, while reproducing the salient features of the time-resolved Coulomb imaging experiment. This work resolves the seeming contradiction between experiment and theory and also calls for careful interpretation of structural information from the widely applied Coulomb momentum imaging method.

The timescale of isomerization in molecules involving ultrafast migration of constituent atoms is difficult to measure. Here the authors report that sub-100 fs isomerization time on acetylene dication in lower electronic states is not possible and point to misinterpretation of recent experimental results.

Electron-lattice energy relaxation in laser-excited thin-film Au-insulator heterostructures studied by ultrafast MeV electron diffraction

We apply time-resolved MeV electron diffraction to study the electron-lattice energy relaxation in thin film Au-insulator heterostructures. Through precise measurements of the transient Debye-Waller-factor, the mean-square atomic displacement is directly determined, which allows to quantitatively follow the temporal evolution of the lattice temperature after short pulse laser excitation. Data obtained over an extended range of laser fluences reveal an increased relaxation rate when the film thickness is reduced or the Au-film is capped with an additional insulator top-layer. This behavior is attributed to a cross-interfacial coupling of excited electrons in the Au film to phonons in the adjacent insulator layer(s). Analysis of the data using the two-temperature-model taking explicitly into account the additional energy loss at the interface(s) allows to deduce the relative strength of the two relaxation channels.

Stationary Phonon Squeezing by Optical Polaron Excitation

We demonstrate that a stationary squeezed phonon state can be prepared by a pulsed optical excitation of a semiconductor quantum well. Unlike previously discussed scenarios for generating squeezed phonons, the corresponding uncertainties become stationary after the excitation and do not oscillate in time. The effect is caused by two-phonon correlations within the excited polaron. We demonstrate by quantum kinetic simulations and by a perturbation analysis that the energetically lowest polaron state comprises two-phonon correlations which, after the pulse, result in an uncertainty of the lattice momentum that is continuously lower than in the ground state of the semiconductor. The simulations show the dynamics of the polaron formation process and the resulting time-dependent lattice uncertainties.

Quantum statistics and squeezing for a microwave-driven interacting magnon system

Theoretical studies are reported for the statistical properties of a microwave-driven interacting magnon system. Both the magnetic dipole-dipole and the exchange interactions are included and the theory is developed for the case of parallel pumping allowing for the inclusion of the nonlinear processes due to the four-magnon interactions. The method of second quantization is used to transform the total Hamiltonian from spin operators to boson creation and annihilation operators. By using the coherent magnon state representation we have studied the magnon occupation number and the statistical behavior of the system. In particular, it is shown that the nonlinearities introduced by the parallel pumping field and the four-magnon interactions lead to non-classical quantum statistical properties of the system, such as magnon squeezing. Also control of the collapse-and-revival phenomena for the time evolution of the average magnon number is demonstrated by varying the parallel pumping amplitude and the four-magnon coupling.

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

We report the first observation of two-phonon quantum coherences in a semiconductor. Two-dimensional terahertz (THz) spectra recorded with a sequence of three THz pulses display strong two-phonon signals, clearly distinguished from signals due to interband two-photon absorption and electron tunneling. The two-phonon coherences originate from impulsive off-resonant excitation in the nonperturbative regime of light-matter interaction. A theoretical analysis provides the relevant Liouville pathways, showing that nonlinear interactions using the large interband dipole moment generate stronger two-phonon excitations than linear interactions.

Photon number statistics uncover the fluctuations in non-equilibrium lattice dynamics

Fluctuations of the atomic positions are at the core of a large class of unusual material properties ranging from quantum para-electricity to high temperature superconductivity. Their measurement in solids is the subject of an intense scientific debate focused on seeking a methodology capable of establishing a direct link between the variance of the atomic displacements and experimentally measurable observables. Here we address this issue by means of non-equilibrium optical experiments performed in shot-noise-limited regime. The variance of the time-dependent atomic positions and momenta is directly mapped into the quantum fluctuations of the photon number of the scattered probing light. A fully quantum description of the non-linear interaction between photonic and phononic fields is benchmarked by unveiling the squeezing of thermal phonons in α-quartz.

THz-Frequency Modulation of the Hubbard U in an Organic Mott Insulator

We use midinfrared pulses with stable carrier-envelope phase offset to drive molecular vibrations in the charge transfer salt ET-F_{2}TCNQ, a prototypical one-dimensional Mott insulator. We find that the Mott gap, which is probed resonantly with 10 fs laser pulses, oscillates with the pump field. This observation reveals that molecular excitations can coherently perturb the electronic on-site interactions (Hubbard U) by changing the local orbital wave function. The gap oscillates at twice the frequency of the vibrational mode, indicating that the molecular distortions couple quadratically to the local charge density.

Ultrafast core-loss spectroscopy in four-dimensional electron microscopy

We demonstrate ultrafast core-electron energy-loss spectroscopy in four-dimensional electron microscopy as an element-specific probe of nanoscale dynamics. We apply it to the study of photoexcited graphite with femtosecond and nanosecond resolutions. The transient core-loss spectra, in combination with ab initio molecular dynamics simulations, reveal the elongation of the carbon-carbon bonds, even though the overall behavior is a contraction of the crystal lattice. A prompt energy-gap shrinkage is observed on the picosecond time scale, which is caused by local bond length elongation and the direct renormalization of band energies due to temperature-dependent electron-phonon interactions.

Perspective: structural dynamics in condensed matter mapped by femtosecond x-ray diffraction

Ultrashort soft and hard x-ray pulses are sensitive probes of structural dynamics on the picometer length and femtosecond time scales of electronic and atomic motions. Recent progress in generating such pulses has initiated new directions of condensed matter research, exploiting a variety of x-ray absorption, scattering, and diffraction methods to probe photoinduced structural dynamics. Atomic motion, changes of local structure and long-range order, as well as correlated electron motion and charge transfer have been resolved in space and time, providing a most direct access to the physical mechanisms and interactions driving reversible and irreversible changes of structure. This perspective combines an overview of recent advances in femtosecond x-ray diffraction with a discussion on ongoing and future developments.

Excitation of coherent phonons in the one-dimensional Bi(114) surface

We present time-resolved photoemission experiments from a peculiar bismuth surface, Bi(114). The strong one-dimensional character of this surface is reflected in the Fermi surface, which consists of spin-polarized straight lines. Our results show that the depletion of the surface state and the population of the bulk conduction band after the initial optical excitation persist for very long times. The disequilibrium within the hot electron gas along with strong electron-phonon coupling cause a displacive excitation of coherent phonons, which in turn are reflected in coherent modulations of the electronic states. Beside the well-known A(1g) bulk phonon mode at 2.76 THz, the time-resolved photoelectron spectra reveal a second mode at 0.72 THz which can be attributed to an optical surface phonon mode along the atomic rows of the Bi(114) surface.

Electron cooling and debye-waller effect in photoexcited bismuth

By means of first principles calculations, we compute the effective electron-phonon coupling constant G(0) governing the electron cooling in photoexcited bismuth. G(0) strongly increases as a function of electron temperature, which can be traced back to the semimetallic nature of bismuth. We also use a thermodynamical model to compute the time evolution of both electron and lattice temperatures following laser excitation. Thereby, we simulate the time evolution of (1 -1 0), (-2 1 1) and (2 -2 0) Bragg peak intensities measured by Sciaini et al. [Nature (London) 458, 56 (2009)] in femtosecond electron diffraction experiments. The effect of the electron temperature on the Debye-Waller factors through the softening of all optical modes across the whole Brillouin zone turns out to be crucial to reproduce the time evolution of these Bragg peak intensities.

Ultrafast changes in lattice symmetry probed by coherent phonons

The electronic and structural properties of a material are strongly determined by its symmetry. Changing the symmetry via a photoinduced phase transition offers new ways to manipulate material properties on ultrafast timescales. However, to identify when and how fast these phase transitions occur, methods that can probe the symmetry change in the time domain are required. Here we show that a time-dependent change in the coherent phonon spectrum can probe a change in symmetry of the lattice potential, thus providing an all-optical probe of structural transitions. We examine the photoinduced structural phase transition in VO(2) and show that, above the phase transition threshold, photoexcitation completely changes the lattice potential on an ultrafast timescale. The loss of the equilibrium-phase phonon modes occurs promptly, indicating a non-thermal pathway for the photoinduced phase transition, where a strong perturbation to the lattice potential changes its symmetry before ionic rearrangement has occurred.

Femtosecond dynamics of the collinear-to-spiral antiferromagnetic phase transition in CuO

We report on the ultrafast dynamics of magnetic order in a single crystal of CuO at a temperature of 207 K in response to strong optical excitation using femtosecond resonant x-ray diffraction. In the experiment, a femtosecond laser pulse induces a sudden, nonequilibrium increase in magnetic disorder. After a short delay ranging from 400 fs to 2 ps, we observe changes in the relative intensity of the magnetic ordering diffraction peaks that indicate a shift from a collinear commensurate phase to a spiral incommensurate phase. These results indicate that the ultimate speed for this antiferromagnetic reorientation transition in CuO is limited by the long-wavelength magnetic excitation connecting the two phases.

The rotating-crystal method in femtosecond X-ray diffraction

We report the first implementation of the rotating-crystal method in femtosecond X-ray diffraction. Applying a pump-probe scheme with 100 fs hard X-ray probe pulses from a laser-driven plasma source, the novel technique is demonstrated by mapping structural dynamics of a photoexcited bismuth crystal via changes of the diffracted intensity on a multitude of Bragg reflections. The method is compared to femtosecond powder diffraction and to Bragg diffraction from a crystal with stationary orientation.

Entropy driven atomic motion in laser-excited bismuth

We introduce a thermodynamical model based on the two-temperature approach in order to fully understand the dynamics of the coherent A(1g) phonon in laser-excited bismuth. Using this model, we simulate the time evolution of (111) Bragg peak intensities measured by Fritz et al. [Science 315, 633 (2007)] in femtosecond x-ray diffraction experiments performed on a bismuth film for different laser fluences. The agreement between theoretical and experimental results is striking not only because we use fluences very close to the experimental ones but also because most of the model parameters are obtained from ab initio calculations performed for different electron temperatures.

Lattice fluctuations at a double phonon frequency with and without squeezing: an exactly solvable model of an optically excited quantum dot

Time-dependent lattice fluctuations of an optically excited strongly confined quantum dot are investigated with the aim to analyze the characteristics commonly used for identifying the presence of squeezed phonon states. It is demonstrated that the appearance of fluctuations oscillating with twice the phonon frequency, commonly regarded as a clear indication of squeezed states, cannot be considered as such. The source of the discrepancy with earlier investigations is discussed. Conditions for generating a squeezed state by using a two-pulse excitation are analyzed.

`Making the molecular movie': first frames

Recent advances in high-intensity electron and X-ray pulsed sources now make it possible to directly observe atomic motions as they occur in barrier-crossing processes. These rare events require the structural dynamics to be triggered by femtosecond excitation pulses that prepare the system above the barrier or access new potential energy surfaces that drive the structural changes. In general, the sampling process modifies the system such that the structural probes should ideally have sufficient intensity to fully resolve structures near the single-shot limit for a given time point. New developments in both source intensity and temporal characterization of the pulsed sampling mode have made it possible to make so-called `molecular movies',i.e.measure relative atomic motions faster than collisions can blur information on correlations. Strongly driven phase transitions from thermally propagated melting to optically modified potential energy surfaces leading to ballistic phase transitions and bond stiffening are given as examples of the new insights that can be gained from an atomic level perspective of structural dynamics. The most important impact will likely be made in the fields of chemistry and biology where the central unifying concept of the transition state will come under direct observation and enable a reduction of high-dimensional complex reaction surfaces to the key reactive modes, as long mastered by Mother Nature.

Non-equilibrium phonon dynamics studied by grazing-incidence femtosecond X-ray crystallography

The timescales for structural changes in a single crystal of bismuth after excitation with an intense near-infrared laser pulse are studied with femtosecond pump-probe X-ray diffraction. Changes in the intensity and reciprocal-lattice vector of several reflections give quantitative information on the structure factor and lattice strain as a function of time, with a resolution of 200 fs. The results indicate that the majority of excess carrier energy that remains near the surface is transferred to vibrational modes on a timescale of about 10 ps, and that the resultant increase in the variance of the atomic positions at these times is consistent with the overall magnitude of lattice strain that develops.

Full reconstruction of a crystal unit cell structure during coherent femtosecond motion

We present a complete characterization of the unit cell dynamics of a laser-excited tellurium crystal using femtosecond x-ray diffraction. The analysis offers a quantitative measure of the unit cell dynamics without making any assumptions on the symmetry of the excited-state motion. The results show a large-amplitude coherently excited A(1) mode quantitatively consistent with the predictions of a density functional theory model.

Ultrafast structural phase transition driven by photoinduced melting of charge and orbital order

We use femtosecond x-ray diffraction to probe directly the structural dynamics of a charge ordered and orbitally ordered thin film of La0.42Ca0.58MnO3 initiated by an ultrafast optical pulse. At low excitation fluences we observe the displacive excitation of a coherent optical A(g) phonon. Under high excitation conditions we observe a complete phase transition within 1 ps via the disappearance of a superlattice reflection. The initial step of the phase transition occurs on a time scale significantly faster than the 200 fs time resolution of our experiment.