The 2021 ultrafast spectroscopic probes of condensed matter roadmap

Ab initio-simulated optical response of hot electrons in gold and ruthenium

Optical femtosecond pump-probe experiments allow to measure the dynamics of ultrafast heating of metals with high accuracy. However, the theoretical analysis of such experiments is often complicated because of the indirect connection of the measured signal and the desired temperature transients. Establishing such a connection requires an accurate model of the optical constants of a metal, depending on both the electron temperature Te and the lattice temperature Tl. In this paper, we present first-principles simulations of the two-temperature scenario with Te ≫ Tl, showing the optical response of hot electrons to laser irradiation in gold and ruthenium. Comparing our simulations with the Kubo-Greenwood approach, we discuss the influence of electron-phonon and electron-electron scattering on the intraband contribution to optical constants. Applying the simulated optical constants to the analysis of ultrafast heating of ruthenium thin films we highlight the importance of the latter scattering channel to understand the measured heating dynamics.

Tracking electron motion within and outside of Floquet bands from attosecond pulse trains in time-resolved ARPES

Floquet engineering has recently emerged as a technique for controlling material properties with light. Floquet phases can be probed with time- and angle-resolved photoelectron spectroscopy (Tr-ARPES), providing direct access to the laser-dressed electronic bands. Applications of Tr-ARPES to date focused on observing the Floquet-Bloch bands themselves, and their build-up and dephasing on sub-laser-cycle timescales. However, momentum and energy resolved sub-laser-cycle dynamics between Floquet bands have not been analyzed. Given that Floquet theory strictly applies in time-periodic conditions, the notion of resolving sub-laser-cycle dynamics between Floquet states seems contradictory-it requires probe pulse durations below a laser cycle that inherently cannot discern the time-periodic nature of the light-matter system. Here we propose to employ attosecond pulse train probes with the same temporal periodicity as the Floquet-dressing pump pulse, allowing both attosecond sub-laser-cycle resolution and a proper projection of Tr-ARPES spectra on the Floquet-Bloch bands. We formulate and employ this approach inab-initiocalculations in light-driven graphene. Our calculations predict significant sub-laser-cycle dynamics occurring within the Floquet phase with the majority of electrons moving within and in-between Floquet bands, and a small portion residing and moving outside of them in what we denote as 'non-Floquet' bands. We establish that non-Floquet bands arise from the pump laser envelope that induces non-adiabatic electronic excitations during the pulse turn-on and turn-off. By performing calculations in systems with poly-chromatic pumps we also show that Floquet states are not formed on a sub-laser-cycle level. This work indicates that the Floquet-Bloch states are generally not a complete basis set for sub-laser-cycle dynamics in steady-state phases of matter.

Numerically Exact Solution for a Real Polaritonic System under Vibrational Strong Coupling in Thermodynamic Equilibrium: Loss of Light-Matter Entanglement and Enhanced Fluctuations

The first numerically exact simulation of a full ab initio molecular quantum system (HD+) under strong ro-vibrational coupling to a quantized optical cavity mode in thermal equilibrium is presented. Theoretical challenges in describing strongly coupled systems of mixed quantum statistics (bosons and Fermions) are discussed and circumvented by the specific choice of our molecular system. Our numerically exact simulations highlight the absence of zero temperature for the strongly coupled matter and light subsystems, due to cavity-induced noncanonical conditions. Furthermore, we explore the temperature dependency of light-matter quantum entanglement, which emerges for the ground state but is quickly lost already in the deep cryogenic regime. This is in contrast to predictions from the Jaynes-Cummings model, which is the standard starting point to model collective strong-coupling chemistry phenomenologically. Moreover, we find that the fluctuations of matter remain modified by the quantum nature of the thermal and vacuum-field fluctuations for significant temperatures, e.g., at ambient conditions. These observations (loss of entanglement and coupling to quantum fluctuations) have implications for the understanding and control of polaritonic chemistry and materials science, since a semiclassical theoretical description of light-matter interaction becomes reasonable, but the typical (classical) canonical equilibrium assumption for the nuclear subsystem remains violated. This opens the door for quantum fluctuation-induced stochastic resonance phenomena under vibrational strong coupling, which have been suggested as a plausible theoretical mechanism to explain the experimentally observed resonance phenomena in the absence of periodic driving that has not yet been fully understood.

Efficient and Continuous Carrier-Envelope Phase Control for Terahertz Lightwave-Driven Scanning Probe Microscopy

The fundamental understanding of quantum dynamics in advanced materials requires precise characterization at the limit of spatiotemporal resolution. Ultrafast scanning tunneling microscopy is a powerful tool combining the benefits of picosecond time resolution provided by single-cycle terahertz (THz) pulses and atomic spatial resolution of a scanning tunneling microscope (STM). For the selective excitation of localized electronic states, the transient field profile must be tailored to the energetic structure of the system. Here, we present an advanced THz-STM setup combining multi-MHz repetition rates, strong THz near fields, and continuous carrier-envelope phase (CEP) control of the transient waveform. In particular, we employ frustrated total internal reflection as an efficient and cost-effective method for precise CEP control of single-cycle THz pulses with >60% field transmissivity, high pointing stability, and continuous phase shifting of up to 0.75 π in the far and near field. Efficient THz generation and dispersion management enable peak THz voltages at the tip-sample junction exceeding 20 V at 1 MHz and 1 V at 41 MHz. The system comprises two distinct THz generation arms, which facilitate individual pulse shaping and amplitude modulation. This unique feature enables the flexible implementation of various THz pump-probe schemes, thereby facilitating the study of electronic and excitonic excited-state propagation in nanostructures and low-dimensional materials systems. Scalability of the repetition rate up to 41 MHz, combined with a state-of-the-art low-temperature STM, paves the way toward the investigation of dynamical processes in atomic quantum systems at their native length and time scales.

Terahertz Emission via Optical Rectification in a Metal-Free Perovskite Crystal

We report on the emission of high-intensity pulsed terahertz radiation from the metal-free halide perovskite single crystal methyl-DABCO ammonium iodide (MDNI) under femtosecond illumination. The power and angular dependence of the THz output implicate optical rectification of the 800 nm pump as the mechanism of THz generation. Further characterization finds that, for certain crystal orientations, the angular dependence of THz emission is modulated by phonon resonances attributable to the motion of the methyl-DABCO moiety. At maximum, the THz emission spectrum of MDNI is free from significant phonon resonances, resulting in THz pulses with a temporal width of <900 fs and a peak-to-peak electric field strength of approximately 0.8 kV cm-1-2 orders of magnitude higher than any other reported halide perovskite emitters. Our results point toward metal-free perovskites as a promising new class of THz emitters that brings to bear many of the advantages enjoyed by other halide perovskite materials. In particular, the broad tunability of optoelectronic properties and ease of fabrication of perovskite materials opens up the possibility of further optimizing the THz emission properties within this material class.

Nonequilibrium Phonon Dynamics and Its Impact on the Thermal Conductivity of the Benchmark Thermoelectric Material SnSe

Thermoelectric materials play a vital role in the pursuit of a sustainable energy system by allowing the conversion of waste heat to electric energy. Low thermal conductivity is essential to achieving high-efficiency conversion. The conductivity depends on an interplay between the phononic and electronic properties of the nonequilibrium state. Therefore, obtaining a comprehensive understanding of nonequilibrium dynamics of the electronic and phononic subsystems as well as their interactions is key for unlocking the microscopic mechanisms that ultimately govern thermal conductivity. A benchmark material that exhibits ultralow thermal conductivity is SnSe. We study the nonequilibrium phonon dynamics induced by an excited electron population using a framework combining ultrafast electron diffuse scattering and nonequilibrium kinetic theory. This in-depth approach provides a fundamental understanding of energy transfer in the spatiotemporal domain. Our analysis explains the dynamics leading to the observed low thermal conductivity, which we attribute to a mode-dependent tendency to nonconservative phonon scattering. The results offer a penetrating perspective on energy transport in condensed matter with far-reaching implications for rational design of advanced materials with tailored thermal properties.

Real-Time GW-Ehrenfest-Fan-Migdal Method for Nonequilibrium 2D Materials

Quantum simulations of photoexcited low-dimensional systems are pivotal for understanding how to functionalize and integrate novel two-dimensional (2D) materials in next-generation optoelectronic devices. First-principles predictions are extremely challenging due to the simultaneous interplay of light-matter, electron-electron, and electron-nuclear interactions. We here present an advanced ab initio many-body method that accounts for quantum coherence and non-Markovian effects while treating electrons and nuclei on equal footing, thereby preserving fundamental conservation laws like the total energy. The impact of this advancement is demonstrated through real-time simulations of the complex multivalley dynamics in a molybdenum disulfide (MoS2) monolayer pumped above gap. Within a single framework, we provide a parameter-free description of the coherent-to-incoherent crossover, elucidating the role of microscopic and collective excitations in the dephasing and thermalization processes.

Progress and Prospects in Optical Ultrafast Microscopy in the Visible Spectral Region: Transient Absorption and Two-Dimensional Microscopy

Ultrafast optical microscopy, generally employed by incorporating ultrafast laser pulses into microscopes, can provide spatially resolved mechanistic insight into scientific problems ranging from hot carrier dynamics to biological imaging. This Review discusses the progress in different ultrafast microscopy techniques, with a focus on transient absorption and two-dimensional microscopy. We review the underlying principles of these techniques and discuss their respective advantages and applicability to different scientific questions. We also examine in detail how instrument parameters such as sensitivity, laser power, and temporal and spatial resolution must be addressed. Finally, we comment on future developments and emerging opportunities in the field of ultrafast microscopy.

Atomistic nonlinear carrier dynamics in Ge

An atomistic technique to successfully demonstrate the ultrafast carrier dynamics in Ge photoconductive samples is reported here. The technique is validated against the experimental findings and with the Drude conductivities. The impact of the various different scattering mechanisms is used to calibrate the experimental results. It is observed that the total scattering rate is not a constant parameter as contrast to Drude model which uses constant scattering rate as the fitting parameter to demonstrate the ultrafast carrier dynamics, but strongly dependent on the applied peak THz field strength. It also contradicts with the relaxation time approximation (RTA) method which uses scattering rate chosen on the empirical basis as the fitting parameter to demonstrate the ultrafast carrier dynamics. On the other hand the limitations and challenges offered by various types of density functional theories (DFT) pose lot of challenges. In current manuscript various types of scattering mechanisms i.e. acoustic, intervalley, Coulomb and impact ionization on the behavior of carrier conductivity are studied in details. The proposed technique has shown capability to extract low and high frequency conductivities accurately which is impossible through the Drude model or DFT based theories. It is observed that the free carrier absorption coefficient depends on the refractive index of the material at low THz frequencies. The solution of Boltzmann transport equation through Monte Carlo technique provides valuable insights for better understanding of ultrafast carrier transportation mechanism. The free carrier absorption spectra are found to be in good agreement with the experimental results at various THz field strengths.

Disentangling Lattice and Electronic Instabilities in the Excitonic Insulator Candidate Ta_{2}NiSe_{5} by Nonequilibrium Spectroscopy

Ta_{2}NiSe_{5} is an excitonic insulator candidate showing the semiconductor or semimetal-to-insulator (SI) transition below T_{c}=326  K. However, since a structural transition accompanies the SI transition, deciphering the role of electronic and lattice degrees of freedom in driving the SI transition has remained controversial. Here, we investigate the photoexcited nonequilibrium state in Ta_{2}NiSe_{5} using pump-probe Raman and photoluminescence spectroscopies. The combined nonequilibrium spectroscopic measurements of the lattice and electronic states reveal the presence of a photoexcited metastable state where the insulating gap is suppressed, but the low-temperature structural distortion is preserved. We conclude that electron correlations play a vital role in the SI transition of Ta_{2}NiSe_{5}.

Ultrafast Electron Microscopy of Nanoscale Charge Dynamics in Semiconductors

The ultrafast dynamics of charge carriers in solids plays a pivotal role in emerging optoelectronics, photonics, energy harvesting, and quantum technology applications. However, the investigation and direct visualization of such nonequilibrium phenomena remains as a long-standing challenge, owing to the nanometer-femtosecond spatiotemporal scales at which the charge carriers evolve. Here, we propose and demonstrate an interaction mechanism enabling nanoscale imaging of the femtosecond dynamics of charge carriers in solids. This imaging modality, which we name charge dynamics electron microscopy (CDEM), exploits the strong interaction of free-electron pulses with terahertz (THz) near fields produced by the moving charges in an ultrafast scanning transmission electron microscope. The measured free-electron energy at different spatiotemporal coordinates allows us to directly retrieve the THz near-field amplitude and phase, from which we reconstruct movies of the generated charges by comparison to microscopic theory. The CDEM technique thus allows us to investigate previously inaccessible spatiotemporal regimes of charge dynamics in solids, providing insight into the photo-Dember effect and showing oscillations of photogenerated electron-hole distributions inside a semiconductor. Our work facilitates the exploration of a wide range of previously inaccessible charge-transport phenomena in condensed matter using ultrafast electron microscopy.

Development of five-dimensional scanning transmission electron microscopy

By combining the scanning transmission electron microscopy with the ultrafast optical pump-probe technique, we improved the time resolution by a factor of ∼10¹² for the differential phase contrast and convergent-beam electron diffraction imaging. These methods provide ultrafast nanoscale movies of physical quantities in nano-materials, such as crystal lattice deformation, magnetization vector, and electric field. We demonstrate the observations of the photo-induced acoustic phonon propagation with an accuracy of 4 ps and 8 nm and the ultrafast demagnetization under zero magnetic field with 10 ns and 400 nm resolution, by utilizing these methods.

Reliable determination of pulse-shape instability in trains of ultrashort laser pulses using frequency-resolved optical gating

We describe a reliable approach for determining the presence of pulse-shape instability in a train of ultrashort laser pulses. While frequency-resolved optical gating (FROG) has been shown to successfully perform this task by displaying a discrepancy between the measured and retrieved traces for unstable trains, it fails if its pulse-retrieval algorithm stagnates because algorithm stagnation and pulse-shape instability can be indistinguishable. So, a non-stagnating algorithm-even in the presence of instability-is required. The recently introduced Retrieved-Amplitude N-grid Algorithmic (RANA) approach has achieved extremely reliable (100%) pulse-retrieval in FROG for trains of stable pulse shapes, even in the presence of noise, and so is a promising candidate for an algorithm that can definitively distinguish stable and unstable pulse-shape trains. But it has not yet been considered for trains of pulses with pulse-shape instability. So, here, we investigate its performance for unstable trains of pulses with random pulse shapes. We consider trains of complex pulses measured by second-harmonic-generation FROG using the RANA approach and compare its performance to the well-known generalized-projections (GP) algorithm without the RANA enhancements. We show that the standard GP algorithm frequently fails to converge for such unstable pulse trains, yielding highly variable trace discrepancies. As a result, it is an unreliable indicator of instability. Using the RANA approach, on the other hand, we find zero stagnations, even for highly unstable pulse trains, and we conclude that FROG, coupled with the RANA approach, provides a highly reliable indicator of pulse-shape instability. It also provides a typical pulse length, spectral width, and time-bandwidth product, even in cases of instability.

Dephasing Dynamics across Different Local Vibrational Modes and Crystalline Environments

The perturbed free induction decay (PFID) observed in ultrafast infrared spectroscopy was used to unveil the rates at which different vibrational modes of the same atomic-scale defect can interact with their environment. The N_{3}VH^{0} defect in diamond provided a model system, allowing a comparison of stretch and bend vibrational modes within different crystal lattice environments. The observed bend mode (first overtone) exhibited dephasing times T_{2}=2.8(1)  ps, while the fundamental stretch mode had surprisingly faster dynamics T_{2}<1.7  ps driven by its more direct perturbation of the crystal lattice, with increased phonon coupling. Further, at high defect concentrations the stretch mode's dephasing rate was enhanced. The ability to reliably measure T_{2} via PFID provides vital insights into how vibrational systems interact with their local environment.

Controlling Floquet states on ultrashort time scales

The advent of ultrafast laser science offers the unique opportunity to combine Floquet engineering with extreme time resolution, further pushing the optical control of matter into the petahertz domain. However, what is the shortest driving pulse for which Floquet states can be realised remains an unsolved matter, thus limiting the application of Floquet theory to pulses composed by many optical cycles. Here we ionized Ne atoms with few-femtosecond pulses of selected time duration and show that a Floquet state can be observed already with a driving field that lasts for only 10 cycles. For shorter pulses, down to 2 cycles, the finite lifetime of the driven state can still be explained using an analytical model based on Floquet theory. By demonstrating that the amplitude and number of Floquet-like sidebands in the photoelectron spectrum can be controlled not only with the driving laser pulse intensity and frequency, but also by its duration, our results add a new lever to the toolbox of Floquet engineering.

Eigenstate Thermalization Hypothesis and Free Probability

Quantum thermalization is well understood via the eigenstate thermalization hypothesis (ETH). The general form of ETH, describing all the relevant correlations of matrix elements, may be derived on the basis of a "typicality" argument of invariance with respect to local rotations involving nearby energy levels. In this Letter, we uncover the close relation between this perspective on ETH and free probability theory, as applied to a thermal ensemble or an energy shell. This mathematical framework allows one to reduce in a straightforward way higher-order correlation functions to a decomposition given by minimal blocks, identified as free cumulants, for which we give an explicit formula. This perspective naturally incorporates the consistency property that local functions of ETH operators also satisfy ETH. The present results uncover a direct connection between the eigenstate thermalization hypothesis and the structure of free probability, widening considerably the latter's scope and highlighting its relevance to quantum thermalization.

X-ray pulse generation with ultra-fast flipping of its orbital angular momentum

A method to temporally tailor the properties of X-ray radiation carrying Orbital Angular Momentum (OAM) is presented. In simulations, an electron beam is prepared with a temporally modulated micro-bunching structure which, when radiating at the second harmonic in a helical undulator, generates OAM light with a corresponding temporally modulated intensity. This method is shown to generate attosecond pulse trains of OAM light without the need for any additional external optics, making the wavelength range tunable. In addition to the OAM pulse train, the method can be adapted to generate radiation where the handedness of the OAM mode may also be temporally modulated (flipped).

A perspective on ab initio modeling of polaritonic chemistry: The role of non-equilibrium effects and quantum collectivity

This Perspective provides a brief introduction into the theoretical complexity of polaritonic chemistry, which emerges from the hybrid nature of strongly coupled light-matter states. To tackle this complexity, the importance of ab initio methods is highlighted. Based on those, novel ideas and research avenues are developed with respect to quantum collectivity, as well as for resonance phenomena immanent in reaction rates under vibrational strong coupling. Indeed, fundamental theoretical questions arise about the mesoscopic scale of quantum-collectively coupled molecules when considering the depolarization shift in the interpretation of experimental data. Furthermore, to rationalize recent findings based on quantum electrodynamical density-functional theory (QEDFT), a simple, but computationally efficient, Langevin framework is proposed based on well-established methods from molecular dynamics. It suggests the emergence of cavity-induced non-equilibrium nuclear dynamics, where thermal (stochastic) resonance phenomena could emerge in the absence of external periodic driving. Overall, we believe that the latest ab initio results indeed suggest a paradigmatic shift for ground-state chemical reactions under vibrational strong coupling from the collective quantum interpretation toward a more local, (semi)-classically and non-equilibrium dominated perspective. Finally, various extensions toward a refined description of cavity-modified chemistry are introduced in the context of QEDFT, and future directions of the field are sketched.

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method, in general, only captures the ultrashort time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

Spatio-spectral couplings in saturated collinear OPCPA

Ultrafast laser pulses featuring both high spatio-temporal beam quality and excellent energy stability are crucial for many applications. Here, we present a seed laser with high beam quality and energy stability, based on a collinear optical parametric chirped pulse amplification (OPCPA) stage, delivering 46 µJ pulses with a 25 fs Fourier limit at 1 kHz repetition rate. While saturation of the OPCPA stage is necessary for achieving the highest possible energy stability, it also leads to a degradation of the beam quality. Using simulations, we show that spectrally dependent, rotationally symmetric aberrations dominate the collinear OPCPA in saturation. We experimentally characterize these aberrations and then remove distinct spatial frequencies to greatly improve the spectral homogeneity of the beam quality, while keeping an excellent energy stability of 0.2 % rms measured over 70 hours.

Light-Tunable Charge Density Wave Orders in MoTe_{2} and WTe_{2} Single Layers

By using constrained density functional theory modeling, we demonstrate that ultrafast optical pumping unveils hidden charge orders in group VI monolayer transition metal ditellurides. We show that irradiation of the insulating 2H phases stabilizes multiple transient charge density wave orders with light-tunable distortion, periodicity, electronic structure, and band gap. Moreover, optical pumping of the semimetallic 1T^{'} phases generates a transient charge ordered metallic phase composed of 2D diamond clusters. For each transient phase we identify the critical fluence at which it is observed and the specific optical and Raman fingerprints to directly compare with future ultrafast pump-probe experiments. Our work demonstrates that it is possible to stabilize charge density waves even in insulating 2D transition metal dichalcogenides by ultrafast irradiation.