Multidimensional high-harmonic echo spectroscopy: Resolving coherent electron dynamics in the EUV regime.

We theoretically propose a multidimensional high-harmonic echo spectroscopy technique which utilizes strong optical fields to resolve coherent electron dynamics spanning an energy range of multiple electronvolts. Using our recently developed semi-perturbative approach, we can describe the coherent valence electron dynamics driven by a sequence of phase-matched and well-separated short few-cycle strong infrared laser pulses. The recombination of tunnel-ionized electrons by each pulse coherently populates the valence states of a molecule, which allows for a direct observation of its dynamics via the high harmonic echo signal. The broad bandwidth of the effective dipole between valence states originated from the strong-field excitation results in nontrivial ultra-delayed partial rephasing echo, which is not observed in standard two-dimensional optical spectroscopic techniques in a two-level molecular systems. We demonstrate the results of simulations for the anionic molecular system and show that the ultrafast valence electron dynamics can be well captured with femtosecond resolution.

Dephasing Dynamics Accessed by High Harmonic Generation: Determination of Electron-Hole Decoherence of Dirac Fermions.

We reveal the critical effect of ultrashort dephasing on the polarization of high harmonic generation in Dirac fermions. As the elliptically polarized laser pulse falls in or slightly beyond the multiphoton regime, the elliptically polarized high harmonic generation is produced and exhibits a characteristic polarimetry of the polarization ellipse, which is found to depend on the decoherence time T2. T2 could then be determined to be a few femtoseconds directly from the experimentally observed polarimetry of high harmonics. This shows a sharp contrast with the semimetal regime of higher pump intensity, where the polarimetry is irrelevant to T2. An access to the dephasing dynamics would extend the prospect of high harmonic generation into the metrology of a femtosecond dynamic process in the coherent quantum control.

High harmonic generation in solids: particle and wave perspectives.

High harmonic generation (HHG) from gas-phase atoms (or molecules) has opened up a new frontier in ultrafast optics, where attosecond time resolution and angstrom spatial resolution are accessible. The fundamental physical pictures of HHG are always explained by the laser-induced recollision of particle-like electron motion, which lay the foundation of attosecond spectroscopy. In recent years, HHG has also been observed in solids. One can expect the extension of attosecond spectroscopy to the condensed matter if a description capable of resolving the ultrafast dynamics is provided. Thus, a large number of theoretical studies have been proposed to understand the underlying physics of solid HHG. Here, we revisit the recollision picture in solid HHG and show some challenges of current particle-perspective methods, and present the recently developed wave-perspective Huygens-Fresnel picture for understanding dynamical systems within the ambit of strong-field physics.

Strong-laser-field physics, non-classical light states and quantum information science.

Strong-laser-field physics is a research direction that relies on the use of high-power lasers and has led to fascinating achievements ranging from relativistic particle acceleration to attosecond science. On the other hand, quantum optics has been built on the use of low photon number sources and has opened the way for groundbreaking discoveries in quantum technology, advancing investigations ranging from fundamental tests of quantum theory to quantum information processing. Despite the tremendous progress, until recently these directions have remained disconnected. This is because the majority of the interactions in the strong-field limit have been successfully described by semi-classical approximations treating the electromagnetic field classically, as there was no need to include the quantum properties of the field to explain the observations. The link between strong-laser-field physics, quantum optics, and quantum information science has been developed in the recent past. Studies based on fully quantized and conditioning approaches have shown that intense laser-matter interactions can be used for the generation of controllable entangled and non-classical light states. These achievements open the way for a vast number of investigations stemming from the symbiosis of strong-laser-field physics, quantum optics, and quantum information science. Here, after an introduction to the fundamentals of these research directions, we report on the recent progress in the fully quantized description of intense laser-matter interaction and the methods that have been developed for the generation of non-classical light states and entangled states. Also, we discuss the future directions of non-classical light engineering using strong laser fields, and the potential applications in ultrafast and quantum information science.

Detecting electronic coherences by time-domain high-harmonic spectroscopy.

Ultrafast spectroscopy is capable of monitoring electronic and vibrational states. For electronic states a few eV apart, an X-ray laser source is required. We propose an alternative method based on the time-domain high-order harmonic spectroscopy where a coherent superposition of the electronic states is first prepared by the strong optical laser pulse. The coherent dynamics can then be probed by the higher-order harmonics generated by the delayed probe pulse. The high nonlinearity typically modeled by the three-step mechanism introduced by Lewenstein and Corkum can serve as a recipe for generation of the coherent excitation with broad bandwidth. The main advantage of the method is that only optical (non-X-ray) lasers are needed. A semiperturbative model based on the Liouville space superoperator approach is developed for the bookkeeping of the different orders of the nonlinear response for the high-order harmonic generation using multiple pulses. Coherence between bound electronic states is monitored in the harmonic spectra from both first- and second-order responses.

Optical Control of High-Harmonic Generation at the Atomic Thickness.

High-harmonic generation (HHG), an extreme nonlinear optical phenomenon beyond the perturbation regime, is of great significance for various potential applications, such as high-energy ultrashort pulse generation with outstanding spatiotemporal coherence. However, efficient active control of HHG is still challenging due to the weak light-matter interaction displayed by currently known materials. Here, we demonstrate optically controlled HHG in monolayer semiconductors via the engineering of interband polarization. We find that HHG can be efficiently controlled in the excitonic spectral region with modulation depths up to 95% and ultrafast response speeds of several picoseconds. Quantitative time-domain theory of the nonlinear optical susceptibilities in monolayer semiconductors further corroborates these experimental observations. Our demonstration not only offers an in-depth understanding of HHG but also provides an effective approach toward active optical devices for strong-field physics and extreme nonlinear optics.

Generating coherent and ultrashort X-ray pulses via HHG-seeding in storage rings.

The generation of fully coherent and femtosecond time-scale radiation pulses in the X-ray regime is one of the most common demands of ring-based synchrotron light source users. In this paper, a method that utilizes the recent proposed angular dispersion induced microbunching technique to convert external light from high-harmonic generation (HHG) to coherent light at shorter wavelength is proposed. Numerical simulations using the practical parameters of a diffraction-limited storage ring demonstrate the generation of coherent pulse trains with photon energy as high as 2 keV, pulse duration as short as ∼10 fs and high peak brightness directly from an HHG source at 13 nm.

Ground-State Photoelectron Circular Dichroism of Methyl p-Tolyl Sulfoxide by Single-Photon Ionisation from a Table-Top Source.

Single-photon ionisation of enantiopure methyl p-tolyl sulfoxide by circularly polarised light at 133 nm shows remarkably strong photoelectron circular dichroism (PECD), which has been measured in a velocity-map-imaging spectrometer. Both enantiomers were measured, each showing a PECD of a similar magnitude (ca. 25 %). These experiments were carried out with a tabletop high-harmonic source with a photon energy of 9.3 eV, capable of ionising the electronic ground state of most organic and inorganic molecules. Ab-initio scattering calculations provide a theoretical value of the expected chiral asymmetry parameter, and agree very well with the measured values once orbital mixing via configuration interaction in the cation is taken into account. This study demonstrates a simple photoionisation scheme that can be readily applied to study the time-resolved PECD of photochemical reactions and suggests a pronounced sensitivity of PECD to electronic configuration interaction in the cation.

Real-time probing of chirality during a chemical reaction.

Chiral molecules interact and react differently with other chiral objects, depending on their handedness. Therefore, it is essential to understand and ultimately control the evolution of molecular chirality during chemical reactions. Although highly sophisticated techniques for the controlled synthesis of chiral molecules have been developed, the observation of chirality on the natural femtosecond time scale of a chemical reaction has so far remained out of reach in the gas phase. Here, we demonstrate a general experimental technique, based on high-harmonic generation in tailored laser fields, and apply it to probe the time evolution of molecular chirality during the photodissociation of 2-iodobutane. These measurements show a change in sign and a pronounced increase in the magnitude of the chiral response over the first 100 fs, followed by its decay within less than 500 fs, revealing the photodissociation to achiral products. The observed time evolution is explained in terms of the variation of the electric and magnetic transition-dipole moments between the lowest electronic states of the cation as a function of the reaction coordinate. These results open the path to investigations of the chirality of molecular-reaction pathways, light-induced chirality in chemical processes, and the control of molecular chirality through tailored laser pulses.

Monitoring Argon L-Shell Auger Decay Using 250-eV Attosecond X-ray Pulses.

Electron correlation describes the interaction between electrons in a multi-electron system. It plays an important role in determining the speed of relaxation of atoms and molecules excited by XUV/X-ray pulses, such as the argon decay rate. Most research on electron correlation has centered on the role of correlation in stationary states. A time-resolved experimental study of electron correlation is a grand challenge due to the required temporal resolution and photon energy. In this research, we investigated Auger decay in argon using 200-attosecond X-ray pulses reaching the carbon K-edge. At such a high photon energy, ionization occurs not only from the outer most levels (3s and 3p), but also from the 2p core shells. We have measured a lifetime of 4.9 fs of L-shell vacancies of argon in pump-probe experiments with a home-built high-resolution time-of-flight spectrometer.

All-Optical Probe of Three-Dimensional Topological Insulators Based on High-Harmonic Generation by Circularly Polarized Laser Fields.

We report the observation of an anomalous nonlinear optical response of the prototypical three-dimensional topological insulator bismuth selenide through the process of high-order harmonic generation. We find that the generation efficiency increases as the laser polarization is changed from linear to elliptical, and it becomes maximum for circular polarization. With the aid of a microscopic theory and a detailed analysis of the measured spectra, we reveal that such anomalous enhancement encodes the characteristic topology of the band structure that originates from the interplay of strong spin-orbit coupling and time-reversal symmetry protection. The implications are in ultrafast probing of topological phase transitions, light-field driven dissipationless electronics, and quantum computation.

Control of High-Harmonic Generation by Tuning the Electronic Structure and Carrier Injection.

High-harmonic generation (HHG), which is the generation of light with multiple optical harmonics, is an unconventional nonlinear optical phenomenon beyond the perturbation regime. HHG, which was initially observed in gaseous media, has recently been demonstrated in solid-state materials. Determining how to control such extreme nonlinear optical phenomena is a challenging subject. Here, we demonstrate the control of HHG through tuning the electronic structure and carrier injection using single-walled carbon nanotubes (SWCNTs). We reveal systematic changes in the high-harmonic spectra of SWCNTs with a series of electronic structures ranging from a metal structure to a semiconductor structure. We demonstrate enhancement or reduction of harmonic generation by more than 1 order of magnitude by tuning the electron and hole injection into the semiconductor SWCNTs through electrolyte gating. These results open a path toward the control of HHG in the context of field-effect transistor devices.

Distinguishing attosecond electron-electron scattering and screening in transition metals.

Electron-electron interactions are the fastest processes in materials, occurring on femtosecond to attosecond timescales, depending on the electronic band structure of the material and the excitation energy. Such interactions can play a dominant role in light-induced processes such as nano-enhanced plasmonics and catalysis, light harvesting, or phase transitions. However, to date it has not been possible to experimentally distinguish fundamental electron interactions such as scattering and screening. Here, we use sequences of attosecond pulses to directly measure electron-electron interactions in different bands of different materials with both simple and complex Fermi surfaces. By extracting the time delays associated with photoemission we show that the lifetime of photoelectrons from the d band of Cu are longer by ∼100 as compared with those from the same band of Ni. We attribute this to the enhanced electron-electron scattering in the unfilled d band of Ni. Using theoretical modeling, we can extract the contributions of electron-electron scattering and screening in different bands of different materials with both simple and complex Fermi surfaces. Our results also show that screening influences high-energy photoelectrons (≈20 eV) significantly less than low-energy photoelectrons. As a result, high-energy photoelectrons can serve as a direct probe of spin-dependent electron-electron scattering by neglecting screening. This can then be applied to quantifying the contribution of electron interactions and screening to low-energy excitations near the Fermi level. The information derived here provides valuable and unique information for a host of quantum materials.

Attosecond soft X-ray high harmonic generation.

High harmonic generation (HHG) of an intense laser pulse is a highly nonlinear optical phenomenon that provides the only proven source of tabletop attosecond pulses, and it is the key technology in attosecond science. Recent developments in high-intensity infrared lasers have extended HHG beyond its traditional domain of the XUV spectral range (10-150 eV) into the soft X-ray regime (150 eV to 3 keV), allowing the compactness, stability and sub-femtosecond duration of HHG to be combined with the atomic site specificity and electronic/structural sensitivity of X-ray spectroscopy. HHG in the soft X-ray spectral region has significant differences from HHG in the XUV, which necessitate new approaches to generating and characterizing attosecond pulses. Here, we examine the challenges and opportunities of soft X-ray HHG, and we use simulations to examine the optimal generating conditions for the development of high-flux, attosecond-duration pulses in the soft X-ray spectral range. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

A new regime of nanoscale thermal transport: Collective diffusion increases dissipation efficiency.

Understanding thermal transport from nanoscale heat sources is important for a fundamental description of energy flow in materials, as well as for many technological applications including thermal management in nanoelectronics and optoelectronics, thermoelectric devices, nanoenhanced photovoltaics, and nanoparticle-mediated thermal therapies. Thermal transport at the nanoscale is fundamentally different from that at the macroscale and is determined by the distribution of carrier mean free paths and energy dispersion in a material, the length scales of the heat sources, and the distance over which heat is transported. Past work has shown that Fourier's law for heat conduction dramatically overpredicts the rate of heat dissipation from heat sources with dimensions smaller than the mean free path of the dominant heat-carrying phonons. In this work, we uncover a new regime of nanoscale thermal transport that dominates when the separation between nanoscale heat sources is small compared with the dominant phonon mean free paths. Surprisingly, the interaction of phonons originating from neighboring heat sources enables more efficient diffusive-like heat dissipation, even from nanoscale heat sources much smaller than the dominant phonon mean free paths. This finding suggests that thermal management in nanoscale systems including integrated circuits might not be as challenging as previously projected. Finally, we demonstrate a unique capability to extract differential conductivity as a function of phonon mean free path in materials, allowing the first (to our knowledge) experimental validation of predictions from the recently developed first-principles calculations.

Perspectives of Attosecond Spectroscopy for the Understanding of Fundamental Electron Correlations.

The description of the electronic structure of molecules in terms of molecular orbitals is a highly successful concept in chemistry. However, it commonly fails if the electrons in a molecule are strongly correlated and cannot be treated as independent particles. Electron correlation is essential to understand inner-valence X-ray spectroscopies, it can drive ultrafast charge migration in molecules, and it is responsible for many exotic properties of strongly correlated materials. Time-resolved spectroscopy with attosecond resolution is generally capable of following electronic motion in real time and can thus provide experimental access to electron-correlation-driven phenomena. High-harmonic spectroscopy in particular uses the precisely timed laser-driven recollision of electrons to interrogate the electronic structure and dynamics of the investigated system on a sub-femtosecond timescale. In this Review, the capabilities of high-harmonic spectroscopy to follow electronic motion in molecules are discussed. Both qualitative and quantitative approaches to unraveling the detailed dynamical responses of molecular systems following ionization are presented. A new theoretical formalism for the reconstruction of correlation-driven charge migration is introduced. The importance of electron-ion entanglement and electronic coherence in the reconstruction of attosecond hole dynamics are discussed. These advances make high-harmonic spectroscopy a promising technique to decode fundamental electron correlations and to provide experimental data on the complex manifestations of multi-electron dynamics.

Real-Time Probing of Electron Dynamics Using Attosecond Time-Resolved Spectroscopy.

Attosecond science has paved the way for direct probing of electron dynamics in gases and solids. This review provides an overview of recent attosecond measurements, focusing on the wealth of knowledge obtained by the application of isolated attosecond pulses in studying dynamics in gases and solid-state systems. Attosecond photoelectron and photoion measurements in atoms reveal strong-field tunneling ionization and a delay in the photoemission from different electronic states. These measurements applied to molecules have shed light on ultrafast intramolecular charge migration. Similar approaches are used to understand photoemission processes from core and delocalized electronic states in metal surfaces. Attosecond transient absorption spectroscopy is used to follow the real-time motion of valence electrons and to measure the lifetimes of autoionizing channels in atoms. In solids, it provides the first measurements of bulk electron dynamics, revealing important phenomena such as the timescales governing the switching from an insulator to a metallic state and carrier-carrier interactions.

Molecular interferometer to decode attosecond electron-nuclear dynamics.

Understanding the coupled electronic and nuclear dynamics in molecules by using pump-probe schemes requires not only the use of short enough laser pulses but also wavelengths and intensities that do not modify the intrinsic behavior of the system. In this respect, extreme UV pulses of few-femtosecond and attosecond durations have been recognized as the ideal tool because their short wavelengths ensure a negligible distortion of the molecular potential. In this work, we propose the use of two twin extreme UV pulses to create a molecular interferometer from direct and sequential two-photon ionization processes that leave the molecule in the same final state. We theoretically demonstrate that such a scheme allows for a complete identification of both electronic and nuclear phases in the wave packet generated by the pump pulse. We also show that although total ionization yields reveal entangled electronic and nuclear dynamics in the bound states, doubly differential yields (differential in both electronic and nuclear energies) exhibit in addition the dynamics of autoionization, i.e., of electron correlation in the ionization continuum. Visualization of such dynamics is possible by varying the time delay between the pump and the probe pulses.

Quantitative Chemically Specific Coherent Diffractive Imaging of Reactions at Buried Interfaces with Few Nanometer Precision.

We demonstrate quantitative, chemically specific imaging of buried nanostructures, including oxidation and diffusion reactions at buried interfaces, using nondestructive tabletop extreme ultraviolet (EUV) coherent diffractive imaging (CDI). Copper nanostructures inlaid in SiO2 are coated with 100 nm of aluminum, which is opaque to visible light and thick enough that neither visible microscopy nor atomic force microscopy can image the buried interface. Short wavelength high harmonic beams can penetrate the aluminum layer, yielding high-contrast images of the buried structures. Quantitative analysis shows that the reflected EUV light is extremely sensitive to the formation of multiple oxide layers, as well as interdiffusion of materials occurring at the metal-metal and metal-insulator boundaries deep within the nanostructure with few nanometers precision.

Charge carrier dynamics of photoexcited Co3O4 in methanol: extending high harmonic transient absorption spectroscopy to liquid environments.

Charge carrier dynamics in Co3O4 thin films are observed using high harmonic generation transient absorption spectroscopy at the Co M2,3 edge. Results reveal that photoexcited Co3O4 decays to the ground state in 600 ± 40 ps in liquid methanol compared to 1.9 ± 0.3 ns in vacuum. Kinetic analysis suggests that surface-mediated relaxation of photoexcited Co3O4 may be the result of hole transfer from Co3O4 followed by carrier recombination at the Co3O4-methanol interface.