Focus on Correlation Effects in Radiation Fields

Many processes in nature are governed by the interaction of electro-magnetic radiation with matter. New tools such as femtosecond and free-electron lasers allow one to study the interaction in unprecedented detail with high temporal and spatial resolution. In addition, much work is devoted to the exploration of novel target systems that couple to radiation in an effective and controllable way or that could serve as efficient sources of energetic particles when being subjected to intense laser fields. The interaction between matter and radiation fields as well as their mutual modification via correlations constitutes a rich field of research that is impossible to cover exhaustively. The papers in this focus issue represent a selection that largely reflects the program of the international conference on 'Correlation Effects in Radiation Fields' held in 2011 in Rostock, Germany.

Magnesium atoms embedded in superfluid helium nanodroplets have been identified to arrange themselves in a metastable network, referred to as foam. In order to investigate the ionization dynamics of this unique structure with respect to a possible light-induced collapse, the femtosecond dual-pulse spectroscopy technique is applied. Around zero optical delay a strong feature is obtained which represents a direct probe of the foam response. We found that upon collapse, ionization is reduced. A particular intensity ratio of the pulses allows us to address either direct ionization or photoactivation of the neutral complexes, thus affecting reaction pathways. A simplified scheme visualizes possible excitation scenarios in accordance with the experimental observations.

Collective excitations in nano-plasmas are described by dynamical bi-local auto-correlation functions. These excitations, which are related to the plasmon excitations in bulk plasmas, arise in the classical as well as the quantum regime. Instead of the wave-vector-dependent dynamical structure factor, which is not well defined in finite systems, two different signatures are considered to characterize collective excitations: the bi-local particle density correlation function and the bi-local current density correlation function. The relation between both signatures is not as trivial as in the homogeneous case and is given here. Exemplary calculations are performed for expanding nearly spherical clusters of sodium atoms after excitation by a high-intensity short pulse laser beam. The lowest collective excitations obtained in the classical regime using molecular dynamics simulations agree well with the lowest collective excitations obtained from quantum calculations using fluid dynamics. The energy, damping and structure of the lowest collective modes are given. The dynamical bi-local correlation functions are of relevance for the optical properties, in particular the determination of photo absorption coefficients of nano-plasmas.

During the coherent diffraction imaging (CDI) of a single object with an intense x-ray free-electron laser (FEL) pulse, the structure of the object changes due to the progressing radiation damage. Electrons are released from atoms and ions during photo-, Auger- and collisional ionization processes. More and more ions appear in the sample. The repulsive force between ions makes them move apart. Form factors of the created ions are reduced when compared with the atomic form factors. Additional scattering of energetic photons from the free electrons confined within the beam focus deteriorates the obtained diffractive signal. Here, we consider pulses short enough to neglect ionic movement and investigate how (i) the decrease of atomic form factors due to the progressing ionization of the sample and (ii) the scattering from the free electrons influence the signal obtained during the CDI. We quantify the loss of structural information about the object due to these effects with hydrodynamic simulations. Our study has implications for the experiments planned on high-resolution three-dimensional imaging of single reproducible particles with x-ray FELs.

We present a theoretical quasi-classical study of the formation, during Coulomb explosion, of two highly excited neutral H atoms (double H*) of strongly driven H₂. In this process, after the laser field is turned off each electron occupies a Rydberg state of an H atom. We identify the route for forming two H* atoms and show that two-electron effects are important. We also find that both ionization steps are 'frustrated' in double H* formation, whereas only one ionization step is 'frustrated' for both the routes leading to single H* formation, as was shown by Emmanouilidou et al (2012 Phys. Rev. A 85 011402). Moreover, we compute the screened nuclear charge that drives the explosion of the nuclei during double H* formation.

Modifications of photoionization arising from resonant electron–electron correlations between neighbouring atoms in an atomic sample are studied. The sample contains atomic species A and B, with the ionization potential of A being smaller than the energy of a dipole-allowed transition in B. The atoms are subject to an external radiation field which is near resonant with the dipole transition in B. Photoionization of an atom A may thus proceed via a two-step mechanism: photoexcitation in the subsystem of species B, followed by interatomic Coulombic decay. As a basic atomic configuration, we investigate resonant photoionization in a three-atomic system A–B–B consisting of an atom A and two neighbouring atoms B. It is found that, under suitable conditions, the presence of neighbouring atoms can strongly affect the photoionization process, including its total probability, time development and photoelectron spectra. In particular, comparing our results with those for photoionization of an isolated atom A and a two-atomic system A–B, respectively, we reveal the characteristic impact made by the third atom.

The size-dependent exciton dynamics of one-dimensional aggregates of substituted perylene bisimides are studied by ultrafast transient absorption spectroscopy and kinetic Monte-Carlo simulations as a function of the excitation density and the temperature in the range of 25–90 °C. For low temperatures, the aggregates can be treated as infinite chains and the dynamics is dominated by diffusion-driven exciton–exciton annihilation. With increasing temperature the aggregates dissociate into small fragments consisting of very few monomers. This scenario is also supported by the time-dependent anisotropy deduced from polarization-dependent experiments.

Three imidazolium-based ionic liquids of the type [C_nmim][NTf₂] with different alkyl chain lengths (n = 1, 2 and 8) at the first position of the imidazolium ring were studied applying infrared, linear Raman and multiplex coherent anti-Stokes Raman scattering spectroscopy. The focus has been on the CH-stretching region of the imidazolium ring, which is supposed to carry information about a possible hydrogen bonding network in the ionic liquid. The measurements are compared with calculations of the corresponding anharmonic vibrational spectra for a cluster of [C₂mim][NTf₂] consisting of four ion pairs. The results support the hypothesis of weak hydrogen bonding involving the C(4)–H and C(5)–H groups and somewhat stronger hydrogen bonds of the C(2)–H groups.

Atoms, molecules or excitonic quasiparticles, for which excitations are induced by external radiation fields and energy is dissipated through radiative decay, are examples of driven open quantum systems. We explain the use of commutator-free exponential time propagators for the numerical solution of the associated Schrödinger or master equations with a time-dependent Hamilton operator. These time propagators are based on the Magnus series but avoid the computation of commutators, which makes them suitable for the efficient propagation of systems with a large number of degrees of freedom. We present an optimized fourth-order propagator and demonstrate its efficiency in comparison to the direct Runge–Kutta computation. As an illustrative example we consider the parametrically driven dissipative Dicke model, for which we calculate the periodic steady state and the optical emission spectrum.

We present experiments on the luminescence of excitons confined in a potential trap at milli-Kelvin bath temperatures under continuous-wave (cw) excitation. They reveal several distinct features like a kink in the dependence of the total integrated luminescence intensity on excitation laser power and a bimodal distribution of the spatially resolved luminescence. Furthermore, we discuss the present state of the theoretical description of Bose–Einstein condensation of excitons with respect to signatures of a condensate in the luminescence. The comparison of the experimental data with theoretical results with respect to the spatially resolved as well as the integrated luminescence intensity shows the necessity of taking into account a Bose–Einstein condensed excitonic phase in order to understand the behaviour of the trapped excitons.

There are two types of two-photon transitions in molecular aggregates: non-local excitations of two monomers and local double excitations to some higher excited intra-monomer electronic state. As a consequence of the inter-monomer Coulomb interaction, these different excitation states are coupled to each other. Higher excited intra-monomer states are rather short-lived owing to the efficient internal conversion of electronic into vibrational energy. Combining both the processes leads to annihilation of an electronic excitation state, which is a major loss channel for establishing high excitation densities in molecular aggregates. Applying theoretical pulse optimization techniques to a Frenkel exciton model, it is shown that the dynamics of two-exciton states in linear aggregates (dimer to tetramer) can be influenced by ultrafast-shaped laser pulses. In particular, we studied the extent to which the decay of the two-exciton population by inter-band transitions can be transiently suppressed. Intra-band dynamics is described by a dissipative hierarchy equation approach, which takes into account strong exciton–vibrational coupling in the non-Markovian regime.

By solving the two-active-electron, time-dependent Schrödinger equation in its full dimensionality, we investigate the carrier-envelope phase (CEP) dependence of single ionization of He to the He⁺(1s) state triggered by an intense few-cycle attosecond pulse with carrier frequency ω corresponding to the energy ℏω = 36 eV. Effects of electron correlations are probed by comparing projections of the final state of the two-electron wave packet onto field-free highly correlated Jacobi matrix wave functions with projections onto uncorrelated Coulomb wave functions. Significant differences are found in the vicinity of autoionizing resonances. Owing to the broad bandwidths of our 115 and 230 as pulses and their high intensities (1–2 PW cm⁻²), asymmetries are found in the differential probability for ionization of electrons parallel and antiparallel to the linear polarization axis of the laser pulse. These asymmetries stem from interference of the one- and two-photon ionization amplitudes for producing electrons with the same momentum along the linear polarization axis. Whereas these asymmetries generally decrease with increasing ionized electron kinetic energy, we find a large enhancement of the asymmetry in the vicinity of two-electron doubly excited (autoionizing) states on an energy scale comparable to the widths of the autoionizing states. The CEP dependence of the energy-integrated asymmetry agrees very well with the predictions of time-dependent perturbation theory (Pronin et al 2009 Phys. Rev. A 80 063403).

We investigate the breakup of bound electron–hole pairs, known as Mott transition of excitons, in GaAs-GaAlAs quantum wells with increasing excitation, comparing two different theoretical approaches. Firstly, a thermodynamic approach is used to investigate the ionization equilibrium between electrons, holes and excitons, where the abrupt jump of the degree of ionization from 0 to 1 indicates the Mott density. It is extended to a self-consistent quasi-particle approximation (QPA) for the carrier properties, including dynamical screening of the Coulomb interaction between carriers. Secondly, a spectral approach based on the semiconductor Bloch equations within linear optical response is used, considering the quasi-particle (QP) properties of carriers and the dynamical screening between electron–hole pairs. While the first is effectively a one-particle approach, in the second the whole two-particle spectrum is analyzed. Within the thermodynamic approach, a simple criterion for the Mott transition can be given: namely, if the sum of chemical potentials of carriers, reflecting the effective shrinkage of the band edge, crosses the exciton energy with increasing excitation. We demonstrate that this simple picture cannot be maintained in the two-particle approach. Here, a compact quantity, which describes the behavior of the band edge, does not exist. In fact, the behavior of the single states in the spectrum is generated by the interplay of dynamical screening in the interband self-energy and the effective interaction of the electron–hole pairs. Moreover, the band edge cannot be clearly resolved, since it is merged with excited exciton states (e.g. 2s state), which show up only for densities far below the Mott density. Instead of a Mott density, only a density range can be given, where the Mott transition appears. We demonstrate that a small damping as a prerequisite for the validation of the extended QPA in the thermodynamic approach breaks down, analyzing (i) the dephasing processes with increasing excitation, (ii) the strong increase of the excitonic linewidth and (iii) comparing with the lifetime of carriers in the QP description.

The interaction between super-intense coherent x-ray light and nuclei is studied theoretically. One of the main difficulties in driving nuclear transitions arises from the very narrow nuclear excited state widths, which limit the coupling between lasers and nuclei. In the context of direct laser–nucleus interaction, we consider the nuclear width broadening that occurs when in solid targets, when the excitation caused by a single photon is shared by a large number of nuclei, forming a collective excited state. Our results show that cooperative effects mostly contribute with a modest increase to the nuclear excited state population except in the case of ⁵⁷Fe, where the enhancement can reach almost two orders of magnitude. Additionally, an update is given of previous estimates of the nuclear excited state population and signal photons for x-ray lasers interacting with solid-state and ion beam nuclear targets taking into account the experimental advances of x-ray coherent light sources. The presented values are an improvement by orders of magnitude and are encouraging as to the future prospects of nuclear quantum optics.

The nanoplasmonic field enhancement effects in the energetic electron emission from few-nm-sized silver clusters exposed to intense femtosecond dual pulses are investigated by high-resolution double differential electron spectroscopy. For moderate laser intensities of 10¹⁴ W cm⁻², the delay-dependent and angular-resolved electron spectra show laser-aligned emission of electrons up to keV kinetic energies, exceeding the ponderomotive potential by two orders of magnitude. The importance of the nanoplasmonic field enhancement due to resonant Mie-plasmon excitation observed for optimal pulse delays is investigated by a direct comparison with molecular dynamics results. The excellent agreement of the key signatures in the delay-dependent and angular-resolved spectra with simulation results allows for a quantitative analysis of the laser and plasmonic contributions to the acceleration process. The extracted field enhancement at resonance verifies the dominance of surface-plasmon-assisted re-scattering.

We discuss the interaction of ultrashort near-infrared laser pulses with sharp metal tips at moderate nominal intensities (I₀ ∼ 10¹¹ W cm⁻²). As external electric fields are strongly enhanced at such tips (enhancement factor ∼10) our system turns out to be an ideal miniature laboratory to investigate strong-field effects at solid surfaces. We analyse the electron-energy spectra as a function of the strength of the laser field and the static extraction field and present an intuitive model for their interpretation. The size of the effective field acting on the metal electrons can be determined from the electron spectra. The latter are also reproduced by time-dependent density functional theory (TDDFT) simulations.

We show that ablation features in poly-methyl methacrylate (PMMA) induced by a single femtosecond laser pulse are imposed by light polarization. The ablation craters are elongated along the major axis of the polarization vector and become increasingly prominent as the pulse energy is increased above the threshold energy. We demonstrate ∼40% elongation for linearly and elliptically polarized light in the fluence range of 4–20 J cm⁻², while circularly polarized light produced near circular ablation craters irrespective of pulse energies. We also show that irradiation with multiple pulses erases the polarization-dependent elongation of the ablation craters. However, for line ablation the orientation of the electric field vector is imprinted in the form of quasi-periodic structures inside the ablated region. Theoretically, we show that the polarization dependence of the ablation features arises from a local field enhancement during light–plasma interaction. Simulations also show that in materials with high nonlinearities such as doped PMMA, in addition to conventional explosive boiling, sub-surface multiple filamentation can also give rise to porosity.

The time-dependent surface flux (t-SURFF) method is extended to single and double ionization of two-electron systems. Fully differential double emission spectra by strong pulses at extreme UV and infrared wavelengths are calculated using simulation volumes that only accommodate the effective range of the atomic binding potential and the quiver radius of free electrons in the external field. For a model system, we found a pronounced dependence of shake-up and non-sequential double ionization on the phase and duration of the laser pulse. The extension to fully three-dimensional calculations is discussed.

In this paper, we address the question of the origin of the charge density wave instability in 1T-TiSe₂. We develop a model considering the direct Coulomb interaction between electrons and holes in the valence and conduction bands near the Fermi energy. Using the Bethe–Salpeter equation, we calculate the electron–hole correlator, which reveals an instability at low temperature leading to a transition toward a commensurate superstructure mediated by the electron–phonon coupling, in agreement with experiments. On the basis of this correlator, the electron self-energies are then calculated and the corresponding photoemission spectra are compared with the experimental ones, revealing good agreement. The signature of electron–hole fluctuations in photoemission is emphasized. Furthermore, we calculate the spectral function of the phonon mode, whose softening is experimentally observed at the transition.

Ionization mechanisms in water irradiated with bandwidth-limited and temporally asymmetric femtosecond laser pulses are investigated via ultrafast spectral interferometry. By using a novel common-path interferometer with an enlarged temporal measurement window, we directly observe the dynamics of free-electron plasma generated by shaped pulses. We found that a temporally asymmetric pulse and its time-reversed counterpart address multiphoton and avalanche ionization mechanisms in a different fashion. Positive third-order dispersion shaped pulses produce a much higher free-electron density than negative ones at the same fluence, instantaneous frequency and focusing conditions. From the experimental data obtained after irradiation with bandwidth-limited and shaped pulses the multiphoton and avalanche coefficients were determined using a generic rate equation. We conclude that temporal tailored femtosecond pulses are suitable for manipulation of the initial steps in laser processing of high band gap materials.

Based on trajectory calculations of xenon clusters up to ≈6000 atoms irradiated by laser pulses (peak intensities I_M = 10¹⁴–10¹⁶ W cm⁻², Gaussian pulse lengths τ = 10–230 fs and frequency 0.35 fs⁻¹), we have analyzed the interrelation between outer ionization and ion kinetic energies. The following three main categories have been identified. (A) For short pulses (τ = 10 fs) of higher intensity I_M = 10¹⁶ W cm⁻², the outer ionization level leads to a sufficiently high positive cluster charge, which confines the remaining nanoplasma electrons to the cluster center. In this case, ion energies can be reasonably well accounted for by a multi-charge state lychee model, according to which outer ionization is vertical and the nanoplasma can be described by a non-expanding neutral cluster interior, causing a zero-energy component in the ion kinetic energy distribution and an expanding electron-free cluster periphery. (B) For a very low outer ionization level, which is realized for short pulses of low intensity (I_M = 10¹⁴ W cm⁻²) and/or large clusters, a slow gradual evaporation of nanoplasma electrons under laser-free conditions on the picosecond time scale is observed, making the entire outer ionization process highly non-vertical despite the short laser pulse. Accordingly, ions are accelerated only by a gradual buildup of the total cluster charge. (C) For long pulses (τ = 230 fs), the cluster expansion during the laser pulse is large and outer ionization is non-vertical. The nanoplasma electrons attain high kinetic energies by resonance heating and are distributed over the entire ion framework without a neutral cluster interior. Consequently, a zero-energy component in the ion energy distribution is missing.

Two-component nanoplasmas generated by strong-field ionization of doped helium nanodroplets are studied in a pump–probe experiment using few-cycle laser pulses in combination with molecular dynamics simulations. High yields of helium ions and a pronounced resonance structure in the pump–probe transients which is droplet size dependent reveal the evolution of the dopant-induced helium nanoplasma with an active role for He shells in the ensuing dynamics. The pump–probe dynamics is interpreted in terms of strong inner ionization by the pump pulse and resonant heating by the probe pulse which controls the final charge states detected via the frustration of electron–ion recombination.

Waveform-controlled light fields offer the possibility of manipulating ultrafast electronic processes on sub-cycle timescales. The optical lightwave control of the collective electron motion in nanostructured materials is key to the design of electronic devices operating at up to petahertz frequencies. We have studied the directional control of the electron emission from 95 nm diameter SiO₂ nanoparticles in few-cycle laser fields with a well-defined waveform. Projections of the three-dimensional (3D) electron momentum distributions were obtained via single-shot velocity-map imaging (VMI), where phase tagging allowed retrieving the laser waveform for each laser shot. The application of this technique allowed us to efficiently suppress background contributions in the data and to obtain very accurate information on the amplitude and phase of the waveform-dependent electron emission. The experimental data that are obtained for 4 fs pulses centered at 720 nm at different intensities in the range (1–4) × 10¹³ W cm⁻² are compared to quasi-classical mean-field Monte-Carlo simulations. The model calculations identify electron backscattering from the nanoparticle surface in highly dynamical localized fields as the main process responsible for the energetic electron emission from the nanoparticles. The local field sensitivity of the electron emission observed in our studies can serve as a foundation for future research on propagation effects for larger particles and field-induced material changes at higher intensities.

4f core level photoelectron spectroscopy has been performed on negatively charged lead clusters, in the size range of 10–90 atoms. We deploy 4.7 nm radiation from the free-electron laser FLASH, yielding sufficiently high photon flux to investigate mass-selected systems in a beam. A new photoelectron detection system based on a hemispherical spectrometer and a time-resolving delayline detector makes it possible to assign electron signals to each micro-pulse of FLASH. The resulting 4f binding energies show good agreement with the metallic sphere model, giving evidence for a fast screening of the 4f core holes. By comparing the present work with previous 5d and valence region data, the paper presents a comprehensive overview of the energetics of lead clusters, from atoms to bulk. Special care is taken to discuss the differences of the valence- and core-level anion cluster photoionizations. Whereas in the valence case the escaping photoelectron interacts with a neutral system near its ground state, core-level ionization leads to transiently highly excited neutral clusters. Thus, the photoelectron signal might carry information on the relaxation dynamics.

We report a theoretical study of the many-body effects of electron–electron interaction on the ground-state and spectral properties of double-layer graphene. Using a projector-based renormalization method we show that if a finite-voltage difference is applied between the graphene layers, electron–hole pairs can be formed and—at very low temperatures—an excitonic instability might emerge in a double-layer graphene structure. The single-particle spectral function near the Fermi surface exhibits a prominent quasiparticle peak, different from neutral (undoped) graphene bilayers. Away from the Fermi surface, we find that the charge carriers strongly interact with plasmons, thereby giving rise to a broad plasmaron peak in the angle-resolved photoemission spectrum.

We discuss a microscopic particle-in-cell (MicPIC) approach that allows bridging of the microscopic and macroscopic realms of laser-driven plasma physics. The simultaneous resolution of collisions and electromagnetic field propagation in MicPIC enables the investigation of processes that have been inaccessible to rigorous numerical scrutiny so far. This is illustrated by the two main findings of our analysis of pre-ionized, resonantly laser-driven clusters, which can be realized experimentally in pump–probe experiments. In the linear response regime, MicPIC data are used to extract the individual microscopic contributions to the dielectric cluster response function, such as surface and bulk collision frequencies. We demonstrate that the competition between surface collisions and radiation damping is responsible for the maximum in the size-dependent lifetime of the Mie surface plasmon. The capacity to determine the microscopic underpinning of optical material parameters opens new avenues for modeling nano-plasmonics and nano-photonics systems. In the non-perturbative regime, we analyze the formation and evolution of recollision-induced plasma waves in laser-driven clusters. The resulting dynamics of the electron density and local field hot spots opens a new research direction for the field of attosecond science.

Inverse bremsstrahlung (IB) heating, an important process in the laser–matter interaction, involves two different kinds of interaction—the interaction of the electrons with the external laser field and the electron–ion interaction. This makes analytical approaches very difficult. In a quantum perturbative approach to the IB heating rate in strong laser fields, usually the first Born approximation with respect to the electron–ion potential is considered, whereas the influence of the electric field is taken exactly in the Volkov wave functions. In this paper, a perturbative treatment is presented adopting a screened electron–ion interaction potential. As a new result, we derive the momentum-dependent, angle-averaged heating rate in the first Born approximation. Numerical results are discussed for a broad range of field strengths, and the conditions for the applicability of a linear approximation for the heating rate are analyzed in detail. Going a step further in the perturbation series, we consider the transition amplitude in the second Born approximation, which enables us to calculate the heating rate up to the third order of the interaction strength.

We have investigated the radiative cooling of initially hot Al⁻₄ and Al⁻₅ cluster anions during storage in a cryogenic ion beam trap at an ambient temperature of <15 K. By applying a statistical rate model to the ions' measured delayed detachment rate following excitation with a laser, we have obtained their vibrational temperature as a function of cooling time. The temperature curves for Al⁻₄ suggest that the vibrational cooling slows down considerably once the ion reaches approximately room temperature. This suggests the participation of transitions from recently found low-lying electronic states of the anion in the cooling process, prior to reaching approximately room temperature. The experimental results for Al⁻₅ suggest slightly slower radiative cooling than for Al⁻₄.

The photophysical and photochemical processes driving the formation of the ultraviolet (UV)-induced DNA Dewar lesion from the T(6-4)T dimer are investigated by time-resolved spectroscopy and quantum chemical modelling. Time-resolved absorption and emission spectroscopy in the UV revealed a biexponential decay of the electronically excited state (S₁) with time constants in the 100 ps and 1 ns range. From the S₁ state the system forms the Dewar lesion (proven by time-resolved infrared spectroscopy), the triplet state of the T(6-4)T dimer and the ground state of the original T(6-4)T dimer. The decay process from the excited singlet is activated and thus temperature dependent. Quantum chemical modelling is used to describe the reaction path via a minimum on the excited electronic potential energy surface in close proximity to a triplet state. The transition to the Dewar isomer competes with internal conversion and with triplet formation. Only if the backbone between the two thymines is closed, is the Dewar isomer formed with a significant yield. The simulations reveal that the tension built up by the backbone is required for guiding the reaction to the conical intersection leading to the Dewar isomer.

Experimental results on relativistic surface HHG at a repetition rate of 10 Hz are presented. Average powers in the 10 μW range are generated in the spectral range of 51 to 26 nm (24–48 eV). The surface harmonic radiation is produced by focusing the second-harmonic of a high-power laser onto a rotating glass surface to moderately relativistic intensities of 3 × 10¹⁹ W cm⁻². The harmonic emission exhibits a divergence of 26 mrad. Together with absolute photon numbers recorded by a calibrated spectrometer, this allows for the determination of the extreme ultraviolet (XUV) yield. The pulse energies of individual harmonics are reaching up to the μJ level, equivalent to an efficiency of 10⁻⁵. The capability of producing stable and intense high-harmonic radiation from relativistic surface plasmas may facilitate experiments on nonlinear ionization or the seeding of free-electron lasers.

In this paper, autoionizing states in the one-dimensional helium atom are investigated by numerical solution of the time-dependent two-electron Schrödinger equation. The atom is irradiated by an extreme ultraviolet (XUV) attosecond pulse and a time-delayed infrared few-cycle laser pulse. The XUV pulse populates a superposition of doubly excited states, leading to Fano resonances in the photoelectron spectrum. It is demonstrated that the Fano line profile is strongly modified by the presence of the laser field. Laser-induced coupling between the different doubly excited states causes the population of autoionizing states that cannot be reached by absorbing a single XUV photon from the ground state. The resulting additional peaks in the photoelectron spectrum are modulated as a function of time delay. Furthermore, the photoelectron spectrum exhibits a fringe pattern that is determined by the time delay but is independent of the details of the laser pulse.

We demonstrate the feasibility to completely characterize entanglement by negativities of quasiprobabilities. This requires the complete solution of a sophisticated mathematical problem, the so-called separability eigenvalue problem. Its solution is obtained for a non-Gaussian continuous variable quantum state, a two-mode squeezed state undergoing dephasing. This is a standard scenario for experiments with quantum-correlated radiation fields.

We calculate the dynamic structure factor (DSF) in warm dense beryllium by means of ab initio molecular dynamics simulations. The dynamic conductivity is derived from the Kubo–Greenwood formula, and a Drude-like behaviour is observed. The corresponding dielectric function is used to determine the DSF. Since the ab initio approach is so far only applicable for wavenumbers k = 0, the k-dependence of the dielectric function is modelled via the Mermin ansatz. We present the results for the dielectric function and DSF of warm dense beryllium and compare these with perturbative treatments such as the Born–Mermin approximation. We found considerable differences between the results of these approaches; this underlines the need for a first-principles determination of the DSF of warm dense matter.

Laser-induced electron detachment or ionization of atoms and negative ions is considered. In the context of the saddle-point evaluation of the strong-field approximation (SFA), the velocity maps of the direct electrons (those that do not undergo rescattering) exhibit a characteristic structure due to the constructive and destructive interference of electrons liberated from their parent atoms/ions within certain windows of time. This structure is defined by the above-threshold ionization rings at fixed electron energy and by two sets of curves in momentum space on which destructive interference occurs. The spectra obtained with the SFA are compared with those obtained by numerical solution of the time-dependent Schrödinger equation. For detachment, the agreement is excellent. For ionization, the effect of the Coulomb field is most pronounced for electrons emitted in a direction close to laser polarization, while for near-perpendicular emission the qualitative appearance of the spectrum is unaffected.

Scattering experiments on xenon nanoclusters with high-intensity soft x-ray laser pulses from the Free-Electron LASer in Hamburg (FLASH) are performed to investigate different cluster morphologies in the gas phase. Three different types of scattering patterns can be identified. The most frequent pattern of concentric rings reflects the event of a single spherical cluster in focus. Fine interference rings similar to Newton rings appear when two clusters are illuminated at μm distance, revealing three-dimensional information about the location of the clusters. Between 10 and 30% of all hits show a previously unknown twin cluster configuration with two clusters in direct contact. Simulations of scattering patterns for twin clusters with different sizes of the two particles, degree of fusion and orientation in space allow us to explain all the observed patterns.

Size-selected metal-cluster dianions of the elements gold, silver and copper have been photoexcited by nanosecond-pulse and continuous laser irradiation, which leads to electron emission and monomer evaporation. In addition to the observation of these competing decay pathways, there is a reduction of the total cluster-ion intensity, which indicates the neutralization of dianions, i.e. the loss of both surplus electrons. In contrast, the activation of singly charged anionic clusters of the same type results primarily in dissociation by monomer evaporation and not by electron emission. These decay processes as observed for doubly and singly charged cluster anions suggest that the dianions emit two electrons simultaneously, i.e. in a correlated fashion. A classical conducting-sphere approximation confirms that the Coulomb barrier for symmetric two-electron emission is lower than the Coulomb barrier for the emission of a single electron.

It is now well established that, under intense laser illumination, clusters undergo enhanced ionization compared to their isolated atomic and molecular counterparts being subjected to the same pulses. This leads to extremely high charge states and concomitant Coulomb explosion. Until now, the cluster size necessary for ionization enhancement has not been quantified. Here, we demonstrate that through the comparison of ion signal from small covalently bound silicon clusters exposed to low intensity laser pulses with semi-classical theory, their ionization potentials (IPs) can be determined. At moderate laser intensities the clusters are not only atomized, but all valence electrons are removed from the cluster, thereby producing up to Si⁴⁺. The effective IPs for the production of the high charge states are shown to be ∼40% lower than the expected values for atomic silicon. Finally, the minimum cluster size responsible for the onset of the enhanced ionization is determined utilizing the magnitude of the kinetic energy released from the Coulomb explosion.

The quantum Wigner function of an electron scattered by an ion in a strong laser field is considered in the framework of a one-dimensional scattering model with a soft-core Coulomb potential. The Wigner function contains much more information on the scattering process than the projected probability distributions in position and momentum space considered previously. The formation of the above-threshold ionization (ATI) energy spectrum, including ATI peaks, modulations and transients, can be easily explained by using the interference of phase-space trajectories.

The screening of a 2p core-hole in Na clusters is investigated using density functional theory (DFT) applied to an extended jellium model with an all-electron atom in the center. The study is related to recent experiments at the free-electron laser at DESY in which photoelectron spectra from mass-selected, core-shell-ionized metal clusters have been recorded. Relaxed and unrelaxed binding energies as well as Kohn–Sham (KS) orbital energies are calculated in Perdew–Zunger self-interaction-corrected exchange-only local spin-density approximation for valence and 2p core electrons in Na clusters up to 58 atoms. The relaxed binding energies follow approximately the metal-sphere behavior. The same behavior is seen in the experiment for sufficiently big clusters, indicating perfect screening and that the relaxation energy due to screening goes to the photoelectron. Instead, calculating the kinetic energy of the photoelectrons using unrelaxed binding energies or KS orbital energies yields the wrong results for core-shell electrons. The screening dynamics are investigated using time-dependent DFT. It is shown that screening occurs on two time scales, a core-shell-dependent inner-atomic and an inter-atomic valence electron time scale. In the case of Na 2p ionization the remaining electrons in the 2p shell screen within tens of attoseconds, while the screening due to cluster valence electrons occurs within several hundreds of attoseconds. The screening time scales may be compared with the photon energy and cluster size-dependent escape times of the photoelectron in order to estimate whether the photoelectron is capable of picking up the relaxation energy or whether the residual system is left in an excited state.

Transient nanoplasmas in laser-excited metal clusters open the route to probing ultrafast collisional and collective laser–plasma processes in a wide and well-tunable range of densities and temperatures. The transition from a fully degenerate to a nearly classical plasma can occur within a few femtoseconds, accompanied by fundamental changes in the relaxation processes driven by electron–electron collisions (EECs). To investigate the resulting implications for laser–metal–cluster interactions, we developed an extended semiclassical Vlasov–Uehling–Uhlenbeck approach where the collision term resolves time-dependent Pauli blocking and local screening effects for arbitrary levels of degeneracy. Our simulation results for resonant dual-pulse excitations of Na₅₅ reveal an unexpected synergy effect of EECs and collective laser–plasma processes, i.e. a strongly enhanced electron acceleration via plasmon-assisted rescattering in the presence of EECs.