Photoionization Amplitudes Research Articles

Attosekundnaya interferometriya pri uchastii diskretnykh sostoyaniy

In the paper we theoretically investigate the features of RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) spectroscopy under conditions when transitions through discrete spectrum states play a significant role. Two approaches are applied in the article: the numerical solution of rate equations with continuum discretization and the perturbation theory up to the third order in amplitude. Both approaches use transition matrix elements and photoionization amplitudes obtained by the high-precision R-matrix method. Within the framework of these approaches, photoelectron spectra, the amplitude and phase of RABBITT oscillations were obtained, and the effect of the seed optical field intensity and detuning from a resonance upon excitation of discrete states was studied.

Biharmonic (ω, 2ω) ionization of atoms by elliptically-polarized light. Carving the photoelectron angular distributions

The biharmonic (ω, 2ω) photoionization of atomic inner-shell electrons opens up new perspectives for studying nonlinear light–atom interactions at intensities in the transition regime from weak to strong-field physics. In particular, the control of the frequency and polarization of biharmonic beams enables one to carve the photoelectron angular distribution and to enhance the resolution of ionization measurements by the (simultaneous) absorption of photons. Apart from its quite obvious polarization dependence, the photoelectron angular distributions are sensitive also to the (relative) intensity, the phase difference and the temporal structure of the incoming beam components, both at resonant and nonresonant frequencies. Here, we describe and analyze several characteristic features of biharmonic ionization in the framework of second-order perturbation theory and (so-called) ionization pathways, as they are readily derived from the interaction of inner-shell electrons with the electric-dipole field of the incident beam. We show how the photoelectron angular distribution and elliptical dichroism can be shaped in rather an unprecedented way by just tuning the properties of the biharmonic field. Since such fields are nowadays accessible from high-harmonic sources or free-electron lasers, these and further investigations might help extract photoionization amplitudes or the phase difference of incoming beams.

Spatiotemporal delay in photoionization by polarization-structured laser fields

Focused laser fields with textured polarization on a subwavelength scale allow extracting information on electronic processes which are not directly accessible by homogeneous fields. Here we consider photoionization in radially and azimuthally polarized laser fields and show that, due to the local polarizations of the transversal and the longitudinal laser electric field components, the detected photoelectron spectra depend on the atom position from which the electron originates. The calculation results show the angular dependence of the photoionization amplitude, the quantum phase, and the time delay of the valence shell electrons as the parent atom's position varies across the laser spot. We discuss the possibility of using the photoelectron spectra to identify the position of the ionized atom within the laser spot on the subwavelength scale. The proposal and its illustrations underline the potential for the detection of the atomic position based on attosecond streaking methods.

Numerical time-of-flight analysis of the strong-field photoeffect

Short-time filtering of the photoionization amplitude extracted straight from the numerical solution of the time-dependent Schr\"{o}dinger equation (TDSE) is used to identify dominant pathways that form photoelectron spectra in strong fields. Thereby, the "black-box nature" of TDSE solvers only giving the final spectrum is overcome, and simpler approaches, e.g., semi-classical based on the strong-field approximation, can be tested and improved. The approach also allows to suppress intercycle quantum interference between pathways removing patterns that are usually washed out in experiments.

New Method for Measuring Angle-Resolved Phases in Photoemission

Quantum mechanically, photoionization can be fully described by the complex photoionization amplitudes that describe the transition between the ground state and the continuum state. Knowledge of the value of the phase of these amplitudes has been a central interest in photoionization studies and newly developing attosecond science, since the phase can reveal important information about phenomena such as electron correlation. We present a new attosecond-precision interferometric method of angle-resolved measurement for the phase of the photoionization amplitudes, using two phase-locked Extreme Ultraviolet pulses of frequency $\omega$ and $2\omega$, from a Free-Electron Laser. Phase differences $\Delta \tilde \eta$ between one- and two-photon ionization channels, averaged over multiple wave packets, are extracted for neon $2p$ electrons as a function of emission angle at photoelectron energies 7.9, 10.2, and 16.6 eV. $\Delta \tilde \eta$ is nearly constant for emission parallel to the electric vector but increases at 10.2 eV for emission perpendicular to the electric vector. We model our observations with both perturbation and \textit{ab initio} theory, and find excellent agreement. In the existing method for attosecond measurement, Reconstruction of Attosecond Beating By Interference of Two-photon Transitions (RABBITT), a phase difference between two-photon pathways involving absorption and emission of an infrared photon is extracted. Our method can be used for extraction of a phase difference between single-photon and two-photon pathways and provides a new tool for attosecond science, which is complementary to RABBITT.

Wigner–Eisenbud–Smith photoionization time delay due to autoioinization resonances

An empirical ansatz for the complex photoionization amplitude and Wigner–Eisenbud–Smith time delay in the vicinity of a Fano autoionization resonance are proposed to evaluate and interpret the time delay in the resonant region. The utility of this expression is evaluated in comparison with accurate numerical calculations employing the ab initio relativistic random phase approximation and relativistic multichannel quantum defect theory. The indisputably good qualitative agreement (and semiquantitative agreement) between corresponding results of the proposed model and results produced by the ab initio theories proves the usability of the model. In addition, the phenomenology of the time delay in the vicinity of multichannel autoionizing resonances is detailed.

Spectral phase measurement of a Fano resonance using tunable attosecond pulses.

Electron dynamics induced by resonant absorption of light is of fundamental importance in nature and has been the subject of countless studies in many scientific areas. Above the ionization threshold of atomic or molecular systems, the presence of discrete states leads to autoionization, which is an interference between two quantum paths: direct ionization and excitation of the discrete state coupled to the continuum. Traditionally studied with synchrotron radiation, the probability for autoionization exhibits a universal Fano intensity profile as a function of excitation energy. However, without additional phase information, the full temporal dynamics cannot be recovered. Here we use tunable attosecond pulses combined with weak infrared radiation in an interferometric setup to measure not only the intensity but also the phase variation of the photoionization amplitude across an autoionization resonance in argon. The phase variation can be used as a fingerprint of the interactions between the discrete state and the ionization continua, indicating a new route towards monitoring electron correlations in time.

Dichroism in the photoionisation of atoms at XUV free-electron lasers

Two-color photoionization of atomic He has been investigated by angle-integrated and angle-resolved electron spectroscopy. The combined action of intense radiation pulses from the XUV free-electron laser (FEL), FERMI or FLASH, and a synchronized optical laser on the target atom gives rise to a rich sideband structure in the photoemission spectrum. Measurements of the angular distribution parameters and the determination of the circular and linear dichroism for the two-color photoionization enable a detailed analysis of the symmetry of the outgoing electron waves and of the dynamics underlying the multi-photon processes. The experimental results are in excellent agreement with theoretical results obtained using perturbation theory (low intensity regime) and the strong field approximation. For the particular case of two-photon ionization the measurements represent an ideal tool for characterizing certain FEL parameters, here for example the degree and the sign of circular polarization. Finally, new features of the dichroism are theoretically predicted originating from the non-dipole contribution into the photoionization amplitudes.

Phase Measurement of a Fano Resonance Using Tunable Attosecond Pulses

SynopsisWe study photoionization of argon atoms close to the 3s23p6 → 3s13p64p Fano resonance using an attosecond pulse train and a weak infrared probe field. An interferometric technique combined with tunable attosecond pulses allows us to determine the phase of the photoionization amplitude as a function of photon energy. We interpret the experimental results using an analytical two-photon model based on the Fano formalism and obtain quantitative agreement.

Photoionization dynamics of the C2+ ion in Rydberg states

The goal of this work is to examine in detail the ionization dynamics of Be-like C ion in Rydberg states. An initial calculation has been done to output the lifetime due to spontaneous decay for unperturbed 1s 22sns (1Se) Rydberg states using the multi-configuration Dirac-Fock (MCDF) method with configuration interaction option implemented in the general-purpose relativistic atomic structure package (GRASP). Both the C2+ ground state and the C3+ target state energies have been carefully calculated. We report results from a detailed and systematic study of the behaviour of complex photoionization amplitudes, the lifetime due to spontaneous decay for unperturbed 1s 22sns (1Se) Rydberg states, the ‘resonant’ phase shift and the rapidly increasing of this shift from well below to well above the resonance position. The sum-over-state method is used to calculate the static dipole polarizability, while the frequency-dependent polarizability values of C2+ ion in these Rydberg states are obtained from two-state model calculation results.

An R-matrix approach to electron–photon–molecule collisions: photoelectron angular distributions from aligned molecules

We present a new extension of the UKRmol electron–molecule scattering code suite, which allows one to compute ab initio photoionization and photorecombination amplitudes for complex molecules, resolved both on the molecular alignment (orientation) and the emission angle and energy of the photoelectron. We illustrate our approach using CO2 as an example, and analyze the importance of multi-channel effects by performing our calculations at different, increasing levels of complexity. We benchmark our method by comparing the results of our calculations with experimental data and with theoretical calculations available in the literature.

On the electron wavepacket dynamics of photoionizing states

To study electron wavepacket dynamics of photoionizing states in polyatomic molecules, we discuss two crucial issues to be overcome in the theory of molecular electronic wavepacket dynamics in an intense laser field (Takatsuka and Yonehara 2011 Phys. Chem. Chem. Phys. 13 4987). One is about the description of the ionization process from electronically excited states composed of many multiply excited configuration-state functions. The other is how to reconstruct the electronic states remaining in the molecular site while electrons are flowing out of the molecular bounds. These are both critical to extend the realm of the theories of electron dynamics based on the so-called expansion (algebraic) method in terms of basis functions. To calculate the photoionization amplitude and thereby to estimate the time-dependent amount of electron loss from a molecule, we extract the electron flux (probability current density) from the electron wavepackets without use of scattering theory. This is justified by the success of the recent works by Bandrauk’s group for attosecond photoionization dynamics from the hydrogen molecule ion, who performed numerical integration of the relevant Schrödinger equation (Yuan et al 2013 J. Chem. Phys. 138 134316). A key feature in the present study, on the other hand, is to calculate the electron flux in terms of complex-valued NOs, which arise from the complex electronic wavepackets. Through the change of these NOs, we reconstruct the involved electronic configurations during the flow of electrons out of molecular regions. These repopulated electronic wavefunctions are (non-adiabatically) evolved in time under laser fields.

Core-valence double photoionization of atomic mercury

Multielectron coincidence spectroscopy has been used to study core $4f$ valence $5d$, $6s$ double photoionization of atomic mercury. Multiconfiguration Dirac--Fock calculations were performed to calculate the energies and to estimate the single-photon intensities of the $4{f}^{13}(5{d}^{9}6{s}^{2}+5{d}^{10}6{s}^{1})$ double-ionized states of atomic mercury. Reasonable agreement between the measured and simulated spectra is found if the relaxation effects of the bound-state density is taken into account in the computation of the photoionization amplitudes.

Atomic photoionization: When does it actually begin?

We analyze a time delay of one- and two-electron photoemission from an atom after absorption of an attosecond XUV pulse. We establish this delay by solving the time dependent Schrödinger equation and by subsequent tracing of the field-free evolution of the photoelectron wave packet. This delay can also be related to the energy derivative of the phase of the complex photoionization amplitude which makes the time delay a sensitive probe of many-electron correlation.

Role of nuclear dynamics in the asymmetric molecular-frame photoelectron angular distributions for C 1sphotoejection from CO2

We report the results of semiclassical calculations of the asymmetric molecular-frame photoelectron angular distributions for C 1$s$ ionization of CO${}_{2}$ measured with respect to the CO${}^{+}$ and ${\mathrm{O}}^{+}$ ions produced by subsequent Auger decay, and show how the decay event can be used to probe ultrafast molecular dynamics of the transient cation. The fixed-nuclei photoionization amplitudes were constructed using variationally obtained electron--molecular-ion scattering wave functions. The amplitudes are then used in a semiclassical manner to investigate their dependence on the nuclear dynamics of the cation. The method introduced here can be used to study other core-level ionization events.

Interference effects on the photoionization cross sections between two neighbouring atoms: nitrogen as an example

Interference effects on the photoionization cross sections between two neighbouring atoms are considered based on the coherent scattering of the ionized electrons by the two nuclei when their separation is less than or comparable to the de Broglie wave length of the ionized electrons. As an example, the single atomic nitrogen ionization cross section and the total cross sections of two nitrogen atoms with coherently added photoionization amplitudes are calculated from the threshold to about 60 Å (1 Å = 0.1 nm) of the photon energy. The photoionization cross sections of atomic nitrogen are obtained by using the close-coupling R-matrix method. In the calculation 19 states are included. The ionization energy of the atomic nitrogen and the photoionization cross sections agree well with the experimental results. Based on the R-matrix results of atomic nitrogen, the interference effects between two neighbouring nitrogen atoms are obtained. It is shown that the interference effects are considerable when electrons are ionized just above the threshold, even for the separations between the two atoms are larger than two times of the bond length of N2 molecules. Therefore, in hot and dense samples, effects caused by the coherent interference between the neighbours are expected to be observable for the total photoionization cross sections.

Asymmetric molecular-frame photoelectron angular distributions for C 1s photoejection from CO2; a theoretical study

We report the results of ab initio calculations of cross sections and molecular-frame photoelectron angular distributions for C 1s ionization of CO2, and propose a mechanism for the recently observed asymmetry of those angular distributions with respect to the CO+ and O+ ions produced by subsequent Auger decay. The fixed-nuclei, photoionization amplitudes were constructed using variationally obtained electron-molecular ion scattering wave functions. We have also carried out electronic structure calculations which identified a dissociative state of the CO2++ dication that is likely populated following Auger decay. We show that a proper accounting of vibrational motion in the computation of the photoelectron angular distributions, along with reasonable assumptions about the nuclear dissociation dynamics, gives results in good agreement with recent experimental observations.

Theoretical study of asymmetric molecular-frame photoelectron angular distributions forC 1sphotoejection fromCO2

We report the results of ab initio calculations of cross sections and molecular-frame photoelectron angular distributions for $\text{C}\text{ }1s$ ionization of ${\text{CO}}_{2}$ and propose a mechanism for the recently observed asymmetry of those angular distributions with respect to the ${\text{CO}}^{+}$ and ${\text{O}}^{+}$ ions produced by subsequent Auger decay. The fixed-nuclei, photoionization amplitudes were constructed using variationally obtained electron-molecular ion scattering wave functions. We have also carried out electronic structure calculations which identify a dissociative state of the ${\text{CO}}_{2}^{2+}$ dication that is likely populated following Auger decay and which leads to ${\text{O}}^{+}+{\text{CO}}^{+}$ fragment ions. We show that a proper accounting of vibrational motion in the computation of the photoelectron angular distributions, along with reasonable assumptions about the nuclear dissociation dynamics, gives results in good agreement with recent experimental observations. We also demonstrate that destructive interference between different partial waves accounts for sudden changes with photon energy in the observed angular distributions.

Relativistic and confinement effects in photoionization of Xe

The effect of a spin–orbit interaction activated interchannel coupling in 4d photoionization channels of Xe on the 5s photoionization amplitudes is studied and analysed. The dramatic effect of confinement of the Xe atom in a C60 cage on the 4d photoionization parameters and the consequent effect on 5s photoionization via an interchannel coupling are also discussed.

Correlation confinement resonances in photoionization of endohedral atoms: Xe@C60

A new type of confinement resonance, termed a correlation confinement resonance, occurring in the photoionization of an atom A encapsulated inside the hollow cage of C60, A@C60, is found and interpreted in this paper. It is multielectron in nature and is induced in the photoionization of an outer shell of the confined atom by ‘ordinary’ confinement resonances in photoionization amplitudes from deeper subshells as a result of interchannel coupling. The effect is illustrated by calculations of the 5s photoionization cross section of endohedral Xe, Xe@C60, in the region of the 4d giant resonance exhibiting ordinary confinement resonances.