Photoionization Transitions Research Articles

Defect levels of 3dn transition-metal series in wide-gap oxide and fluoride insulators: A first-principles study

The defect levels produced in insulators doped with transition metal (TM) ions are important for a variety of defect-related optical processes and magnetic properties. Here, we performed a systematical first-principles study of the defect levels in the band gap for all the $3{d}^{n}$ TM ions occupying octahedral sites in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}, {\mathrm{MgAl}}_{2}{\mathrm{O}}_{4}$, MgO, ${\mathrm{KMgF}}_{3}$, and ${\mathrm{MgF}}_{2}$ based on density functional theory. The spin-polarized hybrid density functional with a dielectric-dependent Hartree-Fock mixing parameter was adopted to improve the band gap. The defect levels, i.e., the charge transition levels, were obtained by calculating the total energy differences of relaxed geometric structures for various valence states, considering image-charge and potential alignment corrections. These results were rationalized with available experimental optical spectra related to the charge transfer or photoionization transitions. The calculation scheme is appropriate for predicting the valence states of TM ions and their defect levels in insulators. The trends of variation of the defect levels across the $3d$ TM series may help interpreting experimental results and aid in the design and optimization of optical materials.

Retrieval of photoionization group delay in chirped-attosecond pulses photoelectron streaking experiments

Photoionization time delays have been investigated in many streaking experiments in which an extreme ultraviolet (XUV) attosecond pulse is used to ionize the target in the presence of a dressing infrared laser field. The discrepancies between the photoionization time delays thus experiment measured and those from many sophisticated theoretical simulations have generated a great deal of controversy in recent years. The difficulty of achieving an accuracy of the retrieved time delays comes from two facts: a so-called wavepacket approximation is introduced to construct the photoionization electron wavepacket, this approximation is invalid if atto-chirp of XUV is non-zero; the other one is that the lower sensitivity of the streaking spectra to the phase of the photoionization transition dipole. Here we present a time delay retrieval method born from our recently proposed ‘phase retrieval of broadband pulses auto correlation’ (PROBP-AC) technology to overcome above limitations. We carefully exam the validity of our method and make a few compare with some other common used retrieval codes, and the simulations demonstrate that more accurate results can be retrieved using PROBP AC. Based on the present method, the angular dependent photoionization time delays can also be retrieved. Our investigation casts doubts on the measured group time delays in previous streaking experiments. We also mention here that a single photoionization group time delay at the XUV peak energy is not enough to represent a complete photoemission process; instead, a fully characterization of the photoionization group time delay over the whole bandwidth of the wave packet is required.

A geometric approach to decoding molecular structure and dynamics from photoionization of isotropic samples.

We propose a geometric approach to the description and analysis of photoelectron angular distributions resulting from isotropic samples in the case of few-photon ionization by electric fields of arbitrary polarization. This approach formulates the standard photoionization observables - the bl,m expansion coefficients of the photoelectron angular distribution, in terms of geometrical properties of the vector field D⃑(k⃑) ≡ 〈k⃑|d⃑|0〉 describing the electronic transition from a bound state |0〉 into a scattering state |k⃑〉 - the photoionization transition dipole. Besides revealing selection rules for the enantio-sensitivity of bl,m coefficients in multiphoton ionization, our approach yields very compact expressions for both chiral and achiral molecules revealing how the molecular rotational invariants couple to the rotational invariants of the setup defined by the electric field polarization and the arrangement of photoelectron detectors. We apply this approach to one-photon ionization and find that the forward-backward asymmetry parameter b1,0, emerging exclusively in chiral molecules and encoded in the field B⃑(k⃑) ≡ iD⃑*(k⃑) × D⃑(k⃑), is sensitive only to the components of D⃑(k⃑) perpendicular to k⃑, while the regular asymmetry parameter b2,0 emerging in chiral and achiral molecules is sensitive only to the component of D⃑(k⃑) parallel to k⃑. Next, we analyze resonantly enhanced two-photon ionization and show that b0,0 and b1,0 can be written in terms of an effectively stretched D⃑(k⃑), and how b1,0 and b3,0 can be used to probe B⃑(k⃑).

Photoionization of Rydberg atoms in optical lattices

We develop a formalism for photoionization (PI) and potential energy curves (PECs) of Rydberg atoms in ponderomotive optical lattices and apply it to examples covering several regimes of the optical-lattice depth. The effect of lattice-induced PI on Rydberg-atom lifetime ranges from noticeable to highly dominant when compared with natural decay. The PI behavior is governed by the generally rapid decrease of the PI cross sections as a function of angular-momentum (ℓ), lattice-induced ℓ-mixing across the optical-lattice PECs, and interference of PI transition amplitudes from the lattice-mixed into free-electron states. In GHz-deep lattices, ℓ-mixing leads to a rich PEC structure, and the significant low-ℓ PI cross sections are distributed over many lattice-mixed Rydberg states. In lattices less than several tens-of-MHz deep, atoms on low-ℓ PECs are essentially ℓ-mixing-free and maintain large PI rates, while atoms on high-ℓ PECs trend towards being PI-free. Characterization of PI in GHz-deep Rydberg-atom lattices may be beneficial for optical control and quantum-state manipulation of Rydberg atoms, while data on PI in shallower lattices are potentially useful in high-precision spectroscopy and quantum-computing applications of lattice-confined Rydberg atoms.

Sydney Leach. 11 April 1924—24 December 2019

Sydney Leach will be remembered as an outstanding and inspirational scientist, an irreplaceable friend to many—artists and musicians as well as academic colleagues. He encouraged and influenced numerous scientists as a mentor. After graduating from King's College London and carrying out war work at Farnborough, he spent all his scientific life based in Paris, working principally at Orsay and, in his later years, at the Observatoire de Paris–Meudon. Sydney was a major influence in establishing chemical physics in France after World War II, founding the highly influential Laboratoire de Photophysique Moléculaire (LPPM) at Orsay, where much of his pioneering work was performed. The ‘Sydney lab’ lives on in the newly created Institut des Sciences Moléculaires d'Orsay. Early experiments often took place at the synchrotron source (ACO, Super-ACO), just a few hundred yards from LPPM. He was a pioneering advocate of synchrotron radiation, and a driving force for its use in spectroscopy and photodynamics, along with free-electron lasers, supersonic jets, coincidence spectroscopy and matrix isolation—techniques that were applied and refined over decades and used to explore fundamental processes such as photoionization, vibronic coupling and radiationless transitions. Sydney's seminal studies of polyatomic molecular ions led him towards fresh horizons in planetary atmospheric and space science. His work opened new vistas in cometary spectroscopy, polycyclic aromatic hydrocarbons, fullerenes and their possible roles in the chemistry of the interstellar medium and, finally, biologically relevant species, helping to instigate the newly developing subject of astrobiology—a perfect example of his sustained prescience in the world of science.

Robust control of the minima of high-order harmonics by fine-tuning the alignment of CO2 molecules for shaping attosecond pulses and probing molecular alignment

In a recent paper [C. Jin, S.-J. Wang, X. Zhao, S.-F. Zhao, and C. D. Lin, Phys. Rev. A 101, 013429 (2020)], we reported that the position and depth of the minima in the harmonic spectra of ${\mathrm{CO}}_{2}$ molecules can be dramatically manipulated by a slight change of the degree of alignment, thus providing a convenient method of shaping attosecond pulses which could lead to the splitting of a typical single attosecond burst into two. Here, we demonstrate that harmonic minima can also be dramatically controlled by changing the pump-probe angles to shape attosecond pulses. In the meanwhile, since the pump-probe angle-dependent harmonic spectra are very sensitive to the degree of alignment, harmonic spectra can also be used to calibrate the alignment distribution of molecules. We identify such robust control of harmonic generation is due to the optical property of ${\mathrm{CO}}_{2}$ and the coherent harmonic emission from the oriented molecules. The photoionization transition dipoles (PITDs) of ${\mathrm{CO}}_{2}$ exhibit deep minima that change rapidly with molecular orientations accompanied by large phase changes of $\ensuremath{\pi}$ in PITDs, thus leading to strong interference when the dipoles are added up coherently.

Shaping attosecond pulses by controlling the minima in high-order harmonic generation through alignment of CO2 molecules

We report a simple method for generating shaped attosecond pulses by using a ${\mathrm{CO}}_{2}$ molecule. Unlike most other molecules, owing to its unique energy and angle dependence and the presence of deep minima in the photoionization transition dipole moment, the shape of harmonic spectra, especially the position and depth of minima, can be readily controlled by tuning the degree of alignment. The sensitive alignment dependence of the minima is due to the coherent interference of a laser-induced dipole from each molecule when ${\mathrm{CO}}_{2}$ molecules are moderately aligned, but not when they are well aligned or when they are isotropically distributed. Such a sensitivity offers a simple way of controlling the spectral amplitude and phase of the generated harmonics and thus shaping the generated attosecond pulses, for example, producing structured attosecond pulses by splitting a single burst into two. We illustrate how such pulses are generated and how to characterize them. This method offers a simple way to shape attosecond pulses at the generation step. It can be easily implemented experimentally to generate attosecond pulses with strong phase variations for unique applications.

Origin band of the first photoionizing transition of hydrogen isocyanide.

The photoelectron spectrum of the X1Σ+ → X+2Σ+ ionizing transition of hydrogen isocyanide (HNC) is measured for the first time at a fixed photon energy (13 eV). The assignment of the spectrum is supported by wave-packet calculations simulating the photoionization transition spectrum and using ab initio calculations of the potential energy surfaces for the three lowest electronic states of the cation. The photoelectron spectrum allows the retrieval of the fundamental of the CN stretching mode of the cationic ground state ([small nu, Greek, tilde]3 = 2260 ± 80 cm-1) and the adiabatic ionization energy of hydrogen isocyanide: IE(HNC) = 12.011 ± 0.010 eV, which is far below that of HCN (IE(HCN) = 13.607 eV). In light of this latter result, the thermodynamics of the HCN+/HNC+ isomers is discussed and a short summary of the values available in the literature is given.

Study of spectral and recombination characteristics of HVPE GaN grown on ammono substrates

A comprehensive study of the bulk ~400 µm thick GaN samples, grown by HVPE technology on AT-GaN seeds, and containing different carbon doping is reported. Spectroscopy of point centres has been implemented by combining several contactless/optical techniques: time resolved photoluminescence (TR-PL), microwave probed photoconductivity (MW-PC) transient and pulsed-photo-ionization spectroscopy (PPIS) techniques, together with steady-state PL (SS-PL) and transmission spectral measurements. The dynamics of the non-radiative and radiative recombination dependent on the excess carrier density and incorporated carbon concentration has been revealed. The cross-section of the photon-electron interaction and broadening factors due to electron-phonon coupling have been evaluated for various centres. Profiling of the excess carrier decay transients by scanning a wafer-edge boundary has been employed for estimation of surface recombination velocity. The asymmetry of surface recombination in heavily carbon doped samples has been corroborated by SS-PL intensity changes when comparing spectra recorded by exciting the opposite wafer surfaces using UV light. It has been inferred that the surface and bulk non-radiative recombination with 70 ns carrier lifetime is efficient only within initial stages of MW-PC and TR-PL transients. Several traps, tentatively attributed to CNON, CN, CI, VGa point defects, have been deduced from pulsed photo-ionization spectroscopy. The CN- defect appeared to be the most efficient in redistribution of the radiative recombination. For these centres, the parameters such as the photon-electron interaction cross-section, broadening factor due to electron-phonon coupling, and concentration have been evaluated for GaN samples, carbon doped with different levels. The CNVGa, CICGa, CGaVN complexes have also been implied by considering TR-PL and SS-PL spectra. The conversion from absorption to emission spectra has been revealed and explained based on van Roosbroeck-Shockley approach. The long-tail photoluminescence decay with durations up to tens of ms has been explained by nearly resonant photo-ionization and photoluminescence transitions in sequence of self-sustaining processes when local excitation travels by hopping over the re-absorption lengths.

Dissociating diatomic molecules in ultrafast and intense light

An ab initio theory is devised for the quantum dynamics of molecules undergoing (multiple) ionization in ultrafast and intense light. Specifically, the intertwined problem of photoionization, radiative, and electronic transitions in the course of dissociation is addressed which arises, e.g., when molecules are exposed to xuv light or x rays from free electron lasers or attosecond light sources, but the approach is equally useful in optical strong-field physics. The coherent interaction of the molecule with the light in a specific charge state is also treated. I set out from an abstract formulation in terms of the quantum optical notion of system-reservoir interaction using a master equation in Lindblad form and analyze its short-time approximation. First, I express it in a direct sum rigged Hilbert space for an efficient solution with numerical methods for systems of differential equations. Second, I derive a treatment via quantum Monte Carlo wave packet (MCWP) propagation. The formalism is concretized to diatomic molecules in Born-Oppenheimer approximation whereby molecular rotation is disregarded. The numerical integration of the master equation is carried out with a suitably factored density matrix that exploits the locality of the Hamiltonian and the Lindblad superoperator with respect to the internuclear distance. The formulation of the MCWP for molecules requires a thorough analysis of the quantum jump process; namely, the dependence on the continuous distance renders a straight wave packet promotion useless and, instead, a projected outer product needs to be employed involving an integrated quantum jump operator.

Reconstruction of the complex angle-dependent photoionization transition dipole from a laser-dressed streaking experiment

We study the retrieval of the angular dependence of the photoionization transition dipole phase of an attosecond XUV pulse in order to reconstruct the whole photoelectron wave packet after the photoemission process. Using a one-electron model Ar atom, we show that the full electron wave packet can be reconstructed from IR-free photoelectron angular distributions and the streaking electron spectra in an IR-dressed XUV photoionization, with photoelectrons along the common polarization direction of the two pulses. The method relies on the validity of the strong-field approximation so it is valid only for higher energy photoelectrons. We also point out that a single photoionization group time delay is not enough to represent a photoemission process; instead, a complete characterization of the electron wave packet requires the retrieval of the spectral phase over the whole bandwidth of the wave packet.

A HIGH-RESOLUTION VACUUM ULTRAVIOLET LASER PHOTOIONIZATION AND PHOTOELECTRON STUDY OF THE CO ATOM

ABSTRACT We have measured the vacuum ultraviolet–photoionization efficiency (VUV–PIE) spectrum of Co in the energy range of 63,500–67,000 cm−1, which covers the photoionization transitions of Co(3d74s2 4F9/2) Co+(3d8 3F4), Co(3d74s2 4F7/2) Co+(3d8 3F3), Co(3d74s2 4F9/2) Co+(3d8 3F3), Co(3d74s2 4F9/2) Co+(3d8 3F2), and Co(3d74s2 4F9/2) Co+(3d74s1 5F5). We have also recorded the pulsed field ionization photoelectron spectrum of Co in the same energy range, allowing accurate determinations of ionization energies (IEs) for the photoionization transitions from the Co(3d74s2 4F9/2) ground neutral state to the Co+(3F J ) (J = 4 and 3) and Co+(5F5) ionic states, as well as from the Co(3d74s2 4F7/2) excited neural state to the Co+(3d8 3F3) ionic state. The high-resolution nature of the VUV laser used has allowed the observation of many well-resolved autoionizing resonances in the VUV–PIE spectrum, among which an autoionizing Rydberg series, 3d74s1(5F5)np (n = 19–38), converging to the Co+(3d74s1 5F5) ionic state from the Co(3d74s2 4F9/2) ground neutral state is identified. The fact that no discernible step-like structures are present at these ionization thresholds in the VUV–PIE spectrum indicates that direct photoionization of Co is minor compared to autoionization in this energy range. The IE values, the autoionizing Rydberg series, and the photoionization cross sections obtained in this experiment are valuable for understanding the VUV opacity and abundance measurement of the Co atom in stars and solar atmospheres, as well as for benchmarking the theoretical results calculated in the Opacity Project and the IRON Project, and thus are of relevance to astrophysics.

Fine- and hyperfine-structure effects in molecular photoionization. I. General theory and direct photoionization.

We develop a model for predicting fine- and hyperfine intensities in the direct photoionization of molecules based on the separability of electron and nuclear spin states from vibrational-electronic states. Using spherical tensor algebra, we derive highly symmetrized forms of the squared photoionization dipole matrix elements from which we derive the salient selection and propensity rules for fine- and hyperfine resolved photoionizing transitions. Our theoretical results are validated by the analysis of the fine-structure resolved photoelectron spectrum of O2 reported by Palm and Merkt [Phys. Rev. Lett. 81, 1385 (1998)] and are used for predicting hyperfine populations of molecular ions produced by photoionization.

Critical evaluation of attosecond time delays retrieved from photoelectron streaking measurements

A photoelectron streaking experiment which was conceived as a means to extract the electron wave packet of single-photon ionization has also been employed to retrieve time delays in the fundamental photoemission processes. The discrepancies between the time delays thus measured and those from many sophisticated theoretical calculations have generated a great deal of controversy in recent years. Here we present a careful examination of the methods that were used to retrieve the time delays and demonstrate the difficulty of achieving an accuracy of the retrieved time delays of a few to tens of attoseconds in typical streaking measurements. The difficulty owes more to the lower sensitivity of the streaking spectra to the phase of the photoionization transition dipole than to the spectral phase of the attosecond light pulse in the experiment. The retrieved time delay contains extra errors when the attochirp of the attosecond pulse is large so that the dipole phase becomes negligible compared to it.

Strong-field approximation and its extension for high-order harmonic generation with mid-infrared lasers

In recent years intense mid-infrared lasers with wavelength of a few microns have become the standard tools for research in strong field physics laboratories worldwide. These lasers offer the opportunities to extend the traditional study of high-order harmonics generation and attosecond sciences from the extreme ultraviolet to soft x-rays. In this tutorial we revisit the familiar strong field approximation and its simplification—the quantum orbits theory. We draw special emphasis on the factorization of laser induced dipole moment as the product of a returning electron wave packet with the photo-recombination dipole transition matrix element. The former depends on the laser properties only (up to a normalization constant) while the latter is related to laser-free photoionization transition dipole. The factorization leads to the suggested modification beyond the strong field approximation—the quantitative rescattering theory. In applying these theories to mid-infrared lasers, we analyze the behavior of the returning electron wave packet and its scaling properties vs the wavelength of the laser. A few examples are given to demonstrate how the quantitative rescattering theory is capable of reproducing experimental harmonic spectra under various conditions. Future opportunities in employing harmonics generated by optimized mid-infrared lasers for probing molecular structure and for serving as useful table-top coherent light sources up to the x-ray region are also discussed.

Molecular frame photoemission by a comb of elliptical high-order harmonics: a sensitive probe of both photodynamics and harmonic complete polarization state.

Due to the intimate anisotropic interaction between an XUV light field and a molecule resulting in photoionization (PI), molecular frame photoelectron angular distributions (MFPADs) are most sensitive probes of both electronic/nuclear dynamics and the polarization state of the ionizing light field. Consequently, they encode the complex dipole matrix elements describing the dynamics of the PI transition, as well as the three normalized Stokes parameters s1, s2, s3 characterizing the complete polarization state of the light, operating as molecular polarimetry. The remarkable development of advanced light sources delivering attosecond XUV pulses opens the perspective to visualize the primary steps of photochemical dynamics in time-resolved studies, at the natural attosecond to few femtosecond time-scales of electron dynamics and fast nuclear motion. It is thus timely to investigate the feasibility of measurement of MFPADs when PI is induced e.g., by an attosecond pulse train (APT) corresponding to a comb of discrete high-order harmonics. In the work presented here, we report MFPAD studies based on coincident electron-ion 3D momentum imaging in the context of ultrafast molecular dynamics investigated at the PLFA facility (CEA-SLIC), with two perspectives: (i) using APTs generated in atoms/molecules as a source for MFPAD-resolved PI studies, and (ii) taking advantage of molecular polarimetry to perform a complete polarization analysis of the harmonic emission of molecules, a major challenge of high harmonic spectroscopy. Recent results illustrating both aspects are reported for APTs generated in unaligned SF6 molecules by an elliptically polarized infrared driving field. The observed fingerprints of the elliptically polarized harmonics include the first direct determination of the complete s1, s2, s3 Stokes vector, equivalent to (ψ, ε, P), the orientation and the signed ellipticity of the polarization ellipse, and the degree of polarization P. They are compared to so far incomplete results of XUV optical polarimetry. We finally discuss the comparison between the outcomes of photoionization and high harmonic spectroscopy for the description of molecular photodynamics.

Electron-impact excitation of open d-shell ions

Astrophysics is driven by observations, and in the present era there are a wealth of state-of-the-art ground-based and satellite facilities. The astrophysical spectra emerging from these are of exceptional quality and quantity and cover a broad wavelength range. To meaningfully interpret these spectra, astronomers employ highly complex modelling codes to simulate the astrophysical observations. Important input to these codes include atomic data such as excitation rates, photoionization cross sections, oscillator strengths, transition probabilities and energy levels/line wavelengths. Due to the relatively low temperatures associated with many astrophysical plasmas, the accurate determination of electron-impact excitation rates in the low energy region is essential in generating a reliable spectral synthesis. Hence it is these atomic data, and the main computational methods used to evaluate them, which we focus on in this publication. We consider in particular the complicated open d- shell structures of the Fe-peak ions in low ionization stages. While some of these data can be obtained experimentally, they are usually of insufficient accuracy or limited to a small number of transitions.

Wigner time delay studies of photoionization of atomic zinc and cadmium

SynopsisWigner time delay has been studied in the shape resonance region for the outer nd→εf photoionization transitions in atomic Zn and Cd.

Photoionization of cobalt impurities in zinc oxide

Electron Spin Resonance investigations allow to attribute a broad absorption band below the band‐to‐band transition of ZnO:Co to photoionization transitions of Co‐ions. This absorption, with the onset at about 2.4–2.6 eV, is due to cobalt recharging, as concluded from the photo‐ESR and pulsed ESR experiments. In these experiments light sensitive ESR signals of Co2+ and shallow donor are observed. Their response to light favors cobalt 2+ to 3+ photoionization.

Sturmian approach to single photoionization of many electron atoms and molecules

The application of generalized Sturmian functions to the study of single photoionization of different atomic and molecular systems is illustrated using model potentials. Sturmian functions have been used successfully to study single and double ionization by electron impact on He, while their implementation to molecular systems is still under development. The radial part of the scattering function is expanded in a generalized Sturmian basis. The solution of the resulting matrix problem provides the expansion coefficients. The latter yield directly the photoionization transition amplitude and thus the cross sections. Here we show our preliminary results for He and Ne atoms on one hand, and for CH4 and H2O molecules on the other.