Table of contents

Resonances leave prominent signatures in atomic and molecular ionization triggered by the absorption of single or multiple photons. These signatures reveal various aspects of the ionization process, characterizing both the initial and final states of the target. Resonant spectral features are typically associated with sharp variations in the photoionization phase, providing an opportunity for laser-assisted interferometric techniques to measure this phase and to convert it into a photoemission time delay. This time delay offers a precise characterization of the timing of the photoemission process. In this review, a unified approach to resonant photoionization is presented by examining the analytic properties of ionization amplitude in the complex photoelectron energy plane. This approach establishes a connection between the resonant photoemission time delay and the corresponding photoionization cross-section. Numerical illustrations of this method include: (i) giant or shape resonances, where the photoelectron is spatially confined within a potential barrier, (ii) Fano resonances, where bound states are embedded in the continuum, (iii) Cooper minima (anti-resonances) arising from kinematic nodes in the dipole transition matrix elements, and (iv) confinement resonances in atoms encapsulated within a fullerene cage. See figure 1 for graphical illustration. The second part of this review focuses on two-photon resonant ionization processes, where the photon energies can be tuned to a resonance in either the intermediate or final state of the atomic target. Our examples include one- or two-electron discrete excitations both below and above the ionization threshold. These resonant states are probed using laser-assisted interferometric techniques. Additionally, we employ laser-assisted photoemission to determine the lifetimes of several atomic autoionizing states.

The recently observed strong-field photoelectron holographic pattern, 'the spiral', is considered as an ideal structure for target probing and the resolution of ultrafast dynamics. This intracycle interference pattern evolves into a carpet-like structure in multicycle laser pulses and is too indistinguishable in the photoelectron momentum distribution to be directly employed as a holographic tool. Using a semiclassical quantum-trajectory Monte Carlo model, we provide a laser field scheme for visualization of the spiral by adding a weak 1600 nm circularly polarized field to the 800 nm linearly polarized fundamental field. The results are verified by solving the time-dependent Schrödinger equation. Furthermore, by combining the variation of the relative phase between the two colors with the rotation direction of the circularly polarized field, we achieved the precise manipulation of the fringe direction of the spiral. Our investigation shows that these are based on the modulation of the proportion of the spiral produced in each single laser cycle, rather than that of the birth time difference between the two types of rescattering electrons that form the spiral.

We present absolute L-shell photoionisation cross sections for the S⁺, S²⁺, S³⁺ ions. The cross sections were obtained using the monochromatised photon beam delivered by the SOLEIL synchrotron source coupled with an ion beam extracted from an electron cyclotron resonance source (ECRIS) in the merged dual-beam configuration. The cross sections for single, double and triple ionisation were measured and combined to generate total photoionisation cross sections. For each of the S⁺, S²⁺ and S³⁺ ions, the photon energy regions corresponding to the excitation and ionisation of a 2p or a 2s electron (∼175–230 eV) were investigated. The experimental results are interpreted with the help of multiconfigurational Dirac–Fock (MCDF) and Breit–Pauli R-Matrix (BPRM) or Dirac R-Matrix (DARC) theoretical calculations. The former generates photoabsorption cross sections from eigenenergies and eigenfunctions obtained by solving variationally the multiconfiguration Dirac Hamiltonian while the latter calculate cross sections for photon scattering by atoms. The cross sectional spectra feature rich resonance structures with narrow natural widths (typically $\unicode{x2A7D}$100 meV) due to $2p\rightarrow n{\textrm{d}}$ excitations below and up to the $2p$ thresholds. This behaviour is consistent with the large number of inner-shell states based on correlation and spin–orbit mixed configurations having three open subshells. Strong and wide (typically ∼1 eV) Rydberg series of resonances due to $2s\rightarrow n{\textrm{p}}$ excitations dominate above the $2p$ threshold.

The effect of impenetrable spherical confinement on alkali systems (H, Li) has been thoroughly examined, emphasizing the distinctive high-momentum oscillatory behavior of the momentum space radial density. We have utilized the Ritz variational framework with a Slater-type basis set to derive the position-space wavefunction and Fourier–Dirac transformation of the former to find the momentum-space wavefunction, analytically. The derived momentum-space density has been analyzed in four asymptotic limits ($R \rightarrow \infty$, $R \rightarrow 0$, $p \rightarrow \infty$, and $p \rightarrow 0$; R being the confinement radius and p being the radial component of linear momentum) and its oscillatory behavior in strong spatial confinement region is critically investigated. Oscillatory behavior is also noticed in the Compton profile of the compressed atomic system. Furthermore, the effects of confinement on Shannon information entropy in both position and momentum spaces are investigated, offering insights into the Bialynicki–Birula–Mycielski inequality and the local variations of information measures in terms of Shannon entropy density.

We present a theoretical study of the inelastic scattering of vortex electrons by a hydrogen atom. In our study, special emphasis is placed on the effects of the Coulomb interaction between a projectile electron and a target atom. To understand these effects, we construct vortex electron wave functions both from free space and distorted solutions of the Schrödinger equation. These wave functions give rise to the first Born and distorted wave scattering amplitudes, respectively. The derived theory has been employed to investigate the $1s \rightarrow 2p$ transition of a hydrogen atom induced by electrons with the kinetic energies in the range from 20 to 100 eV. The results of the calculations have clearly indicated that the Coulomb interaction can significantly affect the phase pattern and probability density of a vortex electron beam as well as the squared transition amplitudes. For the latter, the most pronounced effect was found for the excitation to the $\vert 2p\, m_f = 0\rangle$ sublevel and large scattering angles.

Three-body recombination (TBR) of helium atoms at cold collision energies is studied using the hyperspherical adiabatic method with different realistic interaction potentials. By considering zero angular momentum J = 0 states as well as J > 0 states, we calculate the ⁴He TBR rates up to about 0.1 Kelvin, and analyze the influence of modern potentials on the recombination rates. We also calculate and analyze the collision induced dissociation rates.

We investigate the fundamental three-body Coulomb process of elastic electron–positronium (e⁻-Ps) scattering below the Ps(n = 2) threshold. Using the complex Kohn variational method and trial wave functions that contain highly correlated Hylleraas-type terms, we accurately compute $^{1,3}$S-, $^{1,3}$P-, and $^{1,3}$D-wave phase shifts, which may be considered as benchmark results. We explicitly investigate the effect of the mixed symmetry term in the short-range part of the $^{1,3}$D-wave trial wave function on the phase shifts and resonances. Using the complex Kohn phase shifts we compute, for e⁻-Ps scattering, the elastic differential, elastic integrated, momentum-transfer, and ortho-para conversion cross sections and determine the importance of the complex Kohn D-wave phase shifts on these cross sections. In addition, using the short-range part of the ¹S-wave trial wave function for the bound-state of the purely leptonic ion of Ps⁻, and the complex Kohn ¹P trial wave function for the continuum state, we determine the Ps⁻ photodetachment cross section in the length, velocity, and acceleration forms.

We implement an independent-atom and independent-electron model to investigate the collision systems of He²⁺ and He⁺ ion projectiles impinging on a neon dimer target. The dimer is set to be stationary at its equilibrium bond length with the projectile traveling parallel to the dimer axis at a speed corresponding to the collision energy of 10 keV amu⁻¹. Two approaches, namely multinomial and determinantal, are used as an analysis of these collisions. Each of the analyses is broken down into two types of models that do not and do include a change in the projectile charge state due to electron capture from the dimer. All calculations are performed using both a frozen atomic target and a dynamic response model using the coupled-channel two-center basis generator method for orbital propagation. All one-electron and two-electron removal processes are calculated, though particular attention is paid to those that result in the Ne⁺-Ne⁺ fragmentation channel due to its association with interatomic Coulombic decay (ICD). For He²⁺ impact, we find that Ne(2s) electron removal is strong across all analyses and models, which is in line with previous results that show that ICD contributes to dimer fragmentation through that channel. We also find indications that there is a pure ICD yield when utilizing a He⁺ projectile and applying the model that takes into account the change in projectile charge state.

Faraday rotation spectroscopy and absorption spectroscopy are performed simultaneously in a dual comb spectroscopy arrangement with quantum cascade laser combs operating at ∼8 μm. The system uses free-running laser combs that provide ∼70 cm⁻¹ spectral coverage and ∼2 MHz spectral resolution. Detection of NO₂ in an equilibrium mixture with N₂O₄ and N₂O is used to demonstrate selective measurements of paramagnetic NO₂ in the presence of spectrally interfering diamagnetic species.

Non-Hermitian quantum systems showcase many distinct and intriguing features with no Hermitian counterparts. One of them is the exceptional point which marks the $\mathcal{PT}$ (parity and time) symmetry phase transition, where an enhanced spectral sensitivity arises and leads to novel quantum engineering. Here we theoretically study the multipartite entanglement properties in non-Hermitian superconducting qubits, where high-fidelity entangled states can be created under strong driving fields or strong couplings among the qubits. Under an interplay between driving fields, couplings, and non-Hermiticity, we focus on generations of GHZ states or GHZ classes in three and four qubits with all-to-all couplings, which allows a fidelity approaching unity when relatively low non-Hermitian decay rates are considered. This presents an ultimate capability of non-Hermitian qubits to host a genuine and maximal multipartite entanglement. Our results can shed light on novel quantum engineering of multipartite entanglement generations in non-Hermitian qubit systems.