Journal of Physics B: Atomic, Molecular and Optical Physics

We introduce a complex scaling discrete dipole approximation (CSDDA) method and study single-shot x-ray diffraction patterns from non-spherical, absorbing nanotargets in the limit of linear response. The convergence of the employed Born series-based iterative solution of the discrete dipole approximation problem via optimal complex mixing turns out to be substantially faster than the original approach with real-valued mixing coefficients, without additional numerical effort per iteration. The CSDDA method is employed to calculate soft x-ray diffraction patterns from large icosahedral silver nanoparticles with diameters up to about $250\;\mathrm{nm}$. Our analysis confirms the requirement of relatively long wavelengths to map truly 3D structure information to the experimentally accessible regions of 2D scattering images. On the other hand, we show that short wavelengths are preferable to retain visibility of fine structures such as interference fringes in the scattering patterns when using ultrashort x-ray pulses in the attosecond domain. A simple model is presented to estimate the minimal pulse duration below which the fringe contrast vanishes. Knowledge of the impact of the bandwidth of short pulses on the diffraction images is important to extract information on ultrafast dynamical processes from time-resolved x-ray diffractive imaging experiments on free nanoparticles, in particular at long wavelengths.

Measurements of the positronium (Ps) energy and formation fraction in reflection and transmission from a thin meso-structured silica target have been conducted using single-shot positron annihilation lifetime spectroscopy and Doppler spectroscopy. The silica sample is made using glancing angle deposition of vaporized SiO₂ on a suspended thin carbon foil. Optical access through the silica sample facilitates measurement of the longitudinal Ps energy, and the Ps energy in the reflection geometry is found to decrease with positron energy as expected, with a minimum achievable Ps energy of 0.203(12) and 0.26(3) eV for the transverse and longitudinal directions, respectively. In the transmission geometry cooling of Ps becomes evident at the minimum positron impact energy required for the positrons to penetrate the carbon foil and enter the meso-structured silica. The minimum energies for this geometry are 0.210(12) and 0.287(14) eV in the transverse and longitudinal directions, respectively, and the minimum achievable Ps energy is found to be limited by the thickness of the structured silica target, since the same energy was found in both geometries.

Attosecond science, born at the beginning of this century with the generation of the first bursts of light with durations shorter than a femtosecond, has opened the way to look at electron dynamics in atoms and molecules at its natural timescale. Thus controlling chemical reactions at the electronic level or obtaining time-resolved images of the electronic motion has become a goal for many physics and chemistry laboratories all over the world. The new experimental capabilities have spurred the development of sophisticated theoretical methods that can accurately predict phenomena occurring in the sub-fs timescale. This review provides an overview of the capabilities of existing theoretical tools to describe electron and nuclear dynamics resulting from the interaction of femto- and attosecond UV/XUV radiation with simple molecular targets. We describe one of these methods in more detail, the time-dependent Feshbach close-coupling (TDFCC) formalism, which has been used successfully over the years to investigate various attosecond phenomena in the hydrogen molecule and can easily be extended to other diatomics. In addition to describing the details of the method and discussing its advantages and limitations, we also provide examples of the new physics that one can learn by applying it to different problems: from the study of the autoionization decay that follows attosecond UV excitation to the imaging of the coupled electron and nuclear dynamics in H₂ using different UV-pump/IR-probe and UV-pump/UV-probe schemes.

This topical review addresses how Rydberg atoms can serve as building blocks for emerging quantum technologies. Whereas the fabrication of large numbers of artificial quantum systems with the uniformity required for the most attractive applications is difficult if not impossible, atoms provide stable quantum systems which, for the same species and isotope, are all identical. Whilst atomic ground states provide scalable quantum objects, their applications are limited by the range over which their properties can be varied. In contrast, Rydberg atoms offer strong and controllable atomic interactions that can be tuned by selecting states with different principal quantum number or orbital angular momentum. In addition Rydberg atoms are comparatively long-lived, and the large number of available energy levels and their separations allow coupling to electromagnetic fields spanning over 6 orders of magnitude in frequency. These features make Rydberg atoms highly desirable for developing new quantum technologies. After giving a brief introduction to how the properties of Rydberg atoms can be tuned, we give several examples of current areas where the unique advantages of Rydberg atom systems are being exploited to enable new applications in quantum computing, electromagnetic field sensing, and quantum optics.

A one-dimensional bosonic gas with strong contact repulsion and attractive non-local interactions may form a quantum droplet with a flat-top density profile. We focus on a system in the Tonks–Girardeau limit of infinitely strong contact repulsion. We show that the main system features are the same for a broad class of non-local interaction potentials. Then, we focus on a limiting case, the one of slowly varying density profiles, to find approximate formulas for the surface and bulk energies of a droplet. We further characterise the system by numerically finding the excitation spectrum. It consists of two families: phononic-like excitations inside droplets and scattering modes. Analysis within the linearised regime is supplemented with the full, nonlinear dynamics of small perturbations.

We employ the Markov approximation and the well-known Fresnel-integral to derive in 'one-line' the familiar expression for the Landau–Zener transition probability. Moreover, we provide numerical as well as analytical justifications for our approach, and identify three characteristic motions of the probability amplitude in the complex plane.

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.

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.

Atom-based measurements of length, time, gravity, inertial forces and electromagnetic fields are receiving increasing attention. Atoms possess properties that suggest clear advantages as self calibrating platforms for measurements of these quantities. In this review, we describe work on a new method for measuring radio frequency (RF) electric fields based on quantum interference using either Cs or Rb atoms contained in a dielectric vapor cell. Using a bright resonance prepared within an electromagnetically induced transparency window it is possible to achieve high sensitivities, <1 μV cm⁻¹ Hz^−1/2, and detect small RF electric fields $\lt 1$ μV cm⁻¹ with a modest setup. Some of the limitations of the sensitivity are addressed in the review. The method can be used to image RF electric fields and can be adapted to measure the vector electric field amplitude. Extensions of Rydberg atom-based electrometry for frequencies up to the terahertz regime are described.

We investigate generation of nonclassical photon states via conditional measurement process in a two mode coupled waveguide. Interaction of the fields takes place in a waveguide beamsplitter due to the overlap between normal modes supported therein. A quadratic Hamiltonian of two degrees of freedom describes the hopping interaction. An initial two mode squeezed state undergoes a unitary evolution governed by the interaction Hamiltonian for a specified time. Following this the bipartite state is subjected to a projective measurement that detects nth Fock state in one subsystem. The post-measurement excitation rendered in the residual subsystem depends on the prior time of interaction between the modes as well as the interaction strength. The Wigner quasiprobability distribution of an arbitrary post-selection state is computed. Its nonclassicality is examined via the negativity of the Wigner distribution. The sub-Poissonian nature of the photon statistics is revealed by the Mandel parameter. The dynamically generated squeezing is evidenced in the post-measurement state. In the ultrastrong coupling regime the parity even and odd states display markedly different nonclassical properties. The nonclassicality of the post-measurement states obtained here may be controlled by varying the interaction strength and the time span of interaction between the modes.

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.

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 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.

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 development of atomic many-body methods, capable of incorporating electron correlation effects accurately, is required for isotope shift (IS) studies. In combination with precise measurements, such calculations help to extract nuclear charge radii differences, and to probe for signatures of physics beyond the Standard Model of particle physics. We review here a few recently-developed methods in the relativistic many-body perturbation theory (RMBPT) and relativistic coupled-cluster (RCC) theory frameworks for calculations of IS factors in the highly charged ions (HCIs), and neutral or singly-charged ions, respectively. The results are presented for a wide range of atomic systems in order to demonstrate the interplay between quantum electrodynamics (QED) and electron correlation effects. In view of this, we start our discussions with the RMBPT calculations for a few HCIs by rigorously treating QED effects; then we outline methods to calculate IS factors in the one-valence atomic systems using two formulations of the RCC approach. Then we present calculations for two valence atomic systems, by employing the Fock-space RCC methods. For completeness, we briefly discuss theoretical input required for the upcoming experiments, their possibilities to probe nuclear properties and implications to fundamental physics studies.

Electron–molecule collisions drive many natural phenomena and are playing an increasing role in modern technologies. Over recent years, studies of the collision processes have become increasingly driven by quantum mechanical calculations rather than experiments. This tutorial surveys important issues underlying the physics and theoretical methods used to study electron–molecule collisions. It is aimed at nonspecialists with suitable references for further reading for those interested and pointers to software for those wanting to perform actual calculations.

Ultralong-range Rydberg molecules (ULRMs) comprise a Rydberg atom in whose electron cloud are embedded one (or more) ground-state atoms that are weakly-bound through their scattering of the Rydberg electron. The existence of such novel molecular species was first predicted theoretically in 2000 but they were not observed in the laboratory until 2009. Since that time, interest in their chemical properties, physical characteristics, and applications has increased dramatically. We discuss here recent advances in the study of ULRMs. These have yielded a wealth of information regarding low-energy electron scattering in an energy regime difficult to access using alternate techniques, and have provided a valuable probe of non-local spatial correlations in quantum gases elucidating the effects of quantum statistics. Studies in dense environments, where the Rydberg electron cloud can enclose hundreds, or even thousands, of ground-state atoms, have revealed many-body effects such as the creation of Rydberg polarons. The production of overlapping clouds of different cold atoms has enabled the creation of heteronuclear ULRMs. Indeed, the wide variety of atomic and molecular species that can now be cooled promises, through the careful choice of atomic (or molecular) species, to enable the production of ULRMs with properties tailored to meet a variety of different needs and applications.

With the availability of modern laser and detection technologies, the investigation of ultrafast molecular dynamics induced by intense laser pulses has become a routine practice. In this Topical Review, we present a survey of recent progress in the timing and control of ultrafast molecular dynamics, encompassing processes initiated by both extreme ultraviolet and near infrared pulses. Prospects and perspectives of this field are given. This Review underscores the remarkable potential for further advances in understanding and harnessing ultrafast molecular processes.

The dissociation dynamics of diiodomethane molecules (CH2I2) have been investigated following absorption of 98 eV XUV photons. In the measurement at the reaction microscope endstation at the free-electron laser FLASH2, ionic fragments created by 4d core ionisation followed by Auger decay have been detected in coincidence. In the one-photon absorption channel CH2+ / I+ / I+, a concerted three-ion breakup and a sequential dissociation via a rotating intermediate CH2I++ ion have been identified. Classical simulations based on a Coulomb repulsion model and ab initio molecular dynamics in the frame of the Density Functional Theory have been performed. Both types of simulations reproduce different aspects of the observed fragmentation dynamics, in particular a delayed second bond break after dissociation of the first iodine ion. In the study of the potential energy surface we have located a minimum after the emission of the first I+. We attribute the sequential mechanism to the trapping of the rotationally excited CH2I++ fragment in this transient intermediate, which corresponds to a potential energy well that protects it against the cleavage of the second C-I bond.

Gaining insight into the interaction of charged particles with nitrous oxide (N₂O) is crucial for advancing our understanding of atmospheric processes and the environmental impacts of N₂O. N₂O plays a pivotal role in climate change, specifically contributing to global warming in the troposphere and ozone depletion in the stratosphere. In addition, it is of great importance in the fields of plasma physics, atomic and molecular physics, laser physics, and medicine. The cross sectional data obtained from collision studies provide fundamental information about the dynamics involved in the few-body system under investigation. This paper presents electron impact double differential cross sections (DDCSs) for secondary electrons emitted from N₂O molecules. The measurements were conducted within fixed incident electron energy ranges of 50-350 eV, covering emission angles between 30° and 130°. Notably, a forward-backward angular asymmetry has been observed in the angular distribution of the DDCS for the detected electrons.&#xD;

Molecular ions formed in cold hybrid ion-atom experiments may find interesting applications ranging from precision measurements to controlled chemical reactions. Here, we investigate electronic structure of the Sr₂⁺ molecular ion, which may be produced by photoassociation of laser-cooled Sr⁺ ions immersed into an ultracold gas of Sr atoms or by ionization of ultracold Sr₂ molecules. Using ab initio electronic structure methods, such as the coupled cluster and configuration interaction ones with small-core relativistic energy-consistent pseudopotentials and large Gaussian basis sets, we calculate potential energy curves for the ground and 41 excited electronic states, and electric dipole transition moments between them. We show that alkaline-earth molecular ions despite of their apparently simple structure with three valence electrons only are challenging for state-of-the-art quantum chemistry methods due to their multireference nature and high density of states. Finally, we calculate and analyze Franck-Condon factors governing the photoionization of ground-state Sr₂ molecules into ²Σ_u⁺ and ²Σ_g⁺ states of Sr₂⁺ molecular ions. The present results may be useful for studying and guiding formation and spectroscopy of cold Sr₂⁺ molecular ions.

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.

The dissociation dynamics of diiodomethane molecules (CH2I2) have been investigated following absorption of 98 eV XUV photons. In the measurement at the reaction microscope endstation at the free-electron laser FLASH2, ionic fragments created by 4d core ionisation followed by Auger decay have been detected in coincidence. In the one-photon absorption channel CH2+ / I+ / I+, a concerted three-ion breakup and a sequential dissociation via a rotating intermediate CH2I++ ion have been identified. Classical simulations based on a Coulomb repulsion model and ab initio molecular dynamics in the frame of the Density Functional Theory have been performed. Both types of simulations reproduce different aspects of the observed fragmentation dynamics, in particular a delayed second bond break after dissociation of the first iodine ion. In the study of the potential energy surface we have located a minimum after the emission of the first I+. We attribute the sequential mechanism to the trapping of the rotationally excited CH2I++ fragment in this transient intermediate, which corresponds to a potential energy well that protects it against the cleavage of the second C-I bond.

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 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.

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.

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.

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.

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.

We show that perfect revivals of Rabi oscillations are possible, under certain conditions, in the population inversion of a trapped ion. Based on this property, we find that Schrödinger cat states of the atomic motion are naturally generated by the unitary dynamics. Using a pair of symmetric and antisymmetric Schrödinger cat states of motion, together with an electronic excited or ground state, we find that the interaction leads to four orthonormal maximally entangled states or hybrid Bell states as they are encoded in two partitions of different nature. We also study a quadratic Kerr-type evolution that is possible for short interaction times.