Journal of Physics B: Atomic, Molecular and Optical Physics

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.

This study investigates the dynamics of quantum batteries (QBs), focusing on the pivotal role of quantum entanglement in mediating inter-cellular energy transfer within a two-cell configuration (two-qubit), wherein one cell is directly coupled to the charging source. Employing the Lindblad master equation to model the system's evolution, the influence of coherent state amplitudes, detuning, inter-cellular coupling strength, and dissipation rates on stored energy, ergotropy, energy fluctuations, concurrence-quantified entanglement, and their parametric interrelations is scrutinized. Our results indicate a direct correlation between the entanglement qubits and the efficiency of energy transfer. In particular, stronger entanglement between the primary cell, which is connected to the charger, and the secondary cell leads to more energy transfer. Consequently, entanglement significantly improves energy transfer between the two qubits.

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.

The single-center convergent close-coupling method is utilized to calculate positron scattering from H-like ions from He⁺ to F⁸⁺. Results for the normalized annihilation rate ($Z_{\mathrm{eff}}$) and the electron-loss, elastic, and bound-state excitation cross sections are obtained for energies up to 10 keV. Excellent agreement is found between present and previous theoretical $Z_{\mathrm{eff}}$ results for He⁺, Li²⁺, B⁴⁺, and F⁸⁺. As there is no previous work for the remaining cross sections the results for electron-loss are presented alongside previous theory and experiment for incident electrons. The differences between these cross sections give an insight to the impact of the projectile charge on scattering from highly-charged ions.

Modern light sources such as free electron lasers allow tracking photoinduced events with unprecedented accuracy. Ion spectroscopy is a particularly useful tool, revealing for example momentum correlations in dissociation and Coulomb explosion patterns. Therefore, determining ion momenta and their relationship with the highest achievable accuracy is very valuable. Here, we develop a systematic approach to accurate ion momentum determination in Wiley–McLaren type ion time-of-flight spectrometers taking into account also field penetration effects. The developed analytical formulae at various levels of approximation are compared with ray tracing simulations and the effects are also illustrated in an experimental example.

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.

High-intensity laser fields can ionize atoms and molecules and also initiate molecular dissociation. This review is on the recent progress made using experiments that harness the potential of cold-target recoil-ion momentum spectroscopy and femtosecond laser pulses with tailored intense fields. The possibility to image the molecular structure and the orientation of small molecules via the detection of the momenta of the ions is illustrated. The process of non-adiabatic tunnel ionization is analyzed in detail focusing on the properties of the electronic wave packet at the tunnel exit. It is reviewed how the electron gains angular momentum and energy during tunneling in circularly polarized light. The electron is a quantum object with an amplitude and a phase. Most experiments in strong field ionization focus on the absolute square of the electronic wave function. The technique of holographic angular streaking of electrons enables the retrieval of Wigner time delays in strong field ionization, which is a property of the electronic wave function's phase in momentum space. The relationship between the phase in momentum space and the amplitudes in position space enables access to information about the electron's position at the tunnel exit. Finally, recent experiments studying entanglement in strong field ionization are discussed.

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 ^1,3S-, ^1,3P-, and ^1,3D-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 ^1,3D-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 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.
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 measure the lifetimes of several atomic autoionizing states.

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.

Short intense laser pulses are routinely used to induce rotational wave packet dynamics of molecules. Ro-vibrational wave packet dynamics has been explored comparatively infrequently, focusing predominantly on extremely light and rigid molecules such as H$_2^+$, H$_2$, and D$_2$. This work presents quantum mechanical calculations that account for the rotational {\em{and}} the vibrational degrees of freedom for a heavier and rather floppy diatomic molecule, namely the neon dimer. For pumping by a strong and short non-resonant pump pulse, we identify several phenomena that depend critically on the vibrational (i.e., radial) degree of freedom. Our calculations show (i) fingerprints of the radial dynamics in the alignment signal; (ii) laser-kick induced dissociative dynamics on very short time scales (ejection of highly structured "jets"); and (iii) tunneling dynamics that signifies the existence of resonance states, which are supported by the effective potential curves for selected finite relative angular momenta. Our theory predictions can be explored by existing state-of-the-art experiments.

We study the localization transition in spin-orbit (SO) coupled binary Bose-Einstein condensates (BECs) with collisional inhomogeneous interaction trapped in a one-dimensional quasiperiodic potential. Our numerical analysis shows that the competition between the quasiperiodic disorder and inhomogeneous interaction leads to a localization-delocation transition as the interaction strength is tuned from attractive to repulsive in nature. Furthermore, we analyse the combined effect of the SO and Rabi coupling strengths on the localization transition for different interaction strengths and obtain signatures of similar localization-delocalization transition as a function of SO coupling in the regime of weak interactions. We complement our numerical observation with the analytical model using the Gaussian variational approach. In the end, we show how the localization-delocalization is manifested in the quench dynamics of the condensate. Our study provides an indirect approach to achieve localization transition without tuning the quasiperiodic potential strength, but rather by tuning the inhomogeneity in the interaction.

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.

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 ^1,3S-, ^1,3P-, and ^1,3D-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 ^1,3D-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 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.
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 measure the lifetimes of several atomic autoionizing states.

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.

The single-center convergent close-coupling method is utilized to calculate positron scattering from H-like ions from He⁺ to F⁸⁺. Results for the normalized annihilation rate ($Z_{\mathrm{eff}}$) and the electron-loss, elastic, and bound-state excitation cross sections are obtained for energies up to 10 keV. Excellent agreement is found between present and previous theoretical $Z_{\mathrm{eff}}$ results for He⁺, Li²⁺, B⁴⁺, and F⁸⁺. As there is no previous work for the remaining cross sections the results for electron-loss are presented alongside previous theory and experiment for incident electrons. The differences between these cross sections give an insight to the impact of the projectile charge on scattering from highly-charged ions.

Motional Stark effect (MSE) measurements have been useful for characterizing the magnetic field structure in several tokamaks over the past decades. The Stark splitting in the emission spectrum of injected high-energy neutrals carries information about both the magnetic field strength and direction, although only the directional information is extracted in most measurements. There are several codes capable of simulating the spectrum emitted by neutral beams with the MSE included, aiding the design and utilization of beam emission spectroscopy or MSE diagnostic systems. In this paper, we compare two of such codes, namely Simulation of Spectra by M. v. Hellermann and CASPER based on Cherab & Raysect, both expected to play an important role in the synthetic-diagnostic toolbox of ITER. The basis of the benchmark is an ITER scenario representative of the machine's baseline performance, with emphasis on the relation between spectral components contributing to the background and the MSE spectrum itself. It was found that after carefully matching the inputs of the codes, the MSE simulations show generally good agreement, apart from a known issue regarding the sigma-to-pi line ratios. In terms of the two examined background components, bulk-ion charge exchange shows an overall good agreement, while the line radiation of the SOL region mirrors some fundamental differences in the modeling.

The interaction between freely propagating electrons and light waves is typically described using an approximation in which we assume that the electron velocity remains approximately the same during the interaction. In this article we analytically describe the dynamics of electrons in an interaction potential generated by an optical beat wave beyond this regime and find a structure of sharp electron distribution peaks that periodically alternate in the energy/momentum spectrum. In the classical description we analytically solve the nonlinear equation of motion, which is an analogy to the mathematical pendulum. While addressing the problem using quantum mechanics, we first use a parabolic approximation of the interaction potential and then we also study the evolution of the electron wavepacket in an infinite periodical potential. Using numerical simulations we show the classical and quantum evolution of the electron spectra during the interaction for different conditions and experimental settings.

We introduce a three-component model to determine the fractions of the beam in the metastable $1s2s\,^3\!S$ and $1s2s\,^1\!S$ states as well as in the $1s^2$ ground state, in high-energy ($\mathrm{MeV}\,\mathrm{u}^{-1}$) He-like ion beams produced through charge stripping in foil or gas. This model extends the previous two-component model (Benis and Zouros 2016 J. Phys. B 49 235202), incorporating new analytical expressions in a more comprehensive treatment. We also assume that the initially produced $^1\!S$ fraction, $f_0[^1\!S]$, at the stripper, can be described by the formula $\alpha_0f_0[^3\!S] + \beta_0$, where $\alpha_0 = 1/3$ is derived from spin statistics as also used in the past, while β₀ is a new parameter which accounts for ion excitation processes in the stripper which conserve the singlet spin, not previously considered. We apply our three-component model with values of $\beta_0 = 0\%-30\%$ to published results on C⁴⁺ and O⁶⁺ mixed-state ion beams based on the older two-component model. Our re-analysis shows that including non-negligible (∼10%–20%) amounts of the $^1\!S$ component in our three-component treatment can further improve agreement between theory and experiment in most cases.

We discuss the trapping of heteronuclear diatomic molecules prepared in their electronic and vibrational ground states. We tune and shape the trapping potential for bosonic polar molecules in superpositions of rotational states by dressing rotational excitations with a static sextupole electric field. The translational motion of a molecule is treated classically. We examine the Hamiltonian which governs the center of mass dynamics. The effective potential has a global minimum that provides the trapping ability of this trap. The first term of its Taylor series expansion, corresponding to the quadratic Stark shifts, results in the integrable potential. In terms of cylindrical coordinates the center of mass Hamiltonian splits into axial and radial parts. Corresponding trajectories are parameterized by elliptic functions. At low electric fields, the non-approximated Hamiltonian is treated as a small perturbation of the mentioned integrable system described by Kolmogorov–Arnold–Moser theory. The applicability of this approximation is discussed and illustrated using the Poincaré cross-section method. We present results of numerical simulations illustrating the trapping and confinement of a polar molecule in the trap.

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 syn- chrotron 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 sec- tions 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 ≤ 100 meV) due to 2p → nd 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 hav- ing three open subshells. Strong and wide (typically ∼ 1 eV) Rydberg series of resonances due to 2s → np excitations dominate above the 2p threshold.