Table of contents

In a recent experiment (Wagner et al 2006 Proc. Natl Acad. Sci. USA103 13279) on SF₆, a high-harmonic generating laser pulse is preceded by a pump pulse which stimulates Raman-active modes in the molecule. Varying the time delay between the two pulses modulates high harmonic intensity, with frequencies equal to the vibration frequencies of the Raman-active modes. We propose an explanation of this modulation as a quantum interference between competing pathways that occurs via adjacent vibrational states of the molecule. The Raman and high harmonic processes act as beamsplitters, producing vibrational quantum beats among the Raman-active vibrational modes that are excited by the first pulse. We present an improved version of the widely used three-step model, which tracks the evolution of the molecule's vibrational state and employs a rigorous treatment of the complicated electron–molecule recombination.

The control of quantum dynamics via specially tailored laser pulses is a long-standing goal in physics and chemistry. Partly, this dream has come true, as sophisticated pulse-shaping experiments allow us to coherently control product ratios of chemical reactions. The theoretical design of the laser pulse to transfer an initial state to a given final state can be achieved with the help of quantum optimal control theory (QOCT). This tutorial provides an introduction to QOCT. It shows how the control equations defining such an optimal pulse follow from the variation of a properly defined functional. We explain the most successful schemes to solve these control equations and show how to incorporate additional constraints in the pulse design. The algorithms are then applied to simple quantum systems and the obtained pulses are analysed. Besides the traditional final-time control methods, the tutorial also presents an algorithm and an example to handle time-dependent control targets.

We have calculated static and frequency-dependent polarizabilities for the ground states of neutral Na and four sodium-like ions Mg⁺, Al²⁺, Si³⁺ and P⁴⁺. The polarizability is expressed in terms of the second-order energy correction, when the electric field is treated as a perturbation. The zero- and first-order wavefunctions are expressed as configuration interaction expansions. The radial parts of the one-electron functions are optimized, some on the ground or first excited state energies, others on the second-order energy correction (i.e. the polarizability). The wavefunctions can also be used as target state functions in electron–atom and electron–ion scattering.

Atomic data for electron impact ionization of all the elements from H to Ge are reviewed, the rates for these processes needing to be regularly updated following the publication of new experimental data and new theoretical calculations. Experimental cross sections, along with specific theoretical calculations when experimental data are missing, are fitted as functions of the electron energy, and from these fits ionization rate coefficients can be evaluated. It has been possible to take into account all elements but not all charge states of every element. Since the purpose of the paper is to update the ionization data evaluated and proposed in previous review papers, it is discussed if modifications are needed for the ions not considered. For highly ionized ions starting from the Ne-like iso-electronic sequence corrections do not appear necessary. On the other hand, except for Fe, for slightly ionized ions, specifically below the S-like iso-electronic sequence, the previously proposed data often underestimate the total ionization cross section, since only direct ionization channels have been considered and indirect processes have been neglected. Multiplicative correction coefficients are given to agree with recently published theoretical calculations. Experimental ionization data are considered, even when the presence of populated metastable levels (related to the electron density inside the source) is reported in the ion beams involved in the cross-section data measurements. We deem such a procedure acceptable when the proposed rates have to be included in codes that simulate the impurity behaviour in magnetic-confinement fusion devices, i.e., when radial transport is added to ionization and recombination to predict spatially resolved charge-state distributions. On the other hand, for astrophysical plasmas the contributions of metastable levels to the experimental data may represent a serious problem since, generally, the values of the electron densities that are involved are much lower than those in the ion sources. However, we critically investigated this problem and we found that the presence of metastables does not significantly modify the rates of most of the ions apart from a dozen. For this set of ions we provide different, corrected rates. Recombination is not considered since a review has been recently published.

Normalized differential cross sections for elastic electron scattering from ethylene (C₂H₄) are reported. The measurements are obtained using a novel version of the relative flow method with helium as the standard gas. Here, the relative flow method is applied without any prior knowledge of the gas kinetic molecular diameters of either the standard gas whose differential cross sections for electron scattering are known or the unknown gas whose differential cross sections for electron scattering need to be determined. Removal of this restriction is made possible by using an aperture-collimating source of the target gas instead of a conventional tube source. Importantly, the present method is accurate and more rapid than past elastic electron scattering experiments using the relative flow method, which employed tube-collimating gas sources. Our present measurements are used to test the reliability of past measurements for ethylene and so to resolve a recent disagreement between theory and experiment concerning the elastic electron scattering differential cross-section data for ethylene at low energy, by providing experimental values independent of any systematic errors that might arise when estimating gas kinetic molecular diameters for large polyatomics. Our new arrangement also extends the relative flow method to be applicable to gases whose gas kinetic molecular diameters may not be available, such as gaseous biomolecules.

We theoretically examine the rotation of an atomic Bose–Einstein condensate in an elliptical trap, both in the absence and presence of a quantized vortex. Two methods of introducing the rotating potential are considered—adiabatically increasing the rotation frequency at fixed ellipticity, and adiabatically increasing the trap ellipticity at fixed rotation frequency. Extensive simulations of the Gross–Pitaevskii equation are employed to map out the points where the condensate becomes unstable and ultimately forms a vortex lattice. We highlight the key features of having a quantized vortex in the initial condensate. In particular, we find that the presence of the vortex causes the instabilities to shift to lower or higher rotation frequencies, depending on the direction of the vortex relative to the trap rotation.

The lattice time-dependent Schrödinger equation (LTDSE) and atomic orbital close coupling (AOCC) methods are applied to calculate the charge transfer cross sections for H⁺ + He⁺ and He²⁺ + Li²⁺ collisions in the velocity range of 0.5–4.0 atomic units. The comparison of the results is made with those of other theoretical methods and with measurements. This analysis is used to provide a test of the accuracy of LTDSE and AOCC, and to help establish a consensus of theoretical results in comparison with the measurements for these ion–ion collisions.

We investigate the case of the Xe 5s angular distribution in the region of the second Cooper minimum covering a photon energy region from 80 to 280 eV. We observe a strong drop in the Xe 5s β value from 2.0, reaching a minimum of 1.669(8) at a photon energy of 150 eV. Our results are in good accord with a previously published measurement on the low-energy side of this minimum, but show a much slower return to β = 2.0 on the high-energy side of the minimum. We also compare our results to several different theoretical calculations and find excellent agreement with a relativistic time-dependent density functional theory calculation.

Resonance parameters for more than 1700 doubly excited states in ³S, ³P^o,e and ³D^e,o manifolds up to N = 5 threshold are obtained by means of the B-spline K-matrix method with maximum orbital angular momentum ℓ_max = 8. Excellent agreement is found with the best available data in the literature. A detailed analysis of the resonances based on the propensity rules for all relevant channels arranged in schematic patterns allows one to classify the series according to the usual approximate models. The analysis, made possible by the extended energy range considered, helps to asses the limits of these models for the triplet series and discloses the occurrence of nine intruder states and many 'collisions' between resonance series.

Methane and deuteromethane molecules were core ionized using synchrotron radiation, and the ionic fragments from the molecular dissociation were detected in coincidence with the Auger electrons. The electron–ion coincidence spectra are analysed in terms of partial ion yields and ion kinetic energy distributions, both as functions of electron kinetic energy. The dependence of the fragmentation patterns on the electronic character of the Auger final states as well as on the excess energy available for dissociating the molecule is studied. The analysis reveals marked differences in the dissociation of the 2a⁻²₁ and 2a⁻¹₁1t⁻¹₂ states, interpreted as an 'excess-energy-dependent' concerted dissociation process for the 2a⁻²₁ state and an 'electronic-state-dependent' sequential process for the 2a⁻¹₁1t⁻¹₂ state.

We describe simulations that illustrate the possibility for manipulating the position correlation of atoms in a magneto-optical trap (MOT) using the dipole–dipole interaction. The control scheme utilizes a narrow band laser that is detuned to the high-frequency side of a single-photon Rydberg transition in an isolated atom. As two atoms move near each other, they can be laser excited to repelling diatomic Rydberg–Rydberg potential energy curves which halt their approach. By chirping the laser from large to small detunings, atoms in a MOT can be pushed apart by dipole–dipole forces, thereby controlling nearest-neighbor interactions. Alternatively, by holding the frequency of the Rydberg excitation laser fixed as the MOT is loaded, it should be possible to limit the minimum distance between atoms to a prescribed value.

The total interaction cross sections (σ_t) of some sugars and amino acids and five elements: lithium, carbon, oxygen, aluminium and calcium have been measured for 6.4 keV, 13.95 keV, 14.4 keV, 17.74 keV, 24.14 keV, 30.8 keV, 35 keV, 59.54 keV, 81 keV, 122 keV and 136 keV photons in a narrow beam good geometry set up, by using high resolution detectors such as a Si-PIN diode detector and a high purity germanium detector. The σ_t values have been used in a matrix method to evaluate the effective atomic numbers Z_eff of the samples from their effective atomic cross sections σ_a. The effective atomic cross section of a sample σ_a is the total interaction cross section divided by the total number of atoms of all types in it. Further, a quantity called the effective atomic weight A_eff of a sample was defined as the ratio of the molecular weight A to the total number of atoms of all types in it. The variation of Z_eff was systematically studied with respect to A_eff as well as σ_a at each experimental energy separately and new semi-empirical relations for Z_eff have been evolved. It is felt that these relations can be very convenient for determining the effective atomic number of any sample having H, C, N and O atoms in the energy range 6.4 keV–136 keV irrespective of its chemical structure.

Multiparty remote state preparation (MRSP) is a procedure for multiparty collaboration with each other for remote preparation of a known quantum state to a distant party. We show that it is possible to achieve a unity fidelity remote preparation of the state by properly choosing the measurement basis. This protocol may be used for converging the split information at one point.

The notion of quasi-angular momentum is introduced to label the eigenstates of a Hamiltonian with a discrete rotational symmetry. This concept is recast in an operatorial form where the creation and annihilation operators of a Hubbard Hamiltonian carry units of quasi-angular momentum. Using this formalism, the ground states of ultracold gases of non-interacting fermions in rotating optical lattices are studied as a function of rotation, and transitions between states of different quasi-angular momentum are identified. In addition, previous results for strongly-interacting bosons are re-examined and compared to the results for non-interacting fermions. Quasi-angular momentum can be used to distinguish between these two cases. Finally, an experimentally accessible signature of quasi-angular momentum is identified in the momentum distributions of single-particle eigenstates.

Strong field high harmonic generation (HHG) can reveal the quantum structure of the source molecule. We calculate the effect of interference between the recombining photoelectron and the orbital from which it was field ionized in the single-active-electron standard picture of HHG in N₂ and CO₂. We compare our results for the highest occupied molecular orbitals (HOMO's) to the predictions of a popular two-point scattering model. For N₂, we find an agreement for very large internuclear separations and no agreement for the ground-state internuclear distance. We reduce the arguments to the Fourier transform of the HOMO, which depends on the internuclear separation. For CO₂, we distinguish between two geometries. For one of these, we find a perfect agreement with the two-point scattering model; however, the emitted radiation is not phase matched in this case. The experimentally accessible radiation does not agree with the simple model.

We investigate the classical rotational dynamics of a one-dimensional chain of molecules with permanent electric dipole moments. The molecules are coupled via their dipolar interactions. Low excitations are studied by inspecting the first- and second-order perturbation terms away from the equilibrium position. In this regime, we find no sign of localized excitations (solitons). In the strong excitation (rotary) regime, the classical dynamics is found to be chaotic. For this case, we calculate the time-correlation functions and estimate the Kolmogorov entropy as well as the fractal dimension. In addition, thermodynamical properties are discussed. In the second part of this work, we propose a method for exciting controllably the dipoles by means of a static electric field and a linear polarized, single-mode laser pulse. In the presence of external fields, we study the excitation propagation dynamics in the chain. As a function of the properties of the applied fields (strengths, frequency and pulse duration), we inspect the non-stationary solutions and identify the solitonic, the breather and the classical chaotic regimes as well as where nonlinear resonances emerge.

Measurements of the (e,2e) triply differential cross sections (TDCS) are presented for the ionization of the nitrogen molecule in coplanar asymmetric geometry at an incident energy of about 600 eV and a large energy transfer to the target. The experimental results are compared with state-of-the-art available theoretical models for treating differential electron impact ionization of molecules. The experimental TDCS are characterized by a shift towards larger angles of the angular distribution with respect to the momentum transfer direction, and by a large intensity in the recoil region, especially for ionization of the 'inner' 2σ_g molecular orbital. Such shifts and intensity enhancement are not predicted by the model calculations which rather yield a TDCS symmetrically distributed around the momentum transfer direction.

We present the possibility of population inversion in 3p–3s quantum transitions of Ne-like Fe ions and the consequent laser action in the EUV range in the Centaurus X-3 (Cen X-3) x-ray pulsar. The effect of bulk motions of the ions on the laser gain is considered. The hydrodynamic Doppler broadened gain coefficients for the six lines of Ne-like Fe at 25.5 nm, 20.6 nm, 34.1 nm, 35.6 nm, 38.4 nm and 38.5 nm are calculated. The plasma velocity affects the laser gain by an order of magnitude 3. The gain coefficients are significant in the region of electron density 10¹⁸ < n_e < 10²² cm⁻³ and electron temperature T_e ⋍ 250–1000 eV. The lines at 25.5 nm and 20.6 nm have large linear amplification coefficient which implies that stimulated emission is possible in these lines under the physical conditions of the Cen X-3.