Table of contents

The lowest singlet–triplet pair of states of the two-electron two-dimensional quantum dots and the corresponding pair of states of the two-dimensional helium-like systems have been studied by the full configuration interaction method focusing on the origin of the first Hund rule. The one- and two-electron components of the singlet–triplet energy gap show distinct trends for the systems studied in the regime of small nuclear charge Z_n or of small confinement strength ω. The (0σ_g)(1π_u) singlet state in quantum dots is characterized by a larger electron repulsion than its counterpart triplet state for all values of ω, while this relationship gets inverted for the corresponding (1s)(2p) singlet–triplet pair of He-like systems for small values of Z_n, such as Z_n = 2 or 3. The internal part of the full configuration interaction wavefunctions has been extracted and visualized in the three-dimensional internal space (r₁, r₂, ϕ₋) to rationalize the observed trends. The singlet probability density of He-like systems located originally near the Fermi holes is shown to migrate into regions where either r₁ or r₂ are large while the corresponding singlet probability of quantum dots stays close to the Fermi holes. Their differences and their observed trends are rationalized on the basis of the structure of the genuine and conjugate Fermi holes.

Complete population inversion is demonstrated analytically in the strong-field limit in a three-level system using the rubidium 5s–5p–5d transition. We exploit the pre-transients of an amplitude-shaped laser pulse to direct the dynamics of the Rabi oscillations such that the population transfer to the excited state can be controlled in a wide range from a strongly enhanced to vanishing one. The excitation is performed under off-resonant conditions. During the intense ultrafast pulse, levels shift to such an extent that two-photon resonant excitation becomes possible, even though a frequency spectrum does not contain photons with energies necessary for the excitation of an unperturbed system. Within the reach of experimental parameters, we demonstrate 70% population transfer.

We applied the finite-size scaling method using the B-splines basis set to construct the stability diagram for two-electron atoms with a screened Coulomb potential. The results of this method for two-electron atoms are very accurate in comparison with previous calculations based on Gaussian, Hylleraas and finite-element basis sets. The stability diagram for the screened two-electron atoms shows three distinct regions, i.e. a two-electron region, a one-electron region and a zero-electron region, which correspond to stable, ionized and double ionized atoms, respectively. In previous studies, it was difficult to extend the finite-size scaling calculations to large molecules and extended systems because of the computational cost and the lack of a simple way to increase the number of Gaussian basis elements in a systematic way. Motivated by recent studies showing how one can use B-splines to solve Hartree–Fock and Kohn–Sham equations, this combined finite-size scaling using the B-splines basis set might provide an effective systematic way to treat criticality of large molecules and extended systems. As benchmark calculations, the two-electron systems show the feasibility of this combined approach and provide an accurate reference for comparison.

We calculate accurate eigenvalues and eigenfunctions of the Schrödinger equation for a two-dimensional quantum dipole. This model proved useful for the study of elastic effects of a single edge dislocation. We show that the Rayleigh–Ritz variational method with a basis set of Slater-type functions is considerably more efficient than the same approach with the basis set of point-spectrum eigenfunctions of the two-dimensional hydrogen atom used in earlier calculations.

Static and dynamic polarizabilities are calculated for the non-relativistic hydrogen molecular ion by solving the three-body Schrödinger equation in perimetric coordinates with the Lagrange-mesh method. The static dipole polarizabilities of the ground-state rotational band are computed for total orbital (or rotational) angular momenta from L = 0 to 39 with an absolute accuracy of about 10⁻⁹ au. For L = 0, 1 and 2, slightly less accurate results are also given for the first three vibrational excited levels. For the ground state, dynamic dipole polarizabilities as well as static and dynamic quadrupole polarizabilities are computed. To illustrate the versatility of the method, the static dipole polarizability of the hydrogen molecular ion in a Debye plasma is also determined.

The charge exchange process has been found to play a dominant role in the production of x-rays and/or extreme ultraviolet photons emitted from cometary and planetary atmospheres and from the heliosphere. Charge exchange cross sections, especially state-selective cross sections, are necessary parameters in simulations of this x-ray emission. In this study, charge exchange, or single-electron capture, due to collisions of ground state O^{6 +}(1s^2 1S) with atomic hydrogen has been investigated theoretically using the quantum-mechanical molecular-orbital close-coupling method (QMOCC). The multi-reference single- and double-excitation configuration interaction approach has been applied to compute the adiabatic potentials and nonadiabatic couplings, and the atomic basis sets used have been optimized with a method proposed previously to obtain accurate descriptions of the high-lying Rydberg states of highly charged ions. Total and final-state-selective cross sections are calculated for energies between 0.1 eV/u and 10 keV/u. The QMOCC results are compared to available experimental and theoretical data as well as to new atomic-orbital close-coupling (AOCC) and classical trajectory Monte Carlo (CTMC) calculations. A recommended set of cross sections, based on the QMOCC, AOCC and CTMC calculations, and existing data, are deduced which should aid in x-ray emission modelling studies.

A three-body Coulomb–Born continuum distorted-wave approximation is applied to calculate the differential and total cross sections for single-electron exchange in the collision of fast alpha particles with helium atoms in their ground states. The applied first-order distorted wave theory satisfies correct Coulomb boundary conditions. Both post and prior forms of the transition amplitude are calculated. The nuclear-screening effect of the passive electron on the differential and total cross sections is investigated. The results are compared with those of other theories and with the available experimental data. For differential cross sections, the comparisons show a reasonable agreement with empirical measurements at higher impact energies. The agreement between experimental data and the present calculations for total cross sections with the average of the post and prior forms of the transition amplitude is reasonable at all the specified energies.

The single- and double-electron capture processes in He²⁺–He collisions are investigated by the fully quantum-mechanical molecular orbital close-coupling method employing a basis containing 15 gerade and 14 ungerade molecular states. The energies and wavefunctions of He₂²⁺ molecular states included in the study are determined ab initio by the multireference single- and double-excitation configuration interaction method. The dominant capture mechanisms are discussed and the integral and differential charge transfer cross sections are calculated in the energy range of 0.0005–17.5 keV/u and compared with other available experimental and theoretical results.

The concept of dominant interaction Hamiltonians is introduced. It is applied as a test case to classical planar electron–atom scattering. Each trajectory is governed in different time intervals by two variants of a separable approximate Hamiltonian. Switching between them results in exchange of energy between the two electrons. A second mechanism condenses the electron–electron interaction to instants in time and leads to an exchange of energy and angular momentum among the two electrons in the form of kicks. We calculate the approximate and full classical deflection functions and show that the latter can be interpreted in terms of the switching sequences of the approximate one. Finally, we demonstrate that the quantum results agree better with the approximate classical dynamical results than with the full ones.

The photoabsorption spectrum of the Sc₃N@C₈₀ molecule has been studied in the photon energy range of 30 to 50 eV using the time-dependent density functional theory. The results demonstrate that the confinement effect is related to the location of the encaged element inside the C₈₀ molecule. We conclude that the confinement effect will be strongest if the element is at the centre of the fullerene cage, and that when the element is located at the off-centre position, the peak of the photoabsorption spectrum may be averaged out or even suppressed.

The Ioffe–Pritchard trap is the workhorse of modern cold atom physics. Here, we present a novel Ioffe–Pritchard trap coil configuration based purely on circular coils. By eliminating the traditional Ioffe bars one can increase the gradient and thus the radial trapping frequency by almost a factor 2. We also present a method to achieve minimal coupling between the gradient, curvature and offset fields of the trap, thus facilitating the dynamic control of the trapping frequencies and aspect ratio.

A mixture of two distinguishable Bose–Einstein condensates confined in a ring potential has numerous interesting properties under rotational and solitary-wave excitation. The lowest energy states for a fixed angular momentum coincide with a family of solitary-wave solutions. In the limit of weak interactions, exact diagonalization of the many-body Hamiltonian is possible and permits evaluation of the complete excitation spectrum of the system.

We study the properties of a single-component (spin polarized) degenerate dipolar Fermi gas of ¹⁶¹Dy atoms using a hydrodynamic description. Under axially-symmetric trapping we suggest reduced one- (1D) and two-dimensional (2D) descriptions for the cigar and disc shapes, respectively. In addition to a complete numerical solution of the hydrodynamic model we also consider a variational approximation. For a trapped system under appropriate conditions, the variational approximation as well as the reduced 1D and 2D models are found to yield results for the shape, size and chemical potential of the system in agreement with the full numerical solution of the three-dimensional (3D) model. For the uniform system we consider anisotropic sound propagation in 3D. An analytical result for anisotropic sound propagation in a uniform dipolar degenerate Fermi gas is found to be in agreement with the results of numerical simulation in 3D.

A scheme is proposed for control of pulse propagation from subluminal to superluminal in a four-level Λ-type atomic system. With the relatively intense probe laser and the appropriate detuning of control field, the medium exhibits much lower absorption in the spectral ranges where the dispersion changes from normal to abnormal in the double electromagnetically induced transparency system than in the single electromagnetically induced transparency system. The transmission intensity can be enhanced by several times for the subluminal pulse propagation and by several orders of magnitude for the superluminal pulse propagation without the large distortion in the former compared with those in the latter. We attribute the dramatic absorption reduction to the enhanced nonlinear effects.

The geometric phase in the dynamics of a spin qubit driven by transverse microwave (MW) and longitudinal radio frequency (RF) fields is studied. The phase acquired by the qubit during the full period of the 'slow' RF field manifests in the shift of Rabi frequency ω₁ of a spin qubit in the MW field. We find out that, for a linearly polarized RF field, this shift does not vanish at the second and higher even orders in the adiabaticity parameter ω_rf/ω₁, where ω_rf is the RF frequency. As a result, the adiabatic (Berry) phases for the rotating and counter-rotating RF components compensate each other, and only the higher order geometric phase is observed. We experimentally identify that phase in the frequency shift of the Rabi oscillations detected by a time-resolved electron paramagnetic resonance.

We theoretically demonstrate a new scheme for cancelling the dispersive effects in quantum communication with two entangled photons propagating in optical fibres. In the case of two entangled photons generated by spontaneous parametric down-conversion and propagating in two optical fibres, it is demonstrated that the dispersive effect in the biphoton wavepacket is cancelled by inserting only one Fabry–Perot cavity into one of the fibre's lines. No special dispersive material or interference of the transmitted photons in a beam splitter (or interferometer) is necessary. In the scheme, where one of the photons is reflected by the Fabry–Perot cavity before being transmitted by the fibre, a full dispersion cancellation is shown with no decrease in the number of photons at the optical fibres exit.

The rate coefficient of resonant charge transfer between ³He^{2 +} and ⁴He, at energies below 1 eV, was measured using an rf ion trap and time-of-flight mass spectrometry. We obtain a resonant charge transfer rate coefficient of 5.9 ± 0.6 × 10⁻¹⁰ cm³ s⁻¹ at an equivalent temperature of 1200 K. The measured value compares favourably to existing calculations. This measurement extends our knowledge to a broader spectrum of energies as it provides information on the rate coefficients at a low energy and adds to our understanding of the charge transfer process of ³He^{2 +}, α-particles, with He encountered in astrophysics and nuclear fusion.

The claim by Shojaei et al (2011 J. Phys. B: At. Mol. Opt. Phys.44 235101) that the entropy difference between the cis and gauche conformers of 1-butene changes dramatically upon inclusion of hindered-rotor corrections is shown to be incorrect.

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