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We have realized a magnetic guide for ultracold chromium atoms by continuously loading atoms directly from a Zeeman slower into a horizontal guide. We observe an atomic flux of 2 × 10⁷ atoms s⁻¹ and are able to control the mean velocity of the guided atoms between 0 m s⁻¹ and 3 m s⁻¹. We present our experimental results on loading and controlling the mean velocity of the guided atoms and discuss the experimental techniques that are used.

An adiabatic variational approximation is used to study the monodeuterated water molecule, HDO, accounting for the isotopic effect. The isotopic dipole moment, pointing from D to H, is then calculated for the first time, yielding (1.5 ± 0.1) × 10⁻³ Debye, being helpful in the interpretation of experiments.

We develop a description of laser-assisted x-ray photoionization based on a sudden approximation approach. By splitting the system evolution into three time stages we find necessary and sufficient conditions for spatial and temporal separation of Coulomb and Volkov continuum solutions. Using the separable Coulomb–Volkov wavefunction we present an analytical non-relativistic quantum theory of attosecond photoionization. It applies for arbitrary x-ray parameters, with both Coulomb continuum and laser field treated non-perturbatively. The theory provides a firm basis for characterizing photoelectron phase and atomic and molecular wavefunctions, by extracting them from experimental data. Using the molecular hydrogen ion as a test case, we display a variety of photoelectron interference sources in energy- and angular-resolved spectra for different pulse durations, chirps and delay times between x-ray pulse replicas.

A fully relativistic treatment of the S-matrix elements describing two-photon bound–bound transition amplitudes in hydrogen-like ions is undertaken in the present work. Several selected transitions from the ground state |1²S⟩ towards the L and M shells (|2²S⟩, |3²S⟩, |3²D_3/2⟩ and |3²D_5/2⟩) are described. For that purpose, we use the complete set of relativistic Sturmian functions derived by Szmytkowski (1997 J. Phys. B: At. Mol. Opt. Phys.30 825) from the first-order Sturm–Liouville problems for the Dirac equation. The method followed consists of writing the matrix elements in terms of Green functions expanded over the first-order Dirac–Coulomb Sturmians. Previous approaches used a Sturmian basis associated with the Gell-Mann–Feynman equation. On the other hand, a distinctive feature of our tensor treatment is that the expressions derived are quite general and could be applied to any multipole of the two-photon bound–bound transitions. In the case of dipole transitions, considered also by Szymanowski et al (1997 Phys. Rev. A 56 700) in their calculations, the selection rules derived from our method lead to two additional terms related to l_1p = 2 and l_2p = 2. The numerical results obtained for the transition from the ground state |1²S⟩ towards the L and M shells enable us to draw inferences as to the improvements of our method.

The absorption profile of a four-level ladder atomic system interacting with three driving fields is studied perturbatively and analytical results are presented. Numerical results where the driving field strengths are treated up to all orders are presented. The absorption features are studied in two regimes—(i) the weak middle transition coupling, i.e. Ω₂ ≪ Ω_1,3 and (ii) the strong middle transition coupling Ω₂ ≫ Ω_1,3. In case (i), it is shown that the ground-state absorption and the saturation characteristics of the population of level |2⟩ reveal deviation due to the presence of upper level couplings. In particular, the saturation curve for the population of level |2⟩ shows a dip for Ω₁ = Ω₃. While the populations of levels |3⟩ and |4⟩ show a maxima when this resonance condition is satisfied. Thus the resonance condition provides a criterion for maximally populating the upper levels. A second-order perturbation calculation reveals the nature of these minima (maxima). In the second case, I report two important features: (a) filtering of the Aulter–Townes doublet in the three-peak absorption profile of the ground state, which is achieved by detuning only the uppermost coupling field and (b) control of line-width by controlling the strength of the upper coupling fields. This filtering technique coupled with the control of linewidth could prove to be very useful for high resolution studies.

Previously unknown quantities of a general trial wavefunction ϕ are derived, namely the measure of the splittings between the nodal hypersurfaces obtained from the Hamiltonian operation , the kinetic energy operation , and that of ϕ itself, which occur because ϕ is not the true wavefunction. Insight into the structure of the true nodes is also revealed. In particular, we establish a bound for the location of a node of the exact wavefunction with respect to the node of the trial wavefunction. The nodal structure is of particular interest for quantum Monte Carlo calculations (QMC) and also for assessing and optimizing a trial wavefunction.

The time-frequency properties of high harmonic generation (HHG) driven by a bichromatic field consisting of a fundamental and a weak third harmonic field are investigated. The selection of an individual quantum path contributing to harmonic generation can be achieved by adjusting the relative phase between the two components of the driving field. The classical trajectory simulation of the strong-field electron dynamics is performed to analyse the physical process. Our calculations show that it is the control of the ionization step that leads to the quantum path selection. This quantum selection can be used to generate regular and strong attosecond pulses.

We investigate the accuracy with which the electric dipole polarizability, α_zz, and the hyperpolarizability, β_zzz, can be calculated by using the algebraic approximation, i.e. finite basis set expansions, and by means of the finite difference method in calculations for the ground states of the 14 electron systems N₂, CO and BF within the Hartree–Fock model at their respective experimental equilibrium geometries. For a well-chosen grid, the finite difference technique can provide Hartree–Fock energy and dipole moment expectation values approaching machine precision which can be used to assess the accuracy of corresponding calculations carried out within the algebraic approximation. The finite field approximation is used to determine polarizabilities and hyperpolarizabilities from finite difference Hartree–Fock dipole moment expectation values. The results are compared with finite basis set calculations of the corresponding quantities which are carried out analytically using coupled perturbed Hartree–Fock theory. For the N₂ molecule, the Hartree–Fock polarizability is found to be 14.9512 au within the finite basis set approximation and 14.945 au within the finite difference approach. For the CO molecule, the corresponding results are 14.4668 au and 14.4668 au, whilst for the BF molecule the values are 16.6450 au and 16.6450 au, respectively. The Hartree–Fock hyperpolarizability of the CO molecule is found to be 31.4081 au and 31.411 au within the finite basis set and finite difference approximations, respectively. The corresponding hyperpolarizability values for the BF molecule are 63.9687 au and 63.969 au, respectively.

We explore, by time-dependent MQDT calculations, the potential for coherent control of autoionization using phase-shaped optical pulses. We investigate the effect of step-like spectral phase modulation on the autoionization dynamics of Rydberg wave packets in the Xe atom. It is found that a single step in the spectral phase has a substantial effect on the branching ratio, if the position of the step corresponds to a resonance in the Rydberg system. These effects are enhanced if the optical pulse is engineered to have multiple steps that reflect the periodicity inherent in Rydberg systems. Further calculations indicate that, to a large extent, the effects of phase manipulations are additive and independent. We also compare this new approach with approaches based on sequences of identical coherent optical pulses. The two methods are complementary, and we suggest that in the future they may be combined.

Charge exchange in dense plasmas can result in dips in spectral line profiles of hydrogenlike ions of a nuclear charge Z perturbed by fully-stripped ions of a different nuclear charge Z' ≠ Z. These so-called x-dips were described in detail theoretically and discovered experimentally in our previous works. In the theoretical part of the present paper we show that the x-dip has a structure consisting of the dip itself surrounded by two adjacent bumps. We also show that two different explanations of the x-dip formation, provided in the previous papers, do not describe the same processes: they represent two independent mechanisms working simultaneously. Based on the obtained results, we provide for the first time a method for determining the rate coefficients of charge exchange from the measured shape of the x-dips, namely, from the bump-to-dip ratio of intensities. In the experimental part we present new results on the x-dips in the profile of the L_γ line of Al XIII in a laser-produced plasma. These new experimental data, obtained with a significantly better spectral resolution than in our previous experiments, allow observation for the first time not just of the dip itself (the central minimum), but the entire structure including two adjacent bumps. By combining our new theoretical and experimental results, we determined for the first time the rate coefficient of charge exchange between the hydrogenic Al and a fully-stripped C in the laser-produced plasma. This constitutes the next step towards the employment of the x-dip phenomenon for producing not-yet-available fundamental data on charge exchange between multicharged ions, virtually inaccessible by other experimental methods.

Strong mass signals of H⁻₂ and D⁻₂ ions have been observed from low-pressure dielectric barrier discharge hydrogen and deuterium plasmas via molecular beam mass spectrometry. The observed H⁻₂/H⁻ and D⁻₂/D⁻ ratios (∼0.35–0.4) are over five orders of magnitude higher than those observed by other techniques. The kinetic energy of H⁻₂ and D⁻₂ ions sampled from the plasmas was determined to be widely distributed, from a few eV to >100 eV, giving lifetimes greater than ∼40 µs for H⁻₂ and ∼55 µs for D⁻₂. The highest vib-rotational excitation of neutral H₂ species in the plasma was determined to be about J = 0, v = 5 or J = 19, v = 0 via threshold ionization mass spectrometry. The possible pumping mechanisms for generating H⁻₂ with further high J, required by the current high-rotation model, have been proposed. Similar to the lifetime of D⁻₂ determined recently by another group, the H⁻₂ lifetime observed in this work is about two orders of magnitude longer than that predicted by the current theoretical model. To explain these experimental observations regarding the meta-stability of long-lived H⁻₂ and D⁻₂ ions, the improved current high-rotation model or other new models, including the possible existence of some long-lived electronically excited states of H⁻₂/D⁻₂, need to be developed.

We have measured the relative cross section for photodetachment from the K⁻ ion for the process K⁻ + hν→ K⁺ + 2e⁻ over the photon energy range 21– 24.5 eV. The structures in the measured cross section are associated with correlated processes involving the detachment or excitation of a 3p core electron, processes which are often accompanied by the excitation of one or more valence electrons. The most prominent feature in the cross section is a strong resonance arising from the excitation of a 3p electron from the core and a 4s valence electron. As in previous experiments on double excitation of valence electrons, electron correlation is seen to play an important role in the dynamics of negative ions.

We have developed a many-electron model for multiple ionization of heavy atoms bombarded by bare ions. It is based on the transport equation for an ion in an inhomogeneous electronic density. Ionization probabilities are obtained by employing the shell-to-shell local plasma approximation with the Levine and Louie dielectric function to take into account the binding energy of each shell. Post-collisional contributions due to Auger-like processes are taken into account by employing recent photoemission data. Results for single-to-quadruple ionization of Ne, Ar, Kr and Xe by protons are presented showing a very good agreement with experimental data.

Transition rates, oscillator strengths and line strengths are calculated for electric-dipole (E1) transitions between odd-parity 3s²3p⁶3d⁹4l₁, 3s²3p⁵3d¹⁰4l₂ and 3s3p⁶3d¹⁰4l₁ states and even-parity 3s²3p⁶3d⁹4l₂, 3s²3p⁵3d¹⁰4l₁ and 3s3p⁶3d¹⁰4l₂ (with 4l₁ = 4p, 4f and 4l₂ = 4s, 4d) in Ni-like ions with the nuclear charges ranging from Z = 34 to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate retarded E1 matrix elements in length and velocity forms. The calculations start from a 1s²2s²2p⁶3s²3p⁶3d¹⁰ Dirac–Fock potential. First-order RMBPT is used to obtain intermediate coupling coefficients and second-order RMBPT is used to calculate transition matrix elements. Contributions from negative-energy states are included in the second-order E1 matrix elements to ensure the gauge independence of transition amplitudes. Transition energies used in the calculation of oscillator strengths and transition rates are from second-order RMBPT. Lifetimes of the 3s²3p⁶3d⁹4d levels are given for Z = 34–100. These atomic data are important in modelling of M-shell radiation spectra of heavy ions generated in electron beam ion trap experiments and in M-shell diagnostics of plasmas.

Sudden turn-on of a matter-wave source leads to characteristic oscillations of the density profile which are the hallmark feature of diffraction in time. We show how the use of smooth aperture functions suppresses the diffraction oscillations. The analytical dynamics of non-interacting bosons arising with different aperture functions are discussed systematically for switching-on processes and for single- and many-pulse formation procedures. The possibility and timescale of a revival of the diffraction-in-time pattern is also analysed. Similar modulations in time of the pulsed output coupling in atom lasers are responsible for the dynamical evolution and characteristics of the beam profile. For multiple pulses, different phase schemes and regimes are described and compared. Strongly overlapping pulses lead to a saturated, constant beam profile in time and space, up to the revival phenomenon.

A scheme is proposed for the implementation of phase-covariant anti-cloning in a single step. In the scheme N atoms dispersively interact with a cavity, with the coupling of the first atom different from that of the other atoms. Throughout the procedure the cavity is only virtually excited and thus the cavity decay is suppressed. The asymmetric nonresonant coupling can also be used to perform a one-step entangling operation.

We present a detailed study of the ground state behaviour of two-electron diatomic molecules. The ground state stability diagram for diatomic molecules in the Born–Oppenheimer approximation is obtained and the behaviour of the ground state near the stability line is studied. Two different cases are analysed: the homonuclear two-centre two-electron molecule with the internuclear distance as a free parameter and the diatomic two-electron molecule (in this case, the internuclear distance is determined by equilibrium conditions). Analytical and numerical results for these systems are presented.

We investigate the quantum properties of an ultracold Rydberg atom exposed to a magnetic quadrupole field and a homogeneous electric field. The properly transformed Hamiltonian explicitly depends on the conserved total angular momentum and couples the centre of mass and electronic degrees of freedom. The corresponding Schrödinger equation is solved by an adiabatic separation focusing on a fixed n-manifold. The shape of the adiabatic electronic potential energy surfaces is analysed. With increasing electric field strength, avoided crossings among them become ubiquitous and the electric field-dominated regime spreads out within the centre-of-mass coordinate space. A transition from smooth surfaces for weak electric fields to surfaces involving a cusp-like behaviour in the strong field regime is observed. The latter involves a characteristic splitting behaviour of the surfaces due to the competition of the Stark and magnetic interactions. In contrast to previous investigations, our setup allows for the trapping of quantum states with a comparatively small electronic angular momentum.

The next generation of experiments for making cold anti-hydrogen will attempt to trap them using multipole magnetic fields. We investigate the motion of the anti-protons through the combined electric and magnetic fields of this type of trap. The multipole fields that will prevent the anti-hydrogen from hitting the walls cause the anti-protons to have regions of regular motion and regions of chaotic motion. We find that hexapole fields give motion that would greatly suppress the formation of cold anti-hydrogen; for realistic conditions, less than ∼1/10 could lead to cold anti-hydrogen. For octupole fields, we found that ∼1/4 of the anti-protons could lead to cold anti-hydrogen formation at short times. We discuss the implications of these regions for anti-hydrogen experiments.

The Riemann surface approach to bound and resonant states is generalized to the case of a two-channel model. The approach consists of the construction of the Riemann surface R_g of the S-matrix pole function k = k(g) over the g-plane, where g is the strength of the complex potential in each of the two channels. On the Riemann surface R_g the pole function k = k(g) is single valued and analytic. The branch points of the pole function k = k(g) and their k-plane images are asymptotically and numerically determined and analysed as a function of the strength of the coupling potential. It is shown that besides the branch points which originate from the branch points for the uncoupled channels, there are new branch points which are intrinsic to the coupling. According to the Riemann surface approach to each bound or resonant state a sheet of the Riemann surface R_g is associated. All the natural modes (bound and resonant states) of the system are identified and treated in a unified way. The Riemann surface approach allows introducing two new quantum numbers (m, n) with topological meaning which label each bound or resonant state. The approach provides a new insight into the nature of the resonant states for two coupled channels. The distinct origin and the relationship of the Feshbach and Newton–Fonda resonant states are clarified.

We present calculated and experimentally derived electron–ion recombination rate coefficients for Na-like Si IV, recombining into Mg-like Si III, and provide accurate spectroscopic data for doubly excited states located above the ionization threshold of Si III. The experimental recombination rate coefficients were measured in a merged-beam-type experiment at the heavy-ion storage ring CRYRING at the Manne Siegbahn Laboratory in Stockholm. Changing the electron–ion relative energy from 0 to 20 eV we covered the energy region from the first to the third ionization threshold. We find that even for the low-charged Si²⁺ ion, a relativistic many-body perturbation theory calculation is necessary, to describe the recombination rate coefficients in the low-energy region, up to 1.5 eV, satisfactorily. Doubly excited states, forbidden to form in LS coupling, are responsible for the most prominent dielectronic recombination resonances at low energies and contribute with 40% to the strength. Several wide resonances give rise to a plateau-like formation in the recombination spectrum. A broader energy range, up to 6.7 eV, was covered with a non-relativistic many-body calculation. This range contains, in addition to 3pnℓ resonances, several resonances of the type 3dnℓ, with the LS-forbidden 3d²³F states giving rise to a strong, isolated peak at 2.976 eV. The NIST database lists eleven doubly excited states of Si III with energy positions deviating considerably from our determination. Since the listed lines are also not fully matching those with the largest fluorescence yields it must be concluded that they are misidentified.

Based on the independent particle model, we consider single and multiple ionization of neon and argon atoms induced by fast proton impact. Multiple ionization at high projectile energies (E_P ⪆ 1 MeV/amu) is dominated by Auger-like processes and can be described appropriately by our statistical model introduced recently. In the present work we use several scattering models to extract angular differential cross sections. With our results a long-standing discrepancy between different experimental data sets is resolved.

We consider a protocol recently proposed by Zhen-Biao Yang for teleporting entangled photon states from one bimodal cavity to another. It is shown that the proposed protocol can afford full success probability instead of the 1/4 success probability that the author ascribed to his scheme.

I give a reply to the comment by Cardoso et al on my recent paper (Yang Z-B 2006 J. Phys. B: At. Mol. Opt. Phys.39 603).