Highlights of 2011

Extreme ultraviolet spectra of highly-charged hafnium, tantalum and gold were produced with an electron beam ion trap (EBIT) at the National Institute of Standards and Technology (NIST) and recorded with a flat-field grazing-incidence spectrometer in the wavelength range 4–20 nm. The beam energy was varied between 1.84 and 5.15 keV to selectively enhance spectra from specific ionization stages. Identifications of strong n = 4–n = 4 transitions from Rb-like hafnium (35+) to Co-like gold (52+) were determined with the aid of collisional-radiative modelling of the EBIT plasma. Good quantitative agreement between simulated and measured spectra was achieved. Over 150 spectral lines were identified, 115 of which are new.

Natural radiative lifetimes of nine odd-parity highly excited levels in Eu I and eleven even-parity levels in Eu II have been measured by time-resolved laser-induced fluorescence technique in laser-produced plasma. The lifetime values measured in this paper are in the range from 7.1 to 1520 ns. When they are compared with the previous measurements, good agreement was achieved.

We study the long-range interaction between mutually excited hydrogen atoms in principal quantum numbers n = 4, 8, 16. The quasimolecular states are constructed from the basis of hydrogen-like product states with the configuration interaction method and with the inclusion of all order multipole moments of the total electrostatic interaction. Several common features appear, which are n-insensitive, and will thus remain relevant for the coherent control of cold Rydberg systems with higher values of n. The energy curves are shown to be attractive and repulsive, generally non-intersecting and the repulsion splitting is stronger than the attractive. The electronic probability densities of the selected states are studied as well as their relation to the single product states consisting of linear Stark states (most aligned) on each atom. One of the observed features is that the least bound states are always characterized by a high degree of polarization favoured towards the molecular centre, and therefore well approximated by a product of two Stark states. The most bound states are similarly expressed as a coherent combination of such states which secure symmetry with respect to electron exchange and parity. Coherent control between the attractive and repulsive states can be obtained with almost 100% probability in time-dependent resonant monochromatic microwave fields.

Oxygen 1s excitation and ionization processes in the CO₂ molecule have been studied with dispersed and non-dispersed fluorescence spectroscopy as well as with the vacuum ultraviolet (VUV) photon–photoion coincidence technique. The intensity of the neutral O emission line at 845 nm shows particular sensitivity to core-to-Rydberg excitations and core–valence double excitations, while shape resonances are suppressed. In contrast, the partial fluorescence yield in the wavelength window 300–650 nm and the excitation functions of selected O⁺ and C⁺ emission lines in the wavelength range 400–500 nm display all of the absorption features. The relative intensity of ionic emission in the visible range increases towards higher photon energies, which is attributed to O 1s shake-off photoionization. VUV photon–photoion coincidence spectra reveal major contributions from the C⁺ and O⁺ ions and a minor contribution from C^{2 +}. No conclusive changes in the intensity ratios among the different ions are observed above the O 1s threshold. The line shape of the VUV–O⁺ coincidence peak in the mass spectrum carries some information on the initial core excitation.

A novel cold collision phenomenon is described which is caused by interference within the manifold of electron waves of unit angular momentum (p-waves). Experimental electron scattering data in N₂, down to energies of 10 meV, reveal this phenomenon through the angular distribution of scattered electrons. Ab initio theory, analytical results and a simple physical model illustrate how interference arises through the presence of a quadrupole on the target N₂. The effect is of a general nature and may be found in all systems in which, in the cold regime, charged particles interact with target species with a permanent quadrupole moment.

Combining the WKB expansion at large distances and perturbation theory at small distances a compact uniform approximation for eigenfunctions is constructed. For the lowest states 1sσ_g and 2pσ_u, this approximation provides the relative accuracy ≲ 10⁻⁵ (5 s.d.) for any real x in eigenfunctions and for total energy E(R) it gives 10–11 s.d. for internuclear distances R ∊ [0, 50]. Corrections to proposed approximations are evaluated. Separation constants and the oscillator strength for the transition 1sσ_g → 2pσ_u are calculated and compared with existing data.

In a joint experimental and theoretical effort, we carried out a detailed study of electron impact excitation of the 4p⁵ 5s states of Kr. We present angle-differential cross sections over the entire angular range (0°–180°) for a number of energies in the near-threshold region, as well as energy scans for selected angles. The experimental results are in very satisfactory agreement with predictions from a fully relativistic Dirac B-spline R-matrix model.

We report on detailed calculations of dielectronic recombination (DR) rate coefficients for Sn^{4 +}–Sn^{13 +} using three approaches of differing degrees of complexity. These are configuration-mixed Breit–Pauli using the autostructure code, bundled-nl using the Burgess–Bethe general program (BBGP) and configuration average (CA) using the DRACULA code. We find that target Δn = 0 dipole promotions dominate the total DR rate coefficients; configuration-mixing effects are small for the totals; results for the totals are highly dependent on the initial levels averaged over—the results for averaging over all levels of the ground configuration being typically nearly a factor of 2 smaller than for using only the ground level. On comparing the total DR rate coefficients obtained using the three methods we find that the BBGP results are systematically lower than those obtained from autostructure—in some cases they are significantly lower (by a factor of 2)—while the CA results are systematically and significantly higher (by up to 80%) in general. These findings need to be borne in mind for the finite-density modelling of tin plasma sources for microlithography and tin markers for magnetic fusion plasmas especially when using simple descriptions of DR. They apply also to heavy species in general such as tungsten ions which are of great importance for magnetic fusion plasmas.

The detection of electrons from the surface interaction of Rydberg hydrogen atoms and molecules at a metal surface is investigated experimentally for the first time. The experimental detection of an electron signal in a time gate corresponding to when the Rydberg atoms or molecules are expected to collide with the surface provides evidence for the previously proposed backscattered electron loss (So et al 2009 Phys. Rev. A 79 012901) as a route of surface ionization under electron-extraction fields. Comparison of the ion- and electron-extraction results shows that the dynamics as the Rydberg states approach the surface are very different in the two cases, leading to the possible loss of control of the electronic polarization in the initially prepared Rydberg state from the traversal of level crossings during the Rydberg trajectory. The difference in the ionization dynamics observed for the Rydberg H and H₂ cases also illustrates some of the fundamental differences between atomic and molecular, and hydrogenic and non-hydrogenic systems.

The form of the helium (e, 2e) scattering amplitude near a recently identified vortex singularity in the electron-pair continuum is derived by considering the angular momentum of the electron pair about the vortex. A threshold-like analytic expansion in cylindrical partial waves of the electron pair about the vortex is established, and good fits to the cross section near the vortex are demonstrated with just the two lowest partial waves.

We report on measurements of total cross sections (TCSs) for positron scattering from the fundamental organic molecule formaldehyde (CH₂O). The energy range of these measurements was 0.26–50.3 eV, whereas the energy resolution was ∼260 meV. To assist us in interpreting these data, Schwinger multichannel level calculations for positron elastic scattering from CH₂O were also undertaken (0.5–50 eV). These calculations, incorporating an accurate model for the target polarization, are found to be in good qualitative agreement with our measured data. In addition, in order to compare the behaviour of positron and electron scattering from this species, independent atom model-screened additivity rule theoretical electron TCSs, now for energies in the range 1–10 000 eV, are also reported.

We clarify the relation in interacting systems, and in particular ultracold atomic gases, between energy shifts arising from interparticle interactions and scattering phase shifts. A principle result of this paper is an expression for the energy levels of an atom in a container of arbitrary shape in the presence of a short-range scatterer, generalizing the result of Lüscher to containers of shapes other than cubic. We show that, while the energy shifts for a spherical container are under many conditions proportional to the phase shift, those for a cubic container have a more complicated structure. The general relation is extended to problems of particles in traps with smoothly varying potentials, including, e.g., the interaction of a small neutral atom with a Rydberg atom. Finally, we discuss why, even though individual energy levels are very sensitive to boundary conditions, the energies of many-body systems are not.

We study dark–bright (DB) ring solitons in two-component Bose–Einstein condensates. In the limit of large densities of the dark component, we describe the soliton dynamics by means of an equation of motion for the ring radius. The presence of the bright, 'filling' species is demonstrated to have a stabilizing effect on the ring dark soliton. Near the linear limit, we discuss the symmetry-breaking bifurcations of DB soliton stripes and vortex-bright soliton clusters from the DB ring and relate the stabilizing effect of filling to changes in the bifurcation diagram. Finally, we show that the stabilization by means of a second component is not limited to the radially symmetric structures, but can also be observed in a cross-like DB soliton configuration.

We study rotating two-component Bose–Einstein condensates with equal particle numbers and strong intercomponent repulsion located in a harmonic potential by numerically solving two-dimensional coupled Gross–Pitaevskii equations. The condensates are observed as a dramatic departure, forming a pair of shells located symmetrically in the trap with a small spatial overlap. Projecting the system into a pseudospin space, a spin domain wall is formed at the interface of the two components. The complex and spatial periodic spin texture is formed on the domain-wall region. We discuss the dependence of the spin texture of the domain wall on the angular velocity in detail. The relation among the number of the vortices, the topological charge and the angular momentum, as an extension of Feynman's rule in the two-component Bose–Einstein condensates, is given, based on the spin texture carrying the angular momentum of the condensates.

We studied the nucleation of quadruple-quantized vortices in Bose–Einstein condensates confined in a quadrupole-Ioffe-configuration (QUIC) magnetic trap by means of the topological phase imprinting method, wherein the initially aligned atomic spins were adiabatically reversed by applying an external bias magnetic field. We calculated the change in the magnetic field distributions of the trap when a homogeneous or a gradient bias field was applied for reversing the spins, and almost the same results were obtained for both cases. We applied the gradient bias field using a single coil because of its simplicity and stability. Vortices were successfully created at the reversal time of atomic spins between 2 and 16 ms. Moreover, the vortices were observed at a holding time of up to 9 ms in the magnetic trap after a constant reversal time of 5 ms.

We study the creation of a bosonic N00N state from the evolution of a Fock state in a double well. While noninteracting bosons disappear quickly in the Hilbert space, the evolution under the influence of a Bose–Hubbard Hamiltonian is much more restricted. This restriction is caused by the fragmentation of the spectrum into a high-energy part with doubly degenerate levels and a nondegenerate low-energy part. This degeneracy suppresses transitions to states of the high-energy part of the spectrum. At a moderate interaction strength, this effect supports strongly the dynamical formation of a N00N state. The N00N state is suppressed in a double well, where one well has attractive and the other has repulsive interaction, because the double degeneracy is absent.

We analyse how light-induced coherent population oscillations and ground-state Zeeman coherence in an atomic medium with degenerate two-level transitions can modify spectra of applied cw resonant radiation at the sub-mW power level. The use of mutually coherent optical fields and heterodyne detection schemes allows spectral resolution at a kHz level, well below the laser linewidth. We find that ground-state Zeeman coherence may facilitate nonlinear wave mixing, while coherent population oscillations are responsible for phase and amplitude modulation of the applied fields. Conditions for the generation of new optical fields by nonlinear wave mixing in degenerate two-level atomic media are formulated.

The resonance spectrum of a tilted periodic quantum system for a bichromatic periodic potential is investigated. For such a bichromatic Wannier–Stark system, exceptional points, degeneracies of the spectrum, can be localized in parameter space by means of an efficient method for computing resonances. Berry phases and Petermann factors are analysed. Finally, the influence of a nonlinearity of the Gross–Pitaevskii type on the resonance crossing scenario is briefly discussed.

We demonstrate the use of dynamic decoupling techniques to extend the coherence time of a single memory qubit by nearly two orders of magnitude. By extending the Hahn spin-echo technique to correct for unknown, arbitrary polynomial variations in the qubit precession frequency, we show analytically that the required sequence of π-pulses is identical to the Uhrig dynamic decoupling (UDD) sequence. We compare UDD and Carr–Purcell–Meiboom–Gill (CPMG) sequences applied to a single ⁴³Ca⁺ trapped-ion qubit and find that they afford comparable protection in our ambient noise environment.

Velocity-map imaging has been employed to study the photoemission in Ne and N_4,5OO Auger decay in Xe induced by an isolated 85 eV extreme ultraviolet (XUV) pulse in the presence of a strong few-cycle near-infrared (NIR) laser field. Full three-dimensional momentum information about the released electrons was obtained. The NIR and XUV pulse parameters were extracted from the measured Ne streaking traces using a FROG CRAB retrieval algorithm. The attosecond measurements of the Auger decay in Xe show pronounced broadening of the Auger lines corresponding to the formation of sidebands. The temporal evolution of the sideband signals and their asymmetry along the laser polarization axis exhibit oscillations similar to those known from attosecond streaking measurements. The experimental results are in good agreement with model calculations based on an analytical solution of the Schrödinger equation within the strong field approximation.

Using sequential strong-field double ionization in a pump–probe scheme we show through calculations how electronic dynamics can be prepared and imaged. Electronic dynamics may arise whenever multiple states of the ion are accessed in the ionization step. The dynamics in the cation influence the rate of the second ionization step and the momentum distribution of the ejected electron, allowing their detailed characterization. We show how the probe step is controlled through spatial propensities of the ionizing orbitals and the energy level structure of the dication. Both the final electronic state of the dication and the spin state of the ejected electron pair can be controlled through the time delay between the two ionizing pulses. We discuss how our results will extend to the preparation and measurement of attosecond electron dynamics.

We predict a significant delay of two-electron photoemission from the helium atom after absorption of an attosecond XUV pulse. We establish this delay by solving the time-dependent Schrödinger equation and by subsequently tracing the field-free evolution of the two-electron wave packet. This delay can also be related to the energy derivative of the phase of the complex double-photoionization (DPI) amplitude which we evaluate by using the convergent close-coupling method. Our observations indicate that future attosecond time delay measurements on DPI of He can provide information on the absolute quantum phase and elucidate various mechanisms of this strongly correlated ionization process.

We investigate the generation of even and odd harmonics using an intense laser and a weak second harmonic field. Our theoretical approach is based on solving the saddle-point equations within the strong field approximation. The phase of the even harmonic oscillation as a function of the delay between the fundamental and second harmonic field is calculated and its variation with energy is found to be in good agreement with recent experimental results. We also find that the relationship between this phase variation and the group delay of the attosecond pulses depends on the intensity and wavelength of the fundamental field as well as the ionization potential of the atom.

The resonant and non-resonant two-photon single ionization processes of He were investigated using intense free electron laser light in the extreme ultraviolet (XUV) region (53.4–61.4 nm) covering the 1s–2p and 1s–3p resonant transitions of He. On the basis of the dependences of the yield of He⁺ on the XUV light-field intensity at 53.4, 58.4, 56.0 and 61.4 nm, the absolute values of the two-photon ionization cross sections of He at the four different wavelengths and their dependence on the light-field intensity were determined for the first time.

Resonant inelastic soft x-ray scattering spectra excited at the dissociative 1σ_g → 3σ_u resonance in gas-phase O₂ are presented and discussed in terms of state-of-the-art molecular theory. A new selection rule due to internal spin coupling is established, facilitating a deep analysis of the valence excited final states. Furthermore, it is found that a commonly accepted symmetry selection rule due to orbital parity breaks down, as the core hole and excited electron swap parity, thereby opening the symmetry forbidden 3σ_g decay channel.

The sequential two-photon double ionization of 4d electrons of xenon in intense free-electron laser (FEL) radiation is theoretically investigated for photon energies of 70–200 eV. At these energies, which are available at the free-electron laser FLASH, the 4d photoionization dominates over the ionization of the valence shells, showing a giant resonance. The 4d vacancy produced by the first photon strongly couples to the (Auger) autoionization continuum with a lifetime of only ∼6 fs and thus the Auger decay competes with the second photoionization in a typical FEL pulse. The photoelectron angular distributions and angular correlation between emitted electrons are investigated as associated with the peculiar 4d character of the photoionization and Auger decay.