A many-body theory for a two-component system of spin-polarized interacting fermions in a one-dimensional harmonic trap is developed. The model considers two different states of the same fermionic species and treats the dominant interactions between the two using the bosonization method for forward scattering. Asymptotically exact results for the one-particle matrix elements at zero temperature are given. Using them, occupation probabilities of oscillator states are discussed. Particle and momentum densities are calculated and displayed. It is demonstrated how interactions modify all these quantities. An asymptotic connection with Luttinger liquids is suggested. The relation of the coupling constant of the theory to the dipole-dipole interaction is also discussed.

A time-resolved measurement of the output from the Ni-like Ag transient-collisional-excitation x-ray laser is described. An ultrafast x-ray streak camera was used to diagnose the output of the $J=\overrightarrow{0}1$ $4d-4p$ lasing line at 13.9 nm. The full width at half maximum duration of the x-ray pulse is measured to be of $1.9\pm 0.7\hspace{0.5em}\mathrm{ps}$ at optimum conditions of pump laser irradiation. This is the shortest x-ray laser duration directly demonstrated to date and illustrates the great potential of transient x-ray lasers as a high brightness, picosecond x-ray source for applications.

We predict and experimentally observe temporal self-pulsing in singly resonant intracavity second-harmonic generation under conditions of simultaneous parametric oscillation. The threshold for self-pulsing as a function of cavity tuning and phase mismatch are found from analysis of a three-component mean-field model. Analytical mean-field calculations of the self-pulsing frequency as well as numerical simulations including the effects of a time-dependent pump pulse agree with the experimentally observed frequencies.

We propose a scheme for quantum computation using two eigenstates of ammonia or similar molecules. Individual ammonia molecules are confined inside fullerenes and used as two-level qubit systems. Interaction between these ammonia qubits takes place via the electric dipole moments, and in particular we show how a controlled-NOT gate could be implemented. After computation the qubit is measured with a single-electron electrometer sensitive enough to differentiate between the dipole moments of different states. We also discuss a possible implementation based on a quantum cellular automaton.

The $5p$ photoemission spectrum of atomic europium has been analyzed using high-resolution photoelectron spectroscopy. In contrast to the expected simple multiplet structure of a ${5p}^{-1}{4f}^7{(}^{8}S)$ configuration with six main lines, the observed Eu $5p$ photoemission shows a very complex spectrum. Configuration-interaction calculations reveal that the $5p$ core hole gives rise to a near degeneracy of the valence subshells in the final ionic states, so that the main multiplet structure of the spectrum can only be described by a strong mixture of the configurations ${6s}^2,$ $6s5d,$ ${5d}^2,$ and ${6p}^2.$ This mixing also results in a strong broadening of the lines at higher binding energy.

We demonstrate experimentally that far-off-resonance stimulated Raman scattering in solid hydrogen driven by a strong-coupling field allows us to slow down the pulse-peak velocity of the Stokes and anti-Stokes fields to the order of $c/10\mathrm{}000.$ We observe the splitting of the temporal profile of the sideband-field pulses into a two-peak structure that is a signature of the separation between the copropagating normal modes.

Triply excited states of three-electron ions have been produced by resonant transfer excitation (RTE) in metastable two-electron-ion-beam–${\mathrm{H}}_2$ collisions. Measurements of the Auger-electron emission in the direction of the ion beam is used to determine the absolute cross sections for formation of the triply excited states and the branching ratios of the corresponding elastic and inelastic electron scattering channels. The results are compared to existing theoretical calculations of the Auger decay rates. Accurate measurements of the double differential cross sections are made on the bases of the known metastable ion beam fractions and known cross sections for RTE from the ground-state component of the beam. The system investigated is ${\mathrm{B}}^{3+}\left(1s2s{}^{3}S\right)+{\mathrm{H}}_2$ leading to the ${\mathrm{B}}^{2+}{(2s2p}^2{}^{2}D)$ resonance that decays to ${\mathrm{B}}^{3+}\left(1s2s{}^{3}S\right),$ the elastic scattering channel and to ${\mathrm{B}}^{3+}\left(1s2s{}^{1}S\right)$ and ${\mathrm{B}}^{3+}\left(1s2p{}^{3}P\right),$ two inelastic scattering channels.

In an attempt to obtain a suitable access to the quantum description of a continuum electron in a combined Coulomb and homogeneous magnetic field, we first illustrate the complexity of the problem by selected classical trajectories. Subsequently, we examine the properties and consequences of two particular gauges for representing a homogeneous magnetic field, in particular, their usefulness in describing Coulombic bound and continuum states. We show that in the absence of a Coulomb field, the Landau gauge but not the axial gauge allows for a simple construction of asymptotic states that satisfy the requirement of tending to plane waves in the limit of vanishing field strength.

We study the scattering of an electron from a one-dimensional inverted Gaussian atomic potential in the presence of strong time-periodic electric fields. Using Floquet theory, we construct the Floquet scattering matrix in the Kramers-Henneberger frame. We compute the transmission coefficients as a function of electron incident energy and find that they display asymmetric Fano resonances due to the electron interaction with the driving field. We find that the Fano resonances are associated with zero-pole pairs of the Floquet scattering matrix in the complex energy plane. Another way we “probe” the complex spectrum of the system is by computing the Wigner-Smith delay times. Finally, we find that the eigenphases of the Floquet scattering matrix undergo a number of “avoided crossings” as a function of electron Floquet energy, and this number increases with increasing strength of the driving field. These “avoided crossings” appear to be quantum manifestations of the destruction of the constants of motion and the onset of chaos in classical phase space.

We consider systems of interacting bosons confined to one-dimensional harmonic traps. In the limit of perturbatively weak two-body interactions the system exhibits several universal states that are exact solutions for a large class of two-body interactions. These states are closely related to the exact solutions found previously in rotating Bose-Einstein condensates.

A simple model of an atomic Bose-Einstein condensate in a box whose size varies with time is studied to determine the nature of adiabaticity in the nonlinear dynamics obtained within the Gross-Pitaevskii equation (the nonlinear Schrödinger equation). Analytical and numerical methods are used to determine the nature of adiabaticity in this nonlinear quantum system. Criteria for validity of an adiabatic approximation are formulated.

Combining the one-dimensional propagation equation and wavelet transform of the dipole of an atom in an intense laser field, the spectra of harmonics generated and propagated in an ionizing noble gas have been analyzed. It shows that the spectral lines of harmonics exhibit broadening, blueshifting, and splitting into two peaks owing to the rapid ionization of gases and make the spectra of high-order harmonic emissions become quasicontinuum in the higher-order region.

We present a numerical model for the interaction of a femtosecond probe pulse with a Raman medium excited by two nanosecond laser pulses in solid hydrogen. The model consists of a solution of a system of Bloch equations (for the medium state) and of the two-dimensional wave equation (for the field propagation). It is shown that by optimizing the tilt angle between the two driving pulses and the interaction length, the power of the probe pulse can be converted either into a quasicontinuous broadband spectrum or into a selected high-order sideband. The first situation can be used for generation of subfemtosecond pulses. The second situation can be used for the wavelength conversion of a femtosecond probe pulse from the infrared to the ultraviolet region. Due to the transfer of energy from the driving pulses, the energy conversion efficiency of these processes (with respect to the probe pulse) can be larger than unity.

The absolute cross sections for the ${3d}^2{}^3\overrightarrow{F}3d4p{}^{3}D,$ ${}^{3}F$ excitation of ${\mathrm{Ti}}^{2+}$ ions at electron energies close to threshold (9–10 eV) were measured using the merged electron-ion beams energy-loss technique. The value of the cross-section step for the sum of the 13 allowed transitions to ${}^{3}D$ and ${}^{3}F$ levels, separated in energy by less than $0.1\hspace{0.5em}\mathrm{eV},$ is found to be $(0.84\mathrm{}\pm 0.18)\times {10}^{-16}\hspace{0.5em}{\mathrm{cm}}^2.$ Results from a set of first-order distorted-wave calculations range from $0.53\times {10}^{-16}\hspace{0.5em}{\mathrm{cm}}^2$ to $1.63\times {10}^{-16}\hspace{0.5em}{\mathrm{cm}}^2.$

Resonances of ${}^4{S}^e$ symmetry in ${\mathrm{He}}^{-}$ are searched for in the region above the ${\mathrm{He}}^{+}\mathrm{}(n=1\mathrm{})\mathrm{}$ threshold and below the ${\mathrm{He}}^{+}\mathrm{}(n=2\mathrm{})\mathrm{}$ threshold. The energies and widths of the resonances are calculated with an ab initio three-electron description of the ion. The complex rotation method is combined with the use of B splines in a spherical cavity to describe the ion and the decay channels. Seven resonances are found and five are presented with energy position and width.

We have evaluated electron capture and excitation cross sections in collisions of ${\mathrm{H}}^{+}$ with isoelectronic ${\mathrm{Na}}_{20+q}^{q+}$ clusters $(q=-1,0,+1)$ in the impact energy range 40–500 eV. The theoretical method includes the many-electron aspect of the problem and makes use of realistic cluster potentials obtained with density-functional theory and a spherical jellium model. As expected, electron capture decreases monotonically with cluster charge, but the corresponding mechanism does not follow a common pattern. Excitation cross sections are very similar in the three cases investigated here.

We introduce dimensional perturbation techniques to Bose-Einstein condensation of inhomogeneous alkali-metal gases. The perturbation parameter is $\delta =1/\kappa ,$ where $\kappa$ depends on the effective dimensionality of the condensate and on the angular momentum quantum number. We derive a simple approximation that is more accurate and flexible than the $\overrightarrow{N}\infty$ Thomas-Fermi ground-state approximation of the Gross-Pitaevskii equation. The approximation presented here is well suited for calculating properties of states in three dimensions and in low-effective dimensionality, such as vortex states in a highly anisotropic trap.

Dynamics of fluctuations in unstable Bose-Einstein condensates is analyzed by the solution of approximate operator equations. In the case of a condensate with a negative scattering length the present treatment describes a delay of collapse, in agreement with recent experiments. In the case of a collision of two condensate wave packets it is shown that quantum effects lead to a Bose enhancement of elastic-scattering losses. In both cases the noncondensate atoms are formed as entangled pairs in squeezed states.