Using nuclear-magnetic-resonance techniques, we experimentally investigated the effects of applying a two-bit phase error detection code to preserve quantum information in nuclear spin systems. Input states were stored with and without coding, and the resulting output states were compared with the originals and with each other. The theoretically expected result, net reduction of distortion and conditional error probabilities to second order, was indeed observed, despite imperfect coding operations which increased the error probabilities by approximately 5%. A systematic study of the deviations from the ideal behavior provided quantitative measures of different sources of error, and good agreement was found with a numerical model. Theoretical questions in quantum error correction in bulk nuclear spin systems including fidelity measures, signal strength, and syndrome measurements are discussed.

It was shown recently [D. A. Lidar et al., Phys. Rev. Lett. 81, 2594 (1998)] that within the framework of the semigroup Markovian master equation, decoherence-free (DF) subspaces exist which are stable to first order in time to a perturbation. Here this result is extended to the non-Markovian regime and generalized. In particular, it is shown that within both the semigroup and the non-Markovian operator sum representation, DF subspaces are stable to all orders in time to a symmetry-breaking perturbation. DF subspaces are thus ideal for quantum memory applications. For quantum computation, however, the stability result does not extend beyond the first order. Thus, to perform robust quantum computation in DF subspaces, they must be supplemented with quantum error correcting codes.

To implement many-qubit gates for use in quantum simulations on quantum computers efficiently, we develop and present methods reexpressing $\exp [-{i(H}_1{+H}_2+\cdot \cdot \cdot )\Delta t]$ as a product of factors $\exp \left[-{\mathrm{iH}}_1\Delta t\right],$ $\exp \left[-{\mathrm{iH}}_2\Delta t\right],\dots$, which is accurate to third or fourth order in $\Delta t$. The methods we derive are an extended form of the symplectic method, and can also be used for an integration of classical Hamiltonians on classical computers. We derive both integral and irrational methods, and find the most efficient methods in both cases.

A quantum-convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of the quantum-convolutional code, I report a way to decode certain quantum-convolutional codes based on the classical Viterbi decoding algorithm. This decoding algorithm is optimal for a memoryless channel. I also report three simple criteria to test if decoding errors in a quantum-convolutional code will terminate after a finite number of decoding steps whenever the Hilbert space dimension of each quantum register is a prime power. Finally, I show that certain quantum-convolutional codes are in fact stabilizer codes. And hence, these quantum stabilizer convolutional codes have fault-tolerant implementations.

A density-matrix approach has been developed for the angular distribution and polarization of radiative emission during single-photon atomic transitions for a general set of steady-state excitation processes in an arbitrary arrangement of static (or quasistatic) electric and magnetic fields. Particular attention has been directed at spectroscopic observations in the intense fields of the high-power ion diodes on the Particle Beam Fusion Accelerator II (PBFA II) and SABRE devices at Sandia National Laboratories and at magnetic-field measurements in tokamak plasmas. The field-dependent atomic eigenstates are represented as expansions in a complete basis set of field-free bound and continuum eigenstates. Particular emphasis has been given to directed-electron collisional excitations, which may be produced by an anisotropic incident-electron velocity distribution. We have allowed for the possibility of the coherent excitation of the nearly degenerate field-dependent atomic substates, which can give rise to a complex spectral pattern of overlapping Stark-Zeeman components. Coherent excitations may be produced by a beam of electrons that are spin-polarized at an angle with respect to the propagation direction or by nonparallel electric and magnetic fields. Our main result is a general expression for the matrix elements of the photon-polarization density operator representing the total intensity, angular distribution, and polarization of the atomic radiative emission. For the observation of radiative emission in the direction of the magnetic field, the detection of linearly polarized emission, in addition to the usual circularly polarized radiation, can reveal the presence of a perpendicular electric field or a coherent excitation mechanism.

The dynamical localization of the $\mathrm{O}\hspace{0.5em}1s$ core holes in the ${\mathrm{CO}}_2$ molecule is studied ab initio beyond the linear vibronic coupling model. The vibrational structure of the $\mathrm{O}\hspace{0.5em}1s$ x-ray photoelectron spectrum (XPS) has been calculated employing accurate potential energy surfaces of the ground and ionized diabatic electronic states obtained at the self-consistent field and singles and doubles configuration-interaction (SDCI) methods. A very good agreement of the SDCI computed vibrational structure of the $\mathrm{O}\hspace{0.5em}1s$ XPS with the respective experimental high-resolution spectrum has been obtained. The anharmonicity of the ionic state potential-energy surface induced mostly by the ground-state surface anharmonicity plays a crucial role in the proper description of the vibrational line intensities. The linear model is discussed in detail. The linear model based on the vibronic coupling constants obtained from the geometry change in the ionized state relative to the ground-state reference configuration has been shown to contain a hidden renormalization of the coupling constants. This improves the agreement of the calculated intensities of the vibrational lines in the spectrum with the experiment, compared to the case of the strict linear model. The limitations of this renormalized linear model are discussed. Electron relaxation and correlation considerably affect the vibrational line intensities. The popular equivalent core approximation is tested for ${\mathrm{CO}}_2$. The calculation of the $\mathrm{O}\hspace{0.5em}1s$ XPS performed at the SDCI level with and without this approximation is shown to provide almost identical results on the vibrational intensities.

For the lithium dimer we calculate cross sections for absorption of radiation from the vibrational-rotational levels of the ground $X{}^1{\Sigma }_g^{+}$ electronic state to the vibrational levels and continua of the excited $A{}^1{\Sigma }_u^{+}$ and $B{}^1{\Pi }_u$ electronic states. Theoretical and experimental data are used to characterize the molecular properties taking advantage of knowledge recently obtained from photoassociation spectroscopy and ultra-cold atom collision studies. The quantum-mechanical calculations are carried out for temperatures in the range from 1000 to 2000 K and are compared with previous calculations and measurements where available.

We examine the existence of stable bound states of some diatomic molecular ions where the neutral molecule itself is either unbound or barely bound. Two bound states have been found for the ${\mathrm{HeH}}^{-}$ ion even though HeH is known to be unbound. We have found no bound states for ${\mathrm{He}}_2^{-}$ even though ${}^4{\mathrm{He}}_2$ is known to have one bound state. The predicted binding energies for ${\mathrm{HeH}}^{-}$ are of the order of 1 K and depend sensitively on the isotope combinations. Other weakly bound negative ions such as ${\mathrm{NeH}}^{-}$ and ${\mathrm{ArH}}^{-}$ have also been investigated. These weakly bound molecular ions are good candidates for cold collision experiments.

The $K\alpha$ and $K\beta$ x-ray fluorescence cross sections have been measured for elements in the range $44<~Z<~68$ at an excitation energy of 59.5-keV γ ray from ${}^{241}\mathrm{Am}$ radioisotope with a Si(Li) detector. A reasonable agreement is found between the present experimental results and the theoretically calculated values based on photoionization cross sections by Scofield using Hartree-Slater and Hartree-Fock central potential theory.

The $K\alpha$ and $K\beta$ spectra from metallic scandium, the first of the $3d$ transition elements, were measured using a high-resolution curved crystal spectrometer. The spectrometer resolution was determined employing a narrow emission line from pionic neon. The parameters of the resolution-corrected spectrum are extracted and compared to previous studies and theory. Fits to ab initio relativistic Dirac-Fock calculated spectra show that the $K\alpha$ spectrum can be accounted for using an isolated-atom model with diagram, $\underset{¯}{3d}$- and $\underset{¯}{3p}$- spectator hole transitions. The $K\beta$ spectrum, however, cannot be fitted by such isolated-atom multiplets and may require employing nonlocalized bonding orbitals.

An earlier electron-beam ion-trap (EBIT) lifetime measurement of the ${\mathrm{Ne}}^{8+}\hspace{0.5em}1\mathrm{s}2\mathrm{s}{}^3{S}_1$ level has been improved upon, reducing the uncertainties to less than the scatter in the existing theoretical calculations. The new result, $91.7\pm 0.4\hspace{0.5em}\mu \mathrm{s},$ agrees with the previous value, but is more precise by a factor of 4. The new value distinguishes among theoretical values, as agreement is obtained only with those calculations that employ “exact” nonrelativistic or relativistic wave functions. Routes to measurements with even higher accuracy are discussed.

The $4p$ hole spectral function of Ba metal is calculated by an ab initio atomic Green’s-function method. The atom-metal energy shifts of the interacting hole (particle) states are taken into account. It is shown that for a consistent description of the spectral line positions, intensities, and linewidths, it is necessary to take into account explicitly such energy shifts. The $4p$ x-ray photoelectron spectroscopy spectra of Ba metal and compounds are analyzed in detail. The $2s-4p$ x-ray emission spectroscopy spectrum of La metal is also discussed. For the $4p$ level ionization of Ba metal and compounds, the one-electron approximation breaks down. This is due to the Coster-Kronig (CK) ${4p-4d}^{-2}4f$ process by which an empty $4f$ level is filled by a $4d$ electron rather than by a ligand valence electron [charge-transfer (CT) screening] or a conduction-band electron. A possibility of suppression of both CK and CT core-hole screening in a final state by decay of a resonantly excited core-hole state and a fully relaxed core-hole state where an $4f$ empty level is already occupied in an initial core-hole state is discussed.

The complete spectra of core-valence dicationic states, i.e., states with one vacancy in the core and one in the valence shell, of the molecules ${\mathrm{BF}}_3,$ ${\mathrm{AlF}}_3,$ ${\mathrm{BCl}}_3$, and ${\mathrm{AlCl}}_3$, are investigated by the Green’s-function method. An analysis of the double-hole density in the corresponding correlated states shows that when the core hole is on a ligand (halogen) atom, the valence hole is also strongly localized, either on the same ligand or on a different ligand. As a result these states can be classified as either on-core or off-core site states. We discuss how the localization phenomena are at the origin of the chlorine $\mathrm{KLV}$ Auger spectra of ${\mathrm{BCl}}_3$ and ${\mathrm{AlCl}}_3$ and, in particular, how they provide a complete and conclusive interpretation of these spectra. Due to the intra-atomic nature of the Auger process, the simulation of the chlorine and aluminum $\mathrm{KLV}$ Auger spectra is done by a simple convolution of the respective on-core site component of the computed two-hole density distribution. The ligand atom spectra contain almost no information about the molecular system, representing an indistinct self-image of the ligand atom itself, whereas the central atom spectra render a distinct foreign image of the molecular environment.

Using the most accurate potential curves available for the $a{}^3{\sum }_u^{+}$ and $X{}^1{\sum }_g^{+}$ states of lithium molecules, we compute the positions of shape resonances. We also calculate the deexcitation probability from a bound level $v^{\prime }$ with rotational number $N^{\prime }$ to the continuum of the lower state, and conclude that a shape resonance should be measurable for the transition $2{}^3{\prod }_g\to a{}^3{\sum }_u^{+}$. Such a shape resonance has been identified from the spectra of the transition from the $v^{\prime }{=2,N}^{\prime }=4\mathrm{}$ level of $2{}^3{\prod }_g$ into the $N^{″}=4\mathrm{}$ continuum of $a{}^3{\sum }_u^{+}$. Its position is in good agreement with the theoretical prediction.

The quantum electrodynamical effects of radiative interference in the recombination of electrons with heavy multicharged ions are discussed. Numerical calculations of the corresponding cross sections in the vicinities of ${\mathrm{KL}}_{12}{M}_{12}$ and ${\mathrm{KM}}_{12}{M}_{12}$ dielectronic recombination resonances of the heliumlike uranium have been performed. The results obtained may serve as a focus for near-future experiments with the Super-EBIT facilities.

A theoretical description of dichroism in the photoelectron spectra of atoms polarized in different directions is presented. It is based on the general expression for the photoelectron angular distribution written in $\mathrm{LSJ}$ approximation. We show that, for photon energies far above threshold, the spectral distribution of dichroism in the photoelectron spectrum in most cases does not depend on the photoionization dynamics; for atoms with S symmetry, simple spectral patterns are obtained. Useful sum rules are given for the dichroism integrated over groups of photoelectron multiplet lines. Recent experimental data on magnetic dichroism and linear dichroism in the nonresonant inner-shell spectra of Cr $(3p$ shell), Eu $(4f$ shell), and Fe $(3p$ shell) are analyzed. An outlook is given on the dichroism in the region of autoionization resonances.

A complete set of total and dissociative electron-impact cross sections of vibrationally excited ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ molecules has been calculated by using the impact-parameter method. Transitions to low-lying Rydberg states $(\overrightarrow{X}{B}^{\prime },\overrightarrow{X}{B}^{″},\overrightarrow{X}D,\overrightarrow{X}{D}^{\prime })$ are considered. Finally, vibrational and mass scaling relations, able to reproduce the calculated cross sections, are presented.

In the frame of quantum defect theory, a simplified relativistic configuration-interaction method is developed to study the dielectronic recombination (DR) processes. In this method, the infinite resonant doubly excited states involving high Rydberg states can be treated conveniently in a unified manner by interpolation. This provides an efficient method to check the validity of extrapolation based on the $n^{-3}$ scaling law, which is widely used to treat the DR processes involving high Rydberg states. As an example, we studied the DR processes for Li-like argon, and the results are compared with the scaling laws and the experimental measurements, respectively.

A five-body classical trajectory Monte Carlo model has been developed to study fragmentation of diatomic molecules after double electron removal by highly charged ion impact. A systematic study of the final-state deuteron energy and momentum spectra has been conducted for ${\mathrm{Xe}}^{19+}$ + ${\mathrm{D}}_2$ collisions at impact energies ranging from 1 eV/u to 100 keV/u. At the highest projectile energies, the fragment energies and momenta are determined by the Coulomb explosion of the doubly-ionized molecule via the known Franck-Condon transition for the isolated molecule. The deuterons are emitted back-to-back with nearly equal energies. At the lowest projectile energies, the final state behavior is due mainly to the collisional momentum transfer from the slow-moving projectile. The deuterons are strongly scattered in the direction opposite to the transverse momentum of the projectile with energies far greater than those produced in the Franck-Condon transition. At energies around 150 eV/u, both slow and fast deuterons are predicted. This is due to the vector addition of the collisional momentum transfer to the center of mass of the molecule with that due to the two-body Coulomb breakup of the dissociating ions.

Owing to the crucial role played by elastic scattering in various gas/plasma environments and to its fundamental nature, we consider in the present work low-energy collisions among isotopic variants of ${\mathrm{H}}^{+}+\mathrm{H},\hspace{0.5em}\mathrm{H}+\mathrm{H},$ and ${\mathrm{H}}^{+}+{\mathrm{H}}_2.$ In particular, we present consistent definitions of the elastic-scattering cross section and its common transport relevant moments regarding the quantum indistinguishability or classical distinguishability of particles, correcting some inappropriate definitions found in the literature. Further, we utilize a large collection of fully quantal calculated results for these systems to display the scaling relationships that exist among them.