A redundancy in the existing Deutsch-Jozsa quantum algorithm is removed and a refined algorithm, which reduces the size of the register and simplifies the function evaluation, is proposed. The refined version allows a simpler analysis of the use of entanglement between the qubits in the algorithm and provides criteria for deciding when the Deutsch-Jozsa algorithm constitutes a meaningful test of quantum computation.

We report the successful trapping of $6\times {10}^6$ ${}^{82}\mathrm{Rb}$ ${(t}_{1/2}=75\mathrm{}\mathrm{s})$ atoms with a trap lifetime of $\sim 30\mathrm{s}$ in a magneto-optical trap that is coupled to an off-line mass separator. Efficient sample introduction is achieved by implanting ${}^{82}\mathrm{Rb}$ ions into a small yttrium catcher foil located inside the trapping cell. Upon heating, the radioactive atoms are released from the foil and trapped without significant gas loading. This advancement makes a variety of high-precision electroweak interaction experiments possible, including the measurement of β-decay correlations associated with spin-polarized ${}^{82}\mathrm{Rb}$ nuclei.

Analytical expressions are derived for the asymptotic correlated three-body state of a Coulomb compound consisting of a continuum particle and an electron bound to a residual ion. The extension of these expressions to finite distances is also given. The distortion of the continuum particle’s motion by the Coulomb nuclear field and the field of the bound electron is investigated as well as the amount of polarization of the bound system due to coupling of the bound electron to the continuum particle.

The intensity and angular distribution of emitted electrons have been measured at several photon energies at the Cl ${2p}_{3/2}\to 4p(\sigma ,\pi )$ resonances of the HCl molecule. The orientation of the core hole is concluded from the overall intensity distribution. The final states of resonant Auger transitions are identified with the aid of angular distribution that together with the final-state energy splittings, reveals the σ or π nature of the excited electron also in the intermediate state.

We present autoionization spectra of metastable ${\mathrm{Ar}}^{8+}$ and ${\mathrm{C}}^{4+},{\mathrm{N}}^{5+},{\mathrm{O}}^{6+},$ and ${\mathrm{Ne}}^{8+}$ scattering off an Al(111) surface with incident energies down to 5 eV. The unprecedented statistical quality of the experimental data permits the observation of structures originating from the metastable projectiles compared to corresponding ground-state configurations. Analyzing the peak positions for different projectile species and velocities we demonstrate that the peak must be ascribed to an above-surface transition with the participation of the metastable state.

The scattering theory formulation of the stopping power of a homogeneous electron gas is implemented by consistent velocity-dependent potentials, which are needed to calculate transport cross sections for bare intruders. The method of volume averaging, over the Wigner-Seitz atomic cell of a solid Al target, is employed to characterize inhomogeneities of the electronic system and define average stopping powers for cases of protons and antiprotons. The theoretical results for average energy losses of both projectiles are in remarkable agreement with recent experimental data over a broad range of projectile velocities.

We have studied a single neutral atom stored in a magneto-optical trap by recording arrival times of fluorescence photons emitted by the atom. Photon correlations at nanosecond scales (Rabi oscillations), at microseconds (intensity and polarization correlations), and also at milliseconds (position correlations) reveal the dynamical behavior of the atomic excitation, of the atomic orientation, and of its transport in the trap at both the optical wavelength scale and the trap size.

We propose the engineering of the vibronic coupling of a trapped atom by appropriate laser excitations. This allows one to substantially generalize the available class of Hamiltonians, which are suited for many applications.

A general scheme for mass renormalization of the electron self-energy in strong nuclear fields is developed. In second order the results agree with those recently obtained by Labzowsky and Mitrushenkov [Phys. Rev. A 53, 3029 (1996)], and, in particular, it is shown that the extra counterterm observed by these authors appears quite naturally in the more general scheme developed here.

All-order relativistic many-body calculations of removal energies are carried out for $3s$, ${3p}_{1/2},$ ${3p}_{3/2},$ ${3d}_{3/2},$ ${3d}_{5/2},$ and $4s$ states of sodium and sodiumlike ions with nuclear charges $Z$ in the range 12–16. Hyperfine constants are evaluated for each state, and reduced dipole matrix elements are determined for ${3p}_{1/2}$-$3s$, ${3p}_{3/2}$-$3s$, ${3d}_{3/2}$-${3p}_{1/2},$ ${3d}_{3/2}$-${3p}_{3/2},$ ${3d}_{5/2}$-${3p}_{3/2},$ $4s$-${3p}_{1/2},$ and $4s$-${3p}_{3/2}$ transitions. The calculations include single and double excitations of the Hartree-Fock ground state to all orders in perturbation theory. Corrections to energies are made for a dominant class of triple excitations. The Breit interaction, with all-order correlation corrections, is evaluated. Reduced-mass and mass-polarization corrections are included to third order in perturbation theory. The predicted removal energies, when corrected for the Lamb shift, agree with experiment at the 1–20-${\mathrm{cm}}^{-1}$ level of accuracy for all states considered. Theoretical fine-structure intervals agree with measurements to about 0.3% for $3p$ states and to about 3% for $3d$ states. Theoretical hyperfine constants and line strengths agree with precise measurements to better than 0.3%.

The Rautian-Sobelman approach describing the collision-Doppler shape of spectral line that takes into account both soft and hard velocity-changing collisions is extended to the case when correlation between Doppler and collision broadening as well as the dispersion line asymmetry should be considered. Numerical calculations show that speed-dependent effects can produce the additional line narrowing as well as broadening and also the line asymmetry. It is shown that speed-dependent profiles based on the soft and hard collision models differ much more one from another than those which omit the speed-dependent effects.

$L$-shell fluorescence yields were measured for seven elements Tb, Dy, Ho, Er, Yb, Ta, and W using a Ge(Li) detector. The targets were excited using 59.5-keV γ rays from ${\mathrm{Am}}^{241}$ radioactive source of strengths 100 mCi. The results obtained were compared with the theoretical values and other measured values. It is shown that the present results are in good agreement with earlier experimental and theoretical results.

The results of quantum photoabsorption calculations are presented for H, K, and Cs atoms in static electric fields. The recurrence spectra for $〈L_z〉\ne 0$ show features at scaled actions an order of magnitude shorter than for any classical closed orbit of this system. Two interesting manifestations are presented, and some of the systematics of the peak strengths are explored. These features suggest that closed-orbit theory may need to be generalized to account for these effects. A heuristic formula is presented that reproduces some of these effects.

The $3{}^1\Pi$ and $6{}^1{\Sigma }^{+}$ states of the NaK molecule were investigated by polarization labeling spectroscopy in a heat pipe oven. About 2000 molecular transitions in the $3{}^1\Pi \leftarrow X{}^1{\Sigma }^{+}$ and $6{}^1{\Sigma }^{+}\leftarrow X{}^1{\Sigma }^{+}$ band systems were measured in the $24600–27700{\mathrm{cm}}^{\mathrm{-}1}$ spectral range. The analysis provided molecular constants and the potential-energy curve corresponding to 97% of the potential well of the $3{}^1\Pi$ state. For the double minimum $6{}^1{\Sigma }^{+}$ state nearly the whole inner potential well was characterized. The results are compared with the predictions of recent theoretical calculations.

We present a complete calculation of the leading nonrecoil radiative corrections to the $1s$ hyperfine-structure splitting of highly charged hydrogenlike ions. In particular, we have investigated how the radiative corrections for ions with a high nuclear charge number $Z$ are affected by using an extended nuclear magnetization. We also present the first complete evaluation of the Wichmann-Kroll part of the vacuum polarization correction to all orders in $\left(Z\alpha \right)$. To unambiguously incorporate this effect we have also calculated the vacuum polarization correction to the measured nuclear magnetic moment. Total theoretical results are collected for the experimentally interesting ions ${}^{209}{\mathrm{Bi}}^{82+},$ ${}^{207}{\mathrm{Pb}}^{81+},$ ${}^{185}{\mathrm{Re}}^{74+},$ and ${}^{165}{\mathrm{Ho}}^{66+}.$ Also the low-$Z$ region is considered in order to compare with the known part of the $\left(Z\alpha \right)$ expansion.

Relativistic multiconfiguration Dirac-Fock theory was applied in calculating the atomic structure of Fe XXIII. These calculations are needed in solar-flare spectra and laboratory plasma modeling and diagnostics, as well as the relativistic distorted-wave calculation of electron impact excitation. For Fe XXIII, relativistic effects begin to show a more or less significant influence on the radial wave function and atomic structure in contrast to a lower-$Z$ Be-like ion. In the present calculation, a large-scale configuration expansion was used in describing the target states. These results are extensively compared with those of nonrelativistic and other calculations. Large differences are found in these comparisons. Comparisons with experimental and observed values, wherever available, are also made. Because more relativistic effects and correlation effects are caught than before, the present results should be more accurate and reliable.

The recently reported discrepancy between the experimentally determined value for the dipole polarizabity of the ${\mathrm{H}}_2^{+}$ ground state [Phys. Rev. A 56, R4361 (1997); 57, 4065 (1998)] and the adiabatic value calculated in the clamped nucleus approximation [Mol. Phys. 65, 679 (1988)] has motivated a fully nonadiabatic treatment of the problem. Finite element analysis is used to obtain a direct solution of the zeroth- and first-order equations of perturbation theory. The nonadiabatic value for ${\alpha }_s$ is consistent with the experimental measurement.

High-precision laser absorption spectroscopy in a thermal vapor cell is used in the measurement of the ratio of the $D$-line transition strengths in the cesium atom. We find $\mathbf{|}〈{6p}^2{P}_{3/2}||\overrightarrow{r}||{6s}^2{S}_{1/2}〉{\mathbf{|}}^2/\mathbf{|}〈{6p}^2{P}_{1/2}||\overrightarrow{r}||{6s}^2{S}_{1/2}〉{\mathbf{|}}^2=1.9809\mathrm{}\left(9\right),$ which compares favorably with the ratio calculated from the most precise lifetime measurements of these states and the predictions of ab initio calculation. We also verify the predictions of impact-regime line-broadening calculations for densities of order ${10}^{18}$ atoms per ${\mathrm{m}}^3.$ Theoretical implications and future experimental promise are discussed.

In this work, 14 even-parity ${2l2l}^{\prime }{\mathrm{nl}}^{″}$ $(n>~3)$ resonances of lithium are calculated by using the saddle-point complex-rotation method. Among the 14 resonances, four are ${}^{2}P$ resonances, four are ${}^{2}D$ resonances, and six are ${}^{2}S$ resonances. Relativistic corrections are evaluated with the first-order perturbation theory and the mass-polarization effect is also included. The Auger widths are studied. The partial Auger widths are calculated for the individual open channels and the total width is obtained by coupling the important open channels. These results are compared with recent theoretical and experimental data in the literature.