We consider a quantum computer with $n$ quantum bits (“qubits”), where each qubit is coupled independently to an environment affecting the state in a dephasing or depolarizing way. For mixed states we define a parameter indicating quantum uncertainty on the macroscopic level. We illustrate in which sense a large parameter can be seen as an indicator for large entanglement and give hypersurfaces enclosing the set of separable states. Using methods of the classical theory of maximum likelihood estimation we prove that this parameter is decreasing with $1/\sqrt{n}$ for all those states which have been exposed to the environment. Furthermore we consider a quantum computer with perfect 1-qubit gates and two-qubit gates with a depolarizing error and show that any state which can be obtained from a separable initial state lies inbetween a family of pairs of certain hypersurfaces parallel to those enclosing the separable ones.

One- and two-electron densities are calculated for the ground state of the lithium atom starting from a highly accurate Hylleraas-type wave function. An analytical parametrization for those densities is obtained, which allows one to calculate both the form factor and the structure factor. Electronic correlation effects are discussed in terms of these densities and related functions such as the Coulomb hole. The calculation of the densities has been performed by means of the Monte Carlo method.

The homotopy method is used to obtain a complete set of solutions of multireference coupled-cluster equations within the framework of the state-universal coupled-cluster (SUCC) formalism. The solutions are obtained for an ab initio four-electron model system consisting of four hydrogen atoms in rectangular arrangement. Essential information about the structure of solutions of nonlinear SUCC equations is provided and analyzed, both numerically and analytically, in the form of two theorems. The existence of multiple solutions of SUCC equations provides new insights into the nature of convergence problems often encountered in SUCC calculations. The evidence for the possible association of some solutions of the SUCC equations with the intruder-state problem is presented and briefly discussed.

We point out the potential of the diatomic molecule PbO as a system in which to search for an electron electric dipole moment (EDM). Large oscillator strengths between various electronic states of PbO would be beneficial for such an experiment. As a step toward determining these oscillator strengths, we have measured a number of radiative lifetimes and branching ratios in PbO. We discuss the impact of our measurements on the proposed EDM experiment and point out the need for further experimental and theoretical work on PbO.

Cross sections have been determined for ionization as well as stripping in collisions between protons and ${\mathrm{He}}^{+}$ ions in the $1s,$ $2s,$ or $3s$ state for proton energies from 200 keV to 2 MeV using the coupled-Sturmian-pseudostate approach. Detailed convergence studies are presented. For comparison, and to include neglected higher partial waves, first Born cross sections are also reported. By using a larger basis, this work extends earlier calculations that were limited to the $1s$ initial state [T. G. Winter and S. G. Alston, Phys. Rev. A 45, 1562 (1992)]. Further, a correction has been applied to the uneven distribution of Sturmian-generated energies at the ionization threshold, yielding cross sections much more stable with respect to basis size.

We experimentally demonstrate laser spectroscopy of the electric-quadrupole transition $6s{}^2{S}_{1/2}–5d{}^2{D}_{3/2}$ of a single trapped ${}^{171}\mathrm{Yb}$ ion. The probed transition has a natural linewidth of 3.1 Hz, and is at a wavelength of 435.5 nm. A ${}^{171}\mathrm{Yb}$ ion is laser cooled to the range of the Doppler limit in a radio-frequency Paul trap. The $F=0\mathrm{}–F^{\prime }=2,$ $m_{F^{\prime }}=0\mathrm{}$ hyperfine component of the ${}^2{S}_{1/2}{–}^2{D}_{3/2}$ transition is excited by a laser source whose frequency is controlled by an optical reference cavity of high intrinsic stability. The recoilless carrier component of the vibrational sideband spectrum is resolved with a minimum linewidth of approximately 80 Hz, corresponding to a fractional frequency resolution of $1.2\times {10}^{-13}.$ This resolution limit is attributed to laser frequency instability. The effective decoherence rates of the residual ion motion are inferred from the observation that the axial and two radial low-frequency first-order secular-vibration sidebands show minimum linewidths in the range of 0.2–1 kHz. Prospects for an optical frequency standard based on the investigated atomic system are discussed.

The absorption properties of degenerate two-level atomic systems tested by a weak probe field in the presence of an intense pump field have been analyzed. The theoretical model previously presented in Phys. Rev. A 61, 013801 (1999) that appears to be suitable for arbitrary choices of the pump intensity, level angular momenta, and pump and probe polarizations, was used for the calculation of the spectra for several basic configurations. Experimental absorption spectra obtained on a Rb atomic beam for different pump and probe field polarizations show good agreement with the calculation. The spectra are in general essentially different from and more complex than the classical Mollow absorption triplet.

We investigate the laser equations in the mean-field limit for a homogeneously broadened two-level system, taking into account the local-field correction arising from dipole-dipole interactions. Our analysis concentrates on the dynamical properties of the laser versus the pumping parameter. The effect of detuning between atomic and cavity frequencies is also studied. We first show that the local-field correction reduces the range of the chaotic regime when the frequency detuning is set for minimum instability threshold operation. For a fixed local-field correction, we demonstrate that the symmetry of the dynamical scenario versus the frequency detuning is broken. In addition, we point out generalized bistability between the chaotic regime and the off state of the laser. This bistability results from the smallness of the basins of attraction of the off state.

We have observed various $\Lambda$-type electromagnetically induced transparency (EIT) spectra in laser-cooled ${}^{87}\mathrm{Rb}$ atoms of different laser polarization configurations. Unexpected profiles occur in the EIT spectra. We have found the degenerate Zeeman sublevels are responsible for these profiles. The experimental data are in good agreement with the results from the theoretical calculation which takes into account all the 13 Zeeman levels in the $\Lambda$ system. Our study demonstrates that Zeeman sublevels play important roles in quantum interference phenomena such as EIT and amplification without population inversion (AWI), and should be taken into account in the analysis of these phenomena.

An analytical property is pointed out for the universal differential equation first derived by Dalfovo, Pitaevskii, and Stringari for the condensate wave function at the boundary of a trapped Bose gas. Specifically, the constant multiplying the Airy function of the solution asymptotically outside the trap is $\sqrt{2}.$ Accordingly, the Wentzel-Kramers-Brillouin approximation is determined in the case of a spherically symmetric harmonic potential. This calculation is related to Josephson-type currents flowing between well-separated traps.

A combined precision experimental and theoretical study of $5p{}^2{P}_j\to 5d{}^2{D}_{3/2}$ electric-dipole transition matrix elements in atomic ${}^{87}\mathrm{Rb}$ has shown that they are dominated by electron correlation. The relative size and sign of the measured matrix element ratio is found to be 1.068(8), in very good agreement with the value of 1.135 obtained from relativistic third-order many-body perturbation theory.

Radiative decay of excited ${}^1{P}_1$ states to metastables is expected to limit attainable lifetimes in magneto-optic traps (MOTs) containing alkaline-earth-metal-like atoms. We present measurements of power-dependent loss from a ${(6s}^2{)}^1{S}_0{-\left(6s6p\right)\mathrm{}}^1{P}_1$ ytterbium MOT, show that the observed power dependence is consistent with radiative decay from the ${\mathrm{}\left(6s6p\right)\mathrm{}}^1{P}_1$ excited state leading to population of lower-lying metastable states, and determine the ${\mathrm{}\left(6s6p\right)\mathrm{}}^1{P}_1$-to-metastable state decay rate. With weak excitation of the ${(6s}^2{)}^1{S}_0{-\left(6s6p\right)\mathrm{}}^1{P}_1$ trapping transition, MOT lifetimes approaching 800 ms are observed.

We consider a periodically driven double well as a simplified dynamical model for molecular localization induced by collisions. If the frequency of the collisions is high enough, so that the instability of the states is larger than a critical value, then the states are localized and we have the redshift of the inversion line.

We explore the possibilities of creating radiatively stable entangled states of two three-level dipole-interacting atoms in a Λ configuration by means of laser biharmonic continuous driving or pulses. We propose three schemes for generation of entangled states which involve only the lower states of the Λ system, not vulnerable to radiative decay. Two of them employ coherent dynamics to achieve entanglement in the system, whereas the third one uses optical pumping, i.e., an essentially incoherent process.

Excitation energies, transition probabilities, and lifetimes are calculated for ${3l}_1{3l}_2-{3l}_3{3l}_4$ electric dipole transitions in Mg-like ions with nuclear charges Z ranging from 13 to 100. Relativistic many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded $E1\mathrm{}$ matrix elements in length and velocity forms. The calculations start from a ${1s}^2{2s}^2{2p}^6$ Dirac-Fock potential. First-order perturbation theory is used to obtain intermediate coupling coefficients, and the second-order MBPT is used to determine the matrix elements. The contributions from negative-energy states are included in the second-order $E1\mathrm{}$ matrix elements to achieve agreement between length-form and velocity-form amplitudes. The resulting transition energies and lifetimes are compared with experimental values and with results from other recent calculations.

Proton-beam irradiation, using the 3 MV accelerator at Guelph, has been successful in allowing us to study the emission spectra from liquid helium and hydrogen-doped liquid helium despite the fact that the beam penetrates the target a scant 0.5 mm. ${\mathrm{H}}_2$ emission lines can be observed from liquid samples following doping with small amounts of hydrogen into the helium gas before condensation. The line intensities are a sensitive function of the sample temperature, becoming strongest as the liquid approaches 4.2 K. The ${\mathrm{H}}_2$ lines themselves are much broader than those from ${\mathrm{He}}_2$ because the helium lines actually originate in small bubbles of helium gas trapped in the liquid, which is above the $\lambda$ point. The interesting fact is that electronic emission spectra from ${\mathrm{H}}_2$ are observed at all from liquid helium and a calculation of the widths and shifts of the spectral lines will be presented.

The process of simultaneous excitation and ionization is investigated for He-like uranium $\left({\mathrm{U}}^{90+}\right)$ ions colliding with Ar, Kr, and Xe targets at an incident energy of 223.2 MeV/u. The two-electron transitions, where one of the ground-state electrons is promoted into the continuum and the other into the L-subshell states of the projectile, are identified by the coincident observation of U Lyman-series radiation and ${\mathrm{U}}^{91+}$ ions. The experimental cross sections are compared to relativistic calculations based on the independent particle approximation and first-order perturbation theory. It is shown, that simultaneous excitation-ionization occurs preferably at small impact parameters, for which the excitation process is dominated by the monopole part of the interaction potential and the perturbation potential is largest. Good agreement is found between experimental data and calculations for the Ar target. For heavier targets the experimental results are generally smaller than predicted pointing to the invalidity of the first-order perturbation theory in this energy–target atomic number domain.

Electron-impact ionization cross sections for helium are calculated using time-dependent close-coupling theory. In a frozen-core approximation, the wave function for the three-electron system is expanded in terms of two-electron wave functions which fully describe the ejected and scattered electrons at all times following the collision. The resulting close-coupled partial differential equations for the two-electron radial wave functions include a direct and a local approximation to the exchange interactions with the remaining core electron. By direct projection of the time-dependent wave functions onto continuum lattice eigenstates, both ejected energy differential and total integrated cross sections are extracted. The agreement between theory and previous experimental measurements for helium is excellent.

To determine the direct electron-impact excitation cross sections with the optical method, one must measure all transitions out of a level, as well as the cascade into the level of interest from higher-lying energy levels. Considered here are the ten levels of the ${2p}^{5}3p$ configuration of neon, whose emissions to lower levels fall within a range of 540–810 nm. This allows an investigation via a monochromator-photomultiplier tube system. Cascades into these levels from ${2p}^{5}4s$ and ${2p}^{5}3d,$ however, emit radiation in the 740–1720-nm range, part of which is outside the limit of photomultiplier detection. We employ a Fourier-transform spectrometer to examine the near-infrared lines. We report direct electron excitation cross sections for the ten ${2p}^{5}3p$ levels for electron energies up to 200 eV. In addition, we provide apparent excitation functions for the ${2p}^{5}4s$ and ${2p}^{5}3d$ levels. We have also observed a dependence of the optical emission cross sections on pressure, and describe this effect within the framework of the resonance radiation reabsorption model.

We use the classical trajectory method to study the dynamics of a hydrogen molecular ion interacting with intense laser fields employing a collinear model. We have calculated the probabilities of ionization and dissociation as functions of time and obtained the photoelectron and the nuclear fragmentation kinetic energy distribution spectra for various laser parameters. We have included a preliminary calculation of the harmonic generation spectra of a hydrogen molecular ion. In many cases, the classical results reproduce the qualitative features of the corresponding quantum-mechanical calculations.