Using a particularly accurate and locally correct helium wave function, obtained by direct solution of the three-body Schrödinger equation, calculations were performed for double- and single-electron photoionization cross sections of the helium atom in the limit of high but nonrelativistic photon frequencies. In the dipole approximation, the cross-section ratio is frequency independent and equal to 0.016 45, which should be compared with the values 0.016 44, 0.0167, and 0.0168 calculated recently in the literature using different variational wave functions.

We investigate the extent to which “interaction-free” measurements perturb the state of quantum systems. We show that the absence of energy exchange during the measurement is not a sufficient criterion to preserve that state, as the quantum system is subject to measurement-dependent decoherence. While it is possible in general to design interaction-free measurement schemes that do preserve that state, the requirement of quantum coherence preservation rapidly leads to a very low efficiency. Our results, which have a simple interpretation in terms of “which-way” arguments, open up the way to novel quantum nondemolition techniques.

Using a template-stripping method, macroscopic gold surfaces with root-mean-square roughness $<~0.4\hspace{0.5em}\mathrm{nm}$ have been prepared, making them useful for studies of surface interactions in the nanometer range. The utility of such substrates is demonstrated by measurements of the Casimir force at surface separations between 20 and 100 nm, resulting in good agreement with theory. The significance and quantification of this agreement are addressed, as well as some methodological aspects regarding the measurement of the Casimir force with high accuracy.

The fundamental problem of the transition from quantum to classical physics is usually explained by decoherence, and viewed as a gradual process. The study of entanglement, or quantum correlations, in noisy quantum computers implies that in some cases the transition from quantum to classical is actually a phase transition. We define the notion of entanglement length in d-dimensional noisy quantum computers, and show that a phase transition in entanglement occurs at a critical noise rate where the entanglement length transforms from infinite to finite. Above the critical noise rate, macroscopic classical behavior is expected, whereas, below the critical noise rate, subsystems that are macroscopically distant one from another can be entangled. The macroscopic classical behavior in the supercritical phase is shown to hold not only for quantum computers but for any quantum system composed of macroscopically many finite state particles, with local interactions and local decoherence, subjected to some additional conditions. This phenomenon provides a possible explanation for the emergence of classical behavior in such systems. A simple formula for an upper bound on the entanglement length of any such system in the supercritical phase is given, and in principle can be tested experimentally.

A quantum system is called separable if its density matrix can be written as a mixture of product states. In this paper we apply the separability criterion as well as the distillability criterion to show that any initial inseparable $2\times 2$ system retains its inseparability after its transmission through a noisy channel which consists of a set of harmonic oscillators. Hence the final state of the system can be distilled to a singlet form. For higher dimensions, however, this result is no longer true in general. The distillability of a state with higher dimensions after its transmission through the noisy channel is also discussed in this paper.

For a simple model of mutually interacting qubits it is shown how the errors induced by mutual interactions can be eliminated using concatenated coding. The model is solved exactly for arbitrary interaction strength, for two well-known codes, one and two levels deep: this allows one to see under which circumstances error amplitudes add coherently or incoherently. For deeper concatenation, approximate results are derived that make it possible to calculate an approximate “threshold” value for the product of interaction strength and free evolution time, below which the failure probability for an encoded qubit decreases exponentially with the depth of the encoding. The results suggest that concatenated coding could fully handle the errors arising from mutual interactions, at no extra cost, in terms of resources needed, than what would be required to deal with random environmental errors.

Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single copy of the state. Accordingly, we say that two states have the same kind of entanglement if both of them can be obtained from the other by means of local operations and classical communication (LOCC) with nonzero probability. When applied to pure states of a three-qubit system, this approach reveals the existence of two inequivalent kinds of genuine tripartite entanglement, for which the Greenberger-Horne-Zeilinger state and a W state appear as remarkable representatives. In particular, we show that the W state retains maximally bipartite entanglement when any one of the three qubits is traced out. We generalize our results both to the case of higher-dimensional subsystems and also to more than three subsystems, for all of which we show that, typically, two randomly chosen pure states cannot be converted into each other by means of LOCC, not even with a small probability of success.

We consider the problem of preparing a single copy of an arbitrary two-qubit mixed state $\rho ,$ starting from an entangled pure state $\psi$ and using only local operations assisted with classical communication. We present an analytical expression for the minimal amount of pure-state entanglement required, and describe the corresponding local strategy. We also examine optimal probabilistic generalizations of the previous process.

Charge-transfer processes resulting from collisions of ${\mathrm{H}}^{+}$ ions with ${\mathrm{H}}_2,$ ${\mathrm{D}}_2,$ CO, and ${\mathrm{CO}}_2$ molecules have been experimentally investigated in the energy range of 0.2–4.0 keV by using the initial growth-rate method. Theoretical analysis based on a molecular-orbital expansion method for ${\mathrm{H}}_2$ and CO targets was also carried out. The observed cross sections are compared with previous experimental and theoretical data. The present results for ${\mathrm{H}}_2$ are found to be in excellent accord with the recommended data by Barnett [Oak Ridge National Laboratory Report No. ORNL-6086 (1990)], and hence, confirm the accuracy of the recommended data. But, at 0.2 keV, the present data for ${\mathrm{D}}_2$ are found to be smaller than those for ${\mathrm{H}}_2.$ For the CO molecule, the present data qualitatively agree well with most previous measurements, but show the stronger energy dependence, while the present theory shows a pronounced structure at around 0.25 keV and ties well with other low-energy measurements below 0.1 keV. For the ${\mathrm{CO}}_2$ molecule, the present results are in excellent accord with other measurements above 1 keV, while they show some differences below this energy where our experimental result displays the stronger energy dependence. These data are useful for various applications.

Charge-transfer processes in collisions of ${\mathrm{H}}^{+}$ ions with ${\mathrm{CH}}_4,$ ${\mathrm{C}}_2{\mathrm{H}}_2,$ ${\mathrm{C}}_2{\mathrm{H}}_6,$ and ${\mathrm{C}}_3{\mathrm{H}}_8$ molecules have been studied based on joint experimental and theoretical approaches in the collision energy from 0.2 to 4.0 keV. In the present experiment, the initial growth rate method was employed for determination of cross sections, while in the present theory, the molecular orbital expansion method was utilized for ${\mathrm{CH}}_4$ and ${\mathrm{C}}_2{\mathrm{H}}_2$ molecules. Both experimental and theoretical results indicate that if one assumes vibrationally excited molecular ions $({\mathrm{CH}}_4^{+},$ ${\mathrm{C}}_2{\mathrm{H}}_2^{+},$ ${\mathrm{C}}_2{\mathrm{H}}_6^{+},$ and ${\mathrm{C}}_3{\mathrm{H}}_8^{+})$ in the exit channel, then charge-transfer processes are sometimes found to become more favorable due to an accidental resonant condition. This is the clear indication of the role of vibrational excited states for charge transfer, and is found to be particularly so as the molecular size increases.

Thomas mechanism is theoretically shown to be present for the electron capture to the continuum (ECC) processes in ion-atom ionizing collisions. By focusing on the recoil-ion momentum distribution, a prominent peak structure at $60°$ from the backward direction is observed near the kinematical threshold. This recoil-ion critical angle corresponds to the Thomas double-scattering mechanism for electron capture. The theoretical description of this ECC Thomas peak in ionization collisions requires accounting for the interaction of the electron with both the projectile and the residual target.

The photodetachment cross section, radiative attachment cross section, branching ratio, and angular-distribution asymmetry parameter have been calculated for ${\mathrm{Cl}}^{\mathrm{-}}$ in the relativistic random-phase approximation (RRPA) and modifications of the RRPA which allow for the inclusion of relaxation and polarization effects. Photodetachment cross sections are compared with experiment to assess the effectiveness of the various approximations.

An eigenchannel R-matrix expansion of the T matrix is used to calculate total integrated and ejected energy differential cross sections for the electron-impact ionization of hydrogen in the Temkin-Poet model. In previous close-coupling results, unphysical oscillations in the total ionization cross section could be averaged over due to the smooth dependence of the cross section on the incident energy. For differential ionization cross sections, a step-function behavior in the cross sections’ overall ejected energy dependence has made unphysical oscillation removal much more problematic. By formulation design, the T-matrix method eliminates the step-function problem found in most close-coupling calculations of the ejected energy differential cross section. Total and differential ionization cross sections in a one-state R-matrix expansion are in excellent agreement with Hartree-Fock distorted-wave results. Total and differential ionization cross sections in multiple state R-matrix expansions converge toward the more accurate results given by a time-dependent wave-packet method. Unphysical oscillations appear in the differential ionization cross sections for all the T-matrix results involving more than three states in the R-matrix expansion, but the oscillations are small, symmetric about $E/2,$ and easily averaged to give a smooth uniform result.

Using complex scaling and a correlated basis constructed in terms of B splines, we calculate the ${\mathrm{Li}}^{+}$ photoion yield in the presence of a laser-induced coupling between the triply excited ${2s}^2{2p(}^2{P}^o)$ and ${2s2p}^2{(}^2{D}^e)$ resonances in lithium, the first of which is assumed to be excited by synchrotron radiation from the ground state. The laser coupling between the triply excited states is shown to lead to a significant and readily measurable modification of the line profile which provides a unique probe of the dipole strength between highly correlated triply excited states. We also present results for some higher-lying triply excited states of ${}^2{P}^o$ symmetry.

For ions impinging grazingly on a solid surface, the electron emission from the inner shells of solid atoms is investigated by employing a semiclassical formalism. The emission rate is expressed in terms of probabilities of atomic ionization, which are evaluated with the continuum-distorted-wave–eikonal-initial-state approximation, taking into account the full dependency on the impact parameter. The model is applied to the calculation of the differential yield of ejected electrons for fast protons colliding with an aluminum surface. Inner-shell emission is compared with the electron emission from the valence band of the metal, considering different ejection angles. Calculated energy spectra of emitted electrons are in good agreement with the available experimental data.

The realization of a magneto-optical trap (MOT) for silver atoms is reported. Trapping light at 328 nm was used and the trap was loaded directly from a thermal beam to store over ${10}^6\hspace{0.5em}\mathrm{atoms}$ with storage times of up to 16 s. Evidence of branching from the ${}^2{P}_{3/2}$ excited state to the metastable ${}^2{D}_{5/2}$ level was found and its decay rate determined. The temperature of the atoms is estimated to be $300\left(90\right)\mathrm{}\hspace{0.5em}\mu \mathrm{K}$ by measuring the mechanical properties of the MOT through observation of trap center oscillations.

We use the dressed-atom formalism to calculate the frequency shift in a hydrogen maser induced by applied radiation near the Zeeman frequency, and find excellent agreement with a previous calculation made in the bare-atom basis. The maser oscillates on the $\Delta F=1,$ $\Delta m_F=0\mathrm{}$ hyperfine transition, while the applied field is swept through the $F=1,$ $\Delta m_F=\pm 1$ Zeeman resonance. We determine the effect of the applied field on the Zeeman levels using the dressed-atom picture, and then calculate the maser frequency shift by coupling the dressed states to the microwave cavity. Qualitatively, the dressed-atom analysis gives a simpler physical interpretation of this double-resonance process, which has applications in precision hydrogen Zeeman spectroscopy, e.g., in fundamental symmetry tests.

We consider high-energy electron scattering by hydrogen atoms in the presence of a laser field of moderate power and higher frequencies. If the field is a superposition of a linearly and a circularly polarized laser beam in a particular configuration, then we can show that circular dichroism in two-photon transitions can be observed not only for the differential but also for the integrated cross sections, provided the laser dressing of the atomic target is treated in second-order perturbation theory and the coupling between hydrogenic bound and continuum states is involved.

We investigate the ground and low excited states of a rotating, weakly interacting Bose-Einstein condensed gas in a harmonic trap for a given angular momentum. Analytical results in various limits as well as numerical results are presented, and these are compared with those of previous studies. Within the mean-field approximation and for repulsive interaction between the atoms, we find that for very low values of the total angular momentum per particle, $L/\overrightarrow{N}0,$ where $Lħ$ is the angular momentum and N is the total number of particles, the angular momentum is carried by quadrupole $(|m|=2)$ surface modes. For $L/N=1,$ a vortexlike state is formed and all the atoms occupy the $m=1\mathrm{}$ state. For small negative values of $L/N-1,$ the states with $m=0\mathrm{}$ and $m=2\mathrm{}$ become populated, and for small positive values of $L/N-1,$ atoms in the states with $m=5\mathrm{}$ and $m=6\mathrm{}$ carry the additional angular momentum. In the whole region $0<~L/N<~1,$ we have strong analytic and numerical evidence that the interaction energy drops linearly as a function of $L/N.\mathrm{}$ We have also found that an array of singly quantized vortices is formed as $L/N$ increases. Finally, we have gone beyond the mean-field approximation and have calculated the energy of the lowest state up to order N for small negative values of $L/N-1,$ as well as the energy of the low-lying excited states.

We consider the dynamical Bragg reflection of an atomic matter wave from a finite optical lattice; the resulting energy dependence of the transmittivity allows us to filter out the velocities of the incident atoms. In particular, we show how the coherence length of the incident beam can be inferred from the sharpness of the transmittivity as a function of the lattice intensity. For incident frequencies well inside the reflecting window, the interference of incident and reflected matter waves gives rise to an oscillatory density profile in front of the lattice which can be observed by means of light diffraction. The angular width of the diffracted peaks also provides information on the coherence length of the incident atomic beam.