We investigate the king’s problem of the measurement of operators ${\vec{n}}_k\bullet \vec{\sigma }$ ($k=1$, 2, 3) instead of the three Cartesian components ${\sigma }_x,{\sigma }_y$, and ${\sigma }_z$ of the spin operator $\vec{\sigma }$. Here, ${\vec{n}}_k$ are three-dimensional real unit vectors. We show the condition over three vectors ${\vec{n}}_k$ to ascertain the result for measurement of any one of these operators.

We address the problem of nonorthogonal two-state discrimination when multiple copies of the unknown state are available. We give the optimal strategy when only fixed individual measurements are allowed and show that its error probability saturates the collective (lower) bound asymptotically. We also give the optimal strategy when adaptivity of individual von Neumann measurements is allowed (which requires classical communication) and show that the corresponding error probability is exactly equal to the collective one for any number of copies. We show that this strategy can be regarded as Bayesian updating.

We investigate the motion of neutral fermions and bosons in a three-dimensional magnetic quadrupole trap. Inspecting the underlying Hamiltonian a variety of symmetries is revealed which give rise to degeneracies of the resonance energies. Our numerical approach which involves the eigenvalue problem resulting from a Sturmian basis set together with the complex scaling method enables us to calculate several hundred resonance states. The distributions of the energies and decay widths of the resonances are analyzed for both spin-$\frac{1}{2}$ fermions and spin-1 bosons. We also investigate under what conditions quasibound states with long lifetimes can be achieved. An effective scalar Schrödinger equation describing such states is derived. The results are applied to the cases of the alkali-metal atoms ${}^{87}\mathrm{Rb}$ and ${}^6\mathrm{Li}$ trapped in a hyperfine ground state.

The conditions for optimal reflection-free complex-absorbing potentials (CAPs) are discussed. It is shown that the CAPs as derived from the smooth-exterior-scaling transformation of the Hamiltonian [J. Phys. B 31, 1431 (1998)] serve as optimal reflection-free CAPs (RF CAPs) in wave-packet propagation calculations of open systems. The initial wave packet, $\mathrm{\Phi }(t=0)$, can be located in the interaction region (as in half collision experiments) where the CAPs have vanished or in the asymptote where ${\widehat{V}}_{\mathit{CAP}}\ne 0$. As we show, the optimal CAPs can be introduced also in the region where the physical potential has not vanished. The unavoided reflections due to the use of a finite number of grid points (or basis functions) are discussed. A simple way to reduce the “edge-grid” reflection effect is described.

Surface light-induced drift of a rarefied gas in cells with flat-plate and circular-cylindrical geometries is studied, and exact analytical solutions to the model rate equations are obtained in the limit of large Knudsen number. The work is a continuation of part V of this series of papers, in which the model rate equations were tailored specifically in order to study the roles played by both the tangential and normal momentum molecule-surface accommodation coefficients. In part V, the “spontaneous decay” parameter, $\gamma$, was set equal to zero, and the case of general “laser excitation” parameter, $q$, was studied. In the present paper, we get exact analytical results for the case of arbitrary $\gamma$ in the limit of small $q$; we also get accurate numerical results for arbitrary $\gamma$ and $q$. In passing, one serious, and other less serious, typographical errors in part V are corrected.

We present a method to measure the trap frequency or the spring constant of a magneto-optical atom trap via the parametric resonance. When the intensity of the cooling laser is modulated at around twice its resonant trap frequency, the trapped atoms are parametrically excited and divided into two groups oscillating with the motional phase difference of $\pi$. We find that one can measure the natural trap frequency as the modulation amplitude is decreased down to its threshold value. The experimental results are in good agreement with the three-dimensional Doppler cooling theory based on the rate equation model.

Molecular dynamics simulations of the ion clouds stored in a linear quadrupole rf ion trap are performed at low temperatures (0.1 mK–15 K). The introduction of periodic boundary conditions allowed us to study the translationally uniform ion cloud geometry. The time evolution of the kinetic energy of the ion cloud is monitored during the simulation and the increase in the kinetic energy of the cloud (rf heating) is determined; its dependence on temperature, trapping voltage, and the number of ions is studied. The dependence of rf heating rate on temperature shows that rf heating is undetectable until the temperature reaches approximately 0.5 K; it then increases rapidly until it reaches a maximum at around 2 K. It starts to decrease slowly at higher temperatures. The rf heating rate is shown to increase very sharply with the amplitude of the trapping voltage. The dependence of the rf heating rate on the number of ions shows the influence of the ion crystal shell structure at low temperatures, and has a simple linear dependence at higher temperatures.

We investigate the zero-temperature properties of a dilute two-component Fermi gas with attractive interspecies interaction in the BCS-BEC crossover. We build an efficient parametrization of the energy per particle based on Monte Carlo data and asymptotic behavior. This parametrization provides, in turn, analytical expressions for several bulk properties of the system such as the chemical potential, the pressure, and the sound velocity. In addition, by using a time-dependent density functional approach, we determine the collective modes of the Fermi gas under harmonic confinement. The calculated collective frequencies are compared to experimental data on confined vapors of ${}^6\mathrm{Li}$ atoms and with other theoretical predictions.

We present a Gaussian-state analysis of the entanglement generation between two macroscopic atomic ensembles due the continuous probing of collective spin variables by optical Faraday rotation. The evolution of the mean values and the variances of the atomic variables is determined, and the entanglement is characterized by the Gaussian entanglement of formation and the logarithmic negativity. The effects of induced opposite Larmor rotation of the samples and of light absorption and atomic decay are analyzed in detail.

We show that a special type of entangled states, cluster states, can be created with Heisenberg interactions and local rotations in $2d$ steps where $d$ is the dimension of the lattice. We find that, by tuning the coupling strengths, anisotropic exchange interactions can also be employed to create cluster states. Finally, we propose electron spins in quantum dots as a possible realization of a one-way quantum computer based on cluster states.

Complete electron-electron coincidence maps of doubly photoionized molecular oxygen have been recorded for photon energies below and above the adiabatic double-ionization potential to investigate in detail the mechanisms for ${\mathrm{O}}_2$ photofragmentation leading to the formation of ${\mathrm{O}}^{+}–{\mathrm{O}}^{+}$ ion pairs. Our data analysis reveals that the vibrationally selective path identified in a recent threshold photoelectron-photoelectron coincidence study [P. Bolognesi et al., Phys. Rev. Lett. 82, 2075 (1999)] plays only a minor role and that such reaction paths are not unique for photon energies below the $\mathrm{O}_2{}^{2+}$ threshold. Furthermore, potential energy curve calculations similar to those presented by Bolognesi et al. suggest that the identification of certain decay routes is more ambiguous and will require more sophisticated methods for finding definite answers.

Using the Oak Ridge National Laboratory ion-atom merged-beams apparatus, the absolute total electron-capture cross section has been measured for collisions of ${\mathrm{Ne}}^{4+}$ with hydrogen and deuterium at relative energies in the center-of-mass frame between 0.10 and 1006 eV/u. Comparison with previous measurements shows large discrepancies between 80 and 600 eV/u. For energies below $\sim 1\mathrm{eV}∕\mathrm{u}$, a sharply increasing cross section is attributed to the ion-induced dipole attraction between the reactants. Multichannel Landau-Zener calculations are performed between 0.01 and 5000 eV/u and compare well to the measured total cross sections. Below $\sim 5\mathrm{eV}∕\mathrm{u}$, the present total cross section calculations show a significant target isotope effect. At 0.01 eV/u, the H:D total cross section ratio is predicted to be $\sim 1.4$ where capture is dominated by transitions into the ${\mathrm{Ne}}^{3+}$ $\left(2s^{2}2p^{2}3d\right)$ configuration.

Multicomponent correlation functions are developed by utilizing $d$-outcome measurements. Based on multicomponent correlation functions, we propose a Bell inequality for bipartite $d$-dimensional systems. Violation of the Bell inequality for continuous-variable (CV) systems is investigated. The violation of maximally entangled states can exceed the Cirel’son bound; the maximal violation is 2.969 81. For finite values of the squeezing parameter, the violation strength of CV states increases with dimension $d$. Numerical results show that the violation strength of CV states with finite squeezing parameters is stronger than that of maximally entangled states.

We discuss the problem of determining whether the state of several quantum mechanical subsystems is entangled. As in previous work on two subsystems we introduce a procedure for checking separability that is based on finding state extensions with appropriate properties and may be implemented as a semidefinite program. The main result of this work is to show that there is a series of tests of this kind such that if a multiparty state is entangled this will eventually be detected by one of the tests. The procedure also provides a means of constructing entanglement witnesses that could in principle be measured in order to demonstrate that the state is entangled.

This paper considers a class of qubit channels for which three states are always sufficient to achieve the Holevo capacity. For these channels, it is known that there are cases where two orthogonal states are sufficient, two nonorthogonal states are required, or three states are necessary. Here a systematic theory is given which provides criteria to distinguish cases where two states are sufficient, and determine whether these two states should be orthogonal or nonorthogonal. In addition, we prove a theorem on the form of the optimal ensemble when three states are required, and present efficient methods of calculating the Holevo capacity.

We consider evaluation of matrix elements with the coupled-cluster method. Such calculations formally involve infinite number of terms and we devise a method of partial summation (dressing) of the resulting series. Our formalism is built upon an expansion of the product $C^{\mathrm{†}}C$ of cluster amplitudes $C$ into a sum of $n$-body insertions. We consider two types of insertions: particle (hole) line insertion and two-particle (two-hole) random-phase-approximation-like insertion. We demonstrate how to “dress” these insertions and formulate iterative equations. We illustrate the dressing equations in the case when the cluster operator is truncated at single and double excitations. Using univalent systems as an example, we upgrade coupled-cluster diagrams for matrix elements with the dressed insertions and highlight a relation to pertinent fourth-order diagrams. We illustrate our formalism with relativistic calculations of the hyperfine constant $A\left(6s\right)$ and the $6s_{1∕2}-6p_{1∕2}$ electric-dipole transition amplitude for the Cs atom. Finally, we augment the truncated coupled-cluster calculations with otherwise omitted fourth order diagrams. The resulting analysis for Cs is complete through the fourth order of many-body perturbation theory and reveals an important role of triple and disconnected quadruple excitations.

The total cross sections of electron impact single $K$-shell ionization of atomic targets, with a wide range of atomic numbers from $Z=6–50$, are evaluated in the energy range up to about 10 MeV employing the recently proposed modified version of the improved binary-encounter dipole (RQIBED) model [Uddin et al., Phys. Rev. A 70, 032706 (2004)], which incorporates the ionic and relativistic effects. The experimental cross sections for all targets are reproduced satisfactorily even in the relativistic energies using fixed generic values of the two parameters in the RQIBED model. The relativistic effect is found to be significant in all targets except for C, being profound in Ag and Sn.

We investigate the electron capture from insulator surfaces under grazing impact conditions. The eikonal-impulse approximation is used to describe coherent electron exchange from surface ions. In the model the transition amplitude is expressed as the sum of atomic transition amplitudes, each one associated with capture from a different lattice site. The method is applied to $100\mathrm{keV}$ protons colliding on LiF surfaces. Strong interference effects as a function of the crystal orientation were found for the partial capture from a given initial crystal state. However, these interference structures disappear when the contributions from different crystal states add up to obtain the total capture probability from the surface band.

Resonant Auger spectra of large argon clusters have been measured at the Ar $2p$ edge. The decay spectra can give some information on the states reached in photon absorption. For example, the observation of the $3p^{4}4p$ final states indicates the occurrence of the $2p_{3∕2}\to 4p$ excitation in clusters, whereas in atoms this excitation is dipole forbidden. Also the $3p^{4}3d$ final states are identified in the resonant Auger spectra. A peculiar finding is that the normal Auger transitions in bulk cluster atoms are observed below the $2p$ ionization thresholds. This is explained by the excitation of the $2p$ electrons into the conduction band, followed by a rapid delocalization of the electron.

Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. As we show explicitly, the operators that are usually associated with linear momentum, orbital angular momentum, and spin do not satisfy the algebra of the translation and rotation group. Nevertheless, we identify some components of these operators that represent observable quantities in an appropriate basis, thus characterizing the quantum numbers of Bessel photons. Some physical consequences of these results are discussed.