We derive necessary conditions in terms of the variances of position and momentum linear combinations for all kinds of separability of a multiparty multimode continuous-variable state. Their violations can be sufficient for genuine multipartite entanglement, provided the combinations contain both conjugate variables of all modes. Hence, a complete state determination, for example, by detecting the entire correlation matrix of a Gaussian state, is not needed.

We discuss what can be inferred from measurements on evolving one- and two-qubit systems using a single measurement basis at various times. We show that, given reasonable physical assumptions, carrying out such measurements at quarter-period intervals is enough to demonstrate coherent oscillations of one or two qubits between the relevant measurement basis states. One can thus infer from such measurements alone that an approximately equal superposition of two measurement basis states has been created during a coherent oscillation experiment. Similarly, one can infer that a near-maximally entangled state of two qubits has been created part way through an experiment involving a putative SWAP gate. These results apply even if the relevant quantum systems are only approximate qubits. We discuss applications to fundamental quantum physics experiments and quantum-information processing investigations.

In view of the recent interest in the trapping of antihydrogen atom $\mathrm{H}¯,$ at very low temperatures, $\mathrm{H}¯-\mathrm{H}$ scattering has been investigated at low incident energies using a close-coupling model with the basis set $\mathrm{H}¯(1s,2s,2\mathrm{}\overline{p})+\mathrm{H}(1s,2s,2\mathrm{}\overline{p}).\mathrm{}$ The predicted s-wave elastic phase shifts, scattering length, and effective range are in a good agreement with the other recent predictions of Jonsell et al. and of Armour and Chamberlain. The results indicate that the atomic orbital expansion model is suitable to study the $\mathrm{H}¯-\mathrm{H}$ scattering at ultracold temperatures.

We have constructed a magneto-optical trap (MOT) for metastable triplet helium atoms utilizing the $2{}^3{S}_1\to 3{}^3{P}_2$ line at 389 nm as the trapping and cooling transition. The far-red-detuned MOT (detuning $\Delta =-41\mathrm{MHz})$ typically contains few times ${10}^7$ atoms at a relatively high $\left(\sim {10}^9{\mathrm{cm}}^{-3}\right)$ density, which is a consequence of the large momentum transfer per photon at 389 nm and a small two-body loss rate coefficient $(2\mathrm{}\times {10}^{-10}{\mathrm{cm}}^3/\mathrm{s}<\beta <1.0\mathrm{}\times {10}^{-9}{\mathrm{cm}}^3/\mathrm{s}).\mathrm{}$ The two-body loss rate is more than five times smaller than in a MOT on the commonly used $2{}^3{S}_1\to 2{}^3{P}_2$ line at 1083 nm. Furthermore, laser cooling at 389 nm results in temperatures somewhat lower than those achieved using 1083 nm. The 389-nm MOT exhibits small losses due to two-photon ionization, which have been investigated as well.

A method for generating entangled photons with controllable frequency correlation via spontaneous parametric down-conversion (SPDC) is presented. The method entails initiating counterpropagating SPDC in a single-mode nonlinear waveguide by pumping with a pulsed beam perpendicular to the waveguide. The method offers several advantages over other schemes, including the ability to generate frequency-correlated photon pairs regardless of the dispersion characteristics of the system.

We report a quantum-eraser experiment with frequency-entangled photon pairs generated by nondegenerate parametric down conversion. The relationship between which-path information and two-photon fringe visibility has been investigated by means of photon polarizations in a Hong-Ou-Mandel interferometer. Although photons are not of the same frequency and are not superposed at the beam splitter, the results of the experiment show the revival of the fringe pattern by removing the path information in the interferometer by means of polarizations in front of the detectors.

We derive a general expression for the expectation value of the phase acquired by a time dependent wave function in a multicomponent system, as excursions are made in its coordinate space. We then obtain the mean phase for the (linear dynamic $E\otimes \epsilon )$ Jahn-Teller situation in an electronically degenerate system. We interpret the phase-change as an observable measure of the effective nodal structure of the wave function.

We show how to construct a universal set of quantum logic gates using control over exchange interactions and single- and two-spin measurements only. Single-spin unitary operations are teleported between neighboring spins instead of being executed directly, thus potentially eliminating a major difficulty in the construction of several of the most promising proposals for solid-state quantum computation, such as spin-coupled quantum dots, donor-atom nuclear spins in silicon, and electrons on helium. Contrary to previous proposals dealing with this difficulty, our scheme requires no encoding redundancy. We also discuss an application to superconducting phase qubits.

Analysis and assignment of spectra involving the lowest excited states of the heavier alkali-metal atom dimers are complicated by the strong spin-orbit coupling elements. Here we report an analysis of the Fourier-transform spectroscopy data from laser-induced fluorescence of the coupled $A{}^1{\Sigma }^{+}$ and $b{}^3\Pi$ states of RbCs, using the discrete variable representation. Fitted parameters are given and special effects due to strong coupling are discussed.

An alternative experimental technique for efficient population of triply excited states in atoms and ions is presented. The states are produced by triple electron capture in energetic ion-atom collisions. The method is used to study autoionizing ${2s2p}^{22}S,$ ${}^{2}P,$ ${}^{2}D,$ ${}^{4}P$ and ${2p}^{32}P,$ ${}^{2}D$ states of fluorine. Differential cross sections, resonance energies, and Auger decay branching ratios were determined from the experiment. Results are compared to different calculations based on the hyperspherical close coupling method.

It is shown that the velocity dependence of cross sections for projection-changing transitions in collisions of paramagnetic atoms or molecules with structureless targets near threshold has the form $v^{2\Delta m}$ when $\Delta m$ is even and $v^{2(\Delta m+1)}$ when $\Delta m$ is odd, where $\Delta m$ is the change in the projection quantum number and $v$ is the relative velocity.

We have developed a technique to control the placement of atoms in an optical lattice by using a superlattice comprising two separately manipulated, periodic optical potentials with commensurate periods. We demonstrate selective loading of Bose-condensed ${}^{87}\mathrm{Rb}$ atoms into every third site of a one-dimensional optical lattice. Our technique provides atoms with wide separation yet tight confinement, useful properties for neutral-atom implementations of quantum computing. Interference of atoms released from the optical lattice and optical Bragg reflection from the atoms reveal the tight confinement and wide separation provided by the patterned filling.

We show that a quantum computer operating with a small number of qubits can simulate the dynamical localization of classical chaos in a system described by the quantum sawtooth map model. The dynamics of the system is computed efficiently up to a time $t>~\mathcal{l},$ and then the localization length $\mathcal{l}$ can be obtained with accuracy $\nu$ by means of order $1/{\nu }^2$ computer runs, followed by coarse-grained projective measurements on the computational basis. We also show that in the presence of static imperfections, a reliable computation of the localization length is possible without error correction up to an imperfection threshold which drops polynomially with the number of qubits.

We put forward an experimentally feasible technique to generate engineered entangled states in d-dimensional Hilbert spaces in parametric down-conversion of photons. The scheme is based on the orbital angular momentum of light and translates the classical, topological information imprinted in the light beam that pumps the two-photon source into quantum information contained in the weights and phases of the quantum entangled two-photon states.

We propose two simple implementations of the optimal symmetric $\overrightarrow{1}2$ phase-covariant cloning machine for qubits. The first scheme is designed for qubits encoded into polarization states of photons and it involves a mixing of two photons on an unbalanced beam splitter. This scheme is probabilistic and the cloning succeeds with the probability $1/3.$ In the second setup, the qubits are represented by the states of Rydberg atoms and the cloning is accomplished by the resonant interaction of the atoms with a microwave field confined in a high-Q cavity. This latter approach allows for deterministic implementation of the optimal cloning transformation.

Configuration interaction calculations for the Sm I ${J=0\mathrm{}}^{+}$ and $4^{+}$ with matrix dimensions 1351 and 7325 are carried out. The eigenvalues and eigenfunctions are analyzed for density of states, strength functions, and information entropy in wave functions and compared with the Gaussian forms given by two-body random matrix ensembles (TBRE). Signatures of TBRE are clearly seen in the Sm I example.

There has been impressive progress in the theoretical treatment of electron collisions with atoms in the last decade. As a result, the fundamental collision problems of electron-hydrogen or electron-helium scattering are now understood fairly well. For heavier atoms, an accurate treatment of atomic ionization remains more elusive than atomic excitation due to the final-state three-body Coulomb problem. For higher impact energies, the first-order distorted-wave Born approximation is typically in reasonable agreement with fully differential cross sections (FDCS) for ionization. However, FDCS measurements are starting to be reported for lower incident electron energies and here agreement between experiment and theory is not good. In this paper we examine the importance of exchange distortion and the final-state electron-electron interaction on these collision processes.

The process of recombination of an electron with a bare heavy nucleus via the creation of a free-positron–bound-electron pair is considered. This process is denoted as “negative-continuum dielectronic recombination” because it results in the capture of an incident electron into a bound state accompanied by a transition of a negative-continuum electron into a bound state. The calculations are performed for a wide range of incident electron energies for $Z=82\mathrm{}$ and $92.$

The selective-field-ionization (SFI) dynamics of a Rydberg state of lithium with magnetic quantum number $m=2\mathrm{}$ is studied in detail based on two different theoretical models: (1) a close coupling integration of the Schrödinger equation and (2) the multichannel (incoherent) Landau-Zener (MLZ) model. The $m=2\mathrm{}$ states are particularly interesting, since they define a border zone between fully adiabatic $\mathrm{}(m=0,1\mathrm{})\mathrm{}$ and fully diabatic $\mathrm{}(m>\mathrm{}2\mathrm{})\mathrm{}$ ionization dynamics. Both sets of calculations are performed up to, and above, the classical ionization limit. It is found that the MLZ model is excellent in the description of the fully diabatic dynamics while certain discrepancies between the time dependent quantal amplitudes appear when the dynamics become involved. Thus, in this region, the analysis of experimental SFI spectra should be performed with care.

We have theoretically investigated the role of high lying electronic states $2p{\pi }_u$ and $3d{\sigma }_g$ on multiphoton dissociation of ${\mathrm{D}}_2^{+}$ from initial vibrational-rotational levels $v_i=4,5\mathrm{}$ and $J_i=0,1\mathrm{}$ by linearly polarized light with wavelength 400 nm and intensity $3\times {10}^{13}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2.$ We have found that for initial level $v_i=4\mathrm{}$ and $J_i=1,$ a considerable number of photofragments is ejected perpendicular to the polarization direction of the laser field. It is shown that the perpendicular dissociation is due to the (net) four-photon absorption of the ground $1s{\sigma }_g$ state to the $3d{\sigma }_g$ state through the intermediate five-photon coupling of the $1s{\sigma }_g$ and $2p{\pi }_u$ states at intense laser field with high frequency. Our computed value of the emission of ${\mathrm{D}}^{+}$ ions in the perpendicular direction to that in the parallel direction of the laser polarization reasonably agrees with the recent experimental result of Chin and co-workers at the same laser parameters [Phys. Rev. A 62, 042708 (2000)].