Using the ASTRID heavy-ion storage ring, absolute cross sections for dissociative recombination and dissociative excitation of vibrationally cold ${\mathrm{H}}_3^{+}$ have been measured as a function of energy in the region $E=0\mathrm{}-34\hspace{0.5em}\mathrm{eV}.$ A thermal rate coefficient for dissociative recombination of $(1.0\mathrm{}\pm 0.2)\times {10}^{-7}\hspace{0.5em}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ at 300 K was obtained from cross sections at low energy. At high energy, capture into a group of doubly excited states of ${\mathrm{H}}_3$ gives rise to resonances in the dissociative recombination as well as in the dissociative excitation cross sections.

The single-atom approximation for the $K\beta -\mathrm{to}-K\alpha$ x-ray intensity ratios for chemical compounds of $3d$ elements has been tested with the discrete-variational $X\alpha (\mathrm{DV}-X\alpha )$ molecular-orbital (MO) method. The effective numbers of electrons in each atomic shell are obtained with the $\mathrm{DV}-X\alpha$ method and used to calculate the $I\left(K\beta \right)/I\left(K\alpha \right)$ ratio in the single-atom approximation. The calculated results are in good agreement with the $\mathrm{DV}-X\alpha$ MO values for octahedral symmetry, but systematically smaller for tetrahedral symmetry. The reason for this discrepancy is ascribed to be the $K{\beta }_{2,5}$ component, which is appreciable in some compounds with the tetrahedral symmetry.

We present a full demonstration of unambiguous state discrimination between nonorthogonal quantum states. Using a free-space interferometer we have realized the optimum quantum measurement scheme for two nonorthogonal states of light, known as the Ivanovic-Dieks-Peres (IDP) measurement. We have gained access to all three possible outcomes of this measurement. All aspects of this generalized measurement scheme, including its superiority over a standard von Neumann measurement, have been demonstrated within 1.5% of the IDP predictions.

We introduce a configuration-interaction expansion in terms of Sturmian functions, which provides very accurate nonrelativistic energies for the high-lying singly and doubly excited states of a two-electron system. The approach, which requires a substantially smaller basis size by contrast to the standard configuration interaction methods, provides accurate results even for large total angular momenta. Key features are the use of different numbers of Sturmian functions for each electron, the inclusion of many different pairs of nonlinear parameters in the expansion, as well as complex scaling. The accuracy and convergence of the method, applied to helium, increases with the degree of excitation of one of the two electrons.

We study separability properties in a five-dimensional set of states of quantum systems composed of three subsystems of equal but arbitrary finite Hilbert space dimension. These are the states that can be written as linear combinations of permutation operators, or equivalently, commute with unitaries of the form $U\otimes U\otimes U.\mathrm{}$ We compute explicitly the following subsets and their extreme points: (1) triseparable states, which are convex combinations of triple tensor products, (2) biseparable states, which are separable for a twofold partition of the system, and (3) states with positive partial transpose with respect to such a partition. Tripartite entanglement is investigated in terms of the relative entropy of tripartite entanglement and of the trace norm.

We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian depends on quantities which are external to the constraint manifold, such as the extrinsic curvature of the constraint manifold, the curvature of the ambient space, and the constraining potential. In particular, we find the remarkable fact that the twisting of the constraining potential appears as a gauge potential in the constrained Hamiltonian. This gauge potential is closely related to the geometric phase originally discussed by Berry. The constrained Hamiltonian also contains an effective potential depending on the extrinsic curvature of the constraint manifold, the curvature of the ambient space, and the twisting of the constraining potential. The general nature of our analysis allows applications to a wide variety of problems, such as rigid molecules, the evolution of molecular systems along reaction paths, and quantum strip waveguides.

For the description of ground-state correlation phenomena an accurate mapping of many-body quantum mechanics onto four particles is developed. The energy for a quantum system with no more than two-particle interactions may be expressed in terms of a two-particle reduced density matrix (2-RDM), but variational optimization of the 2-RDM requires that it corresponds to an N-particle wave function. We derive N-representability conditions on the 2-RDM that guarantee the validity of the uncertainty relations for all operators with two-particle interactions. One of these conditions is shown to be necessary and sufficient to make the RDM solutions of the dispersion condition equivalent to those from the contracted Schrödinger equation (CSE) [Mazziotti, Phys. Rev. A 57, 4219 (1998)]. In general, the CSE is a stronger N-representability condition than the dispersion condition because the CSE implies the dispersion condition as well as additional N-representability constraints from the Hellmann-Feynman theorem. Energy minimization subject to the representability constraints is performed for a boson model with 10, 30, and 75 particles. Even when traditional wave-function methods fail at large perturbations, the present method yields correlation energies within 2%.

A number of atomic beam experiments, related to the Ramsey experiment and a recent experiment by Brune et al. [Phys. Rev. Lett. 77, 4887 (1996)], are studied with respect to the question of complementarity. Three different procedures for obtaining information on the state of the incoming atom are compared. Positive operator-valued measures (POVMs) are explicitly calculated. It is demonstrated that, in principle, it is possible to choose the experimental arrangement so as to admit an interpretation as a joint nonideal measurement yielding interference and “which-way” information. Comparison of the different measurements gives insight into the question of which information is provided by a (generalized) quantum mechanical measurement. For this purpose the subspaces of Hilbert-Schmidt space, spanned by the operators of the POVM, are determined for different measurement arrangements and different values of the parameters.

A concern has been expressed that “the Jaynes principle can produce fake entanglement” [R. Horodecki et al., Phys. Rev. A 59, 1799 (1999)]. In this paper we discuss the general problem of distilling maximally entangled states from N copies of a bipartite quantum system about which only partial information is known, for instance, in the form of a given expectation value. We point out that there is indeed a problem with applying the Jaynes principle of maximum entropy to more than one copy of a system, but the nature of this problem is classical and was discussed extensively by Jaynes. Under the additional assumption that the state ${\rho }^{\mathrm{}\left(N\right)\mathrm{}}$ of the N copies of the quantum system is exchangeable, one can write down a simple general expression for ${\rho }^{\mathrm{}\left(N\right)\mathrm{}}.$ By measuring one or more of the subsystems, one can gain information and update the state estimate for the remaining subsystems with the quantum version of the Bayes rule. Using this rule, we show how to modify two standard entanglement purification protocols, one-way hashing and recurrence, so that they can be applied to exchangeable states. We thus give an explicit algorithm for distilling entanglement from an unknown or partially known quantum state.

It is shown that optical experimental tests of Bell inequality violations can be described by SU(1,1) transformations of the vacuum state, followed by photon coincidence detections. The set of all possible tests are described by various SU(1,1) subgroups of $\mathrm{Sp}(8,R).\mathrm{}$ In addition to establishing a common formalism for physically distinct Bell inequality tests, the similarities and differences of post-selected tests of Bell inequality violations are also made clear. A consequence of this analysis is that Bell inequality tests are performed on a very general version of SU(1,1) coherent states, and the theoretical violation of the Bell inequality by coincidence detection is calculated and discussed. This group theoretical approach to Bell states is relevant to Bell state measurements, which are performed, for example, in quantum teleportation.

A nonperturbative numerical evaluation of the one-photon electron self-energy for the K- and L-shell states of hydrogenlike ions with nuclear charge numbers $Z=1\mathrm{}$ to 5 is described. Our calculation for the ${1S}_{1/2}$ state has a numerical uncertainty of 0.8 Hz in atomic hydrogen, and for the L-shell states ${(2S}_{1/2},$ ${2P}_{1/2},$ and ${2P}_{3/2})$ the numerical uncertainty is 1.0 Hz. The method of evaluation for the ground state and for the excited states is described in detail. The numerical results are compared to results based on known terms in the expansion of the self-energy in powers of $Z\alpha .$

Visible and near-UV emission lines of titaniumlike highly charged ions Sb, I, Xe, Ba, Cs, Sm, Eu, Hf, Ta, W, Re, and Pt were observed using an electron beam ion trap. The wavelengths of the magnetic dipole transitions between ground-state fine-structure levels, ${(3d}^4{)}^5{D}_J,$ were measured for these elements. These were compared with our own theoretical values, which were obtained with an extended set of configurations, and yielded differences of less than 0.6% for the elements below $Z=60,$ and about 0.1% for those over $Z=60.\mathrm{}$

The angular distribution of neutral hydrogen atoms following electron detachment from ${\mathrm{H}}^{-}$ ion beams has been measured at 2, 4 and 6 MeV for targets of nitrogen and hydrogen gas. For this purpose, a vertically oriented, slit shaped ${\mathrm{H}}^{-}$ beam was developed with lateral opening angle of about 3 μrad. When account is taken of the angular acceptance of the slit detector system, good agreement is found with existing Born approximation theory for the scattering process [Wright, Franz and Genoni, Phys. Rev. A 32, 1215 (1985)]. The angular distributions are very sharply forward peaked. At 4 MeV, on a hydrogen target, the measurements are compatible with a relative differential cross section, of which the width at half maximum is about 7 $\mu \mathrm{RAD};$ results were similar on nitrogen. Measurements were also made at the same energies on a nitrogen target for outgoing hydrogen atoms in the $2S$ first excited state. Coincidence with the induced decay of the Lyman-alpha photon defined the signal. For these cases the experimental width at half maximum was almost three times greater than that for the undifferentiated neutral state. An account will be given of the experiment, including mention of diagnostic charge fraction measurements on nitrogen, and the results will be compared with theory.

Electron capture resulting from collisions of ${\mathrm{Si}}^{4+}$ ions with He atoms below 25 keV/u is investigated using a molecular-orbital representation within both the semiclassical and quantal representations. Nine molecular states connecting both to single and double electron-capture processes are included, and hence radial and rotational couplings among these channels are fully considered. Electronic states and corresponding couplings are determined by the multireference single- and double-excitation configuration interaction method. The present results tie in well with the earlier calculations of Stancil et al. at lower energies, but show a rather different magnitude from the theoretical results of Bacchus-Montabonel and Ceyzeriat and are somewhat smaller than the measurements of Tawara et al. The present rate constants do not support the experimental finding of Fang and Kwong at 4,600 K.

A circularly polarized electric field is used to create a trap that can guide the rotational motion of diatomic molecules. Theoretical analyses and numerical calculations support the existence of trapped nonspreading wave packets rotating with a electric field. Optimal coherent control of the rotational motion of diatomic molecules can be achieved by manipulating the nonspreading wave packets with a circularly polarized electric field whose amplitude and frequency are changed adiabatically.

We show that it is possible to associate a de Broglie wavelength with a composite system even when the constituent particles are separated spatially. The nonlocal de Broglie wavelength $(\lambda /2)$ of a two-photon system separated spatially is measured with an appropriate detection system. The two-photon system is prepared in an entangled state in space-momentum variables. We propose that the same result can be obtained for a system of massive particles separated spatially in an entangled state in space-momentum variables.

Due to a production error, the incorrect figures and captions appeared in our article Phys. Rev. A 63, 012501 (2000). The corrected article follows.

The notion of entanglement can be naturally extended from quantum states to the level of general quantum evolutions. This is achieved by considering multipartite unitary transformations as elements of a multipartite Hilbert space and then extended to general quantum operations. We show some connection between this entanglement and the entangling capabilities of the quantum evolution.

We study the generation of vortices in rotating Bose-Einstein condensates, a situation that has been realized in a recent experiment [K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, Phys. Rev. Lett. 84 806 (2000)]. By combining a linear stability analysis with the global optimization of the nonlinear free-energy functional, we study the regimes that can be reached in current experiments. We find a hysteresis phenomenon in the vortex nucleation due to the metastabilization of the vortexless condensate. We also prove that for a fast enough rotating trap, the ground state of the condensate hosts one or more bent vortex lines.

The classical and the quantal problem of a particle interacting in one dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability of this system is established by evaluating the exact invariant closely related to the Lewis and Riesenfeld invariant for the time-dependent harmonic oscillator. We study extensively the special and interesting case of a kicked-quadratic potential from which we derive a new integrable, nonlinear, area preserving, two-dimensional map that may, for instance, be used in numerical algorithms that integrate the Calogero-Sutherland-Moser Hamiltonian. The dynamics, both classical and quantal, is studied via the time-evolution operator that we evaluate using a recent method of integrating the quantum Liouville-Bloch equations [A. R. P. Rau, Phys. Rev. Lett. 81, 4785 (1990)]. The results show the exact one-to-one correspondence between the classical and the quantal dynamics. Our analysis also sheds light on the connection between properties of the $\mathrm{su}\mathrm{}(1,1)\mathrm{}$ algebra and that of simple dynamical systems.