This paper continues a quantum-mechanical (QM) and semiclassical (SC) study of the collinear three-body Coulomb problem [O. I. Tolstikhin and C. Namba, 70, 062721 (2004)], extending it to resonances. Our QM treatment is based on the theory of Siegert pseudostates (SPS) implemented in hyperspherical coordinates by means of the slow/smooth variable discretization method. A consistent formulation of this approach for arbitrary dimension of configuration space and number of open channels is given. Not only resonance energy and total width, but also partial widths are defined in terms of the SPS; for the cases of one and two open channels, they are expressed in terms of the SPS eigenvalues only. The SC results are obtained in the leading-order approximation from the asymptotic solution of the problem for $h\to 0$, where $h$ is a dimensionless parameter that depends only on the masses of particles, varies in the interval $0⩽h⩽1$, and has the meaning of an effective Planck’s constant for the motion in hyperradius. It is shown that resonance widths as functions of $1∕h$ oscillate with an exponentially decaying amplitude and almost constant period. The SC theory qualitatively explains such a behavior as a manifestation of interference effects in the nonadiabatic process of decay of the resonance state and provides surprisingly good quantitative results even for systems with $h\sim 1$.

We report on the multiphoton ionization processes in the soft-x-ray region $\left(\lambda ⩽30\mathrm{nm}\right)$. On the basis of the measured time-of-flight spectra for both ions and electrons obtained using intense soft-x-ray pulses produced by high-order harmonics, the cross sections of the two-photon double ionization and above-threshold ionization of $\mathrm{He}$ are estimated. The high-intensity soft-x-ray radiation achieved by phase-matched high-order harmonics enables the investigation of these nonlinear optical processes, which were beyond the reach of conventional light sources.

The excess number of atoms around an ion immersed in a Bose-Einstein condensate is determined as a function of the condensate density far from the ion. We use thermodynamic arguments to demonstrate that in the limit of low densities the excess number of atoms is proportional to the ratio of the atom-ion and atom-atom scattering lengths. For denser systems we calculate the excess number from solutions of the Gross-Pitaevskii equation using a model potential that has a $1∕r^4$ attraction coming from the polarization of the neutral atoms and a hard-core repulsion at short distances. We show that there exist in general many solutions to the Gross-Pitaevskii equation for a given condensate density, the maximum number of solutions being related to the number of bound states of the Schrödinger equation for the same potential. With increasing density, pairs of these solutions merge and disappear, implying a discontinuous change of the state of the system.

We study scalar and vector modulation instabilities induced by the vacuum fluctuations in birefringent optical fibers. To this end, stochastic coupled nonlinear Schrödinger equations are derived. The stochastic model is equivalent to the quantum field operators equations and allows for dispersion, nonlinearity, and arbitrary level of birefringence. Numerical integration of the stochastic equations is compared to analytical formulas in the case of scalar modulation instability and nondepleted pump approximation. The effect of classical noise and its competition with vacuum fluctuations for inducing modulation instability is also addressed.

The maximally entangled mixed states of Munro et al. [Phys. Rev. A 64, 030302 (2001)] are shown to exhibit interesting features vis á vis conditional entropic measures. The same happens with the Ishizaka and Hiroshima states [Phys. Rev. A 62, 022310 (2000)], whose entanglement degree cannot be increased by acting on them with logic gates. Special types of entangled states that do not violate classical entropic inequalities are seen to exist in the space of two qubits. Special meaning can be assigned to the Munro et al. special participation ratio of 1.8.

The low-energy end of the spectrum of photoelectrons detached from hydrogenic ions exposed to an intense low-frequency few-cycle pulse is calculated within the strong-field approximation (SFA). The effect on the detached photoelectron of the Coulomb field of the nucleus is taken into account quasiclassically. The results are compared with those of an ab initio solution of the time-dependent Schrödinger equation, for the case of an ${\mathrm{He}}^{+}$ ion irradiated by a $400\text{−}\mathrm{nm}$ pulse of $1\times {10}^{16}\mathrm{W}{\mathrm{cm}}^{-2}$ peak intensity. Many of the features of the ab initio spectra can be understood within the SFA.

We construct a general state which is an eigenvector of the annihilation operator of the generalized Heisenberg algebra. We show, for several systems characterized by different energy spectra, that this general state satisfies the minimal set of conditions required to obtain Klauder’s minimal coherent states.

We provide a detailed analysis of the recently proposed setup for a loophole-free test of Bell inequality violation using conditionally generated non-Gaussian states of light and balanced homodyning. In the proposed scheme, a two-mode squeezed vacuum state is de-Gaussified by subtracting a single photon from each mode with the use of an unbalanced beam splitter and a standard low-efficiency single-photon detector. We thoroughly discuss the tolerance of the achievable Bell violation in the various experimentally relevant parameters such as the detector efficiencies, the electronic noise, the mixedness of the initial Gaussian state, and the probability of false triggers. We also consider several alternative schemes involving squeezed states, linear optical elements, conditional photon subtraction, and homodyne detection.

A necessary precondition for secure quantum key distribution is that sender and receiver can prove the presence of entanglement in a quantum state that is effectively distributed between them. In order to deliver this entanglement proof one can use the class of entanglement witness (EW) operators that can be constructed from the available measurements results. This class of EWs can be used to provide a necessary and sufficient condition for the existence of quantum correlations even when a quantum state cannot be completely reconstructed. The set of optimal EWs for two well-known entanglement-based (EB) schemes, the six-state and the four-state EB protocols, has been obtained recently [M. Curty et al., Phys. Rev. Lett. 92, 217903 (2004).] Here we complete these results, now showing specifically the analysis for the case of prepare and measure (PM) schemes. For this, we investigate the signal states and detection methods of the four-state and the two-state PM schemes. For each of these protocols we obtain a reduced set of EWs. More importantly, each set of EWs can be used to derive a necessary and sufficient condition to prove that quantum correlations are present in these protocols.

Radiative corrections to $E1$ matrix elements for $ns\text{−}np$ transitions in the alkali-metal atoms lithium through francium are evaluated. They are found to be small for the lighter alkali metals but significantly larger for the heavier alkali metals, and in the case of cesium much larger than the experimental accuracy. The relation of the matrix element calculation to a recent decay rate calculation for hydrogenic ions is discussed, and application of the method to parity nonconservation in cesium is described.

We discuss consequences of Fermi exchange symmetry on collisions of polar molecules at low temperatures (below 1 K), considering the OD radical as a prototype. At low fields and low temperatures, Fermi statistics can stabilize a gas of OD molecules against state-changing collisions. We find, however, that this stability does not extend to temperatures high enough to assist with evaporative cooling. In addition, we establish that a novel “field-linked” resonance state of OD dimers exists, in analogy with the similar states predicted for bosonic OH.

It is demonstrated that the potential-energy surface and the lowest-energy path for a polyatomic molecule (applied to the $\mathrm{C}\mathrm{H}+\mathrm{O}$ system) is accurately calculated via bond-length-dependent tight-binding Hamiltonian, fitted to ab initio configuration-interaction (CI) total energies. This Hamiltonian not only reproduces the CI energies accurately and efficiently, but also effectively recognizes and identifies CI energy values that may erroneously converge to excited states. The resulting normal mode frequencies are in very good agreement with experiment.

We present theoretical and experimental studies of the center-of-mass (c.m.) stability of ions in a Penning trap with a quadrupole rotating electric field. The rotation frequency of an ion cloud in a Penning trap determines the cloud density and shape, and it can be precisely controlled by a rotating electric field. The quadrupole rotating-field scheme can control pure single-species plasmas in contrast to the dipole field, which is effective only for plasmas composed of two or more species of ions. However, the quadrupole field can modify the trap stability because of the spatial dependence of the electric field. In this study, we theoretically and experimentally determine the c.m. stability condition for ions in a Penning trap with a rotating quadrupole field. The experimental results agree well with the theoretical prediction. In the limit of zero magnetic field we obtain a type of rf trap which uses a rotating quadrupole field and in which the c.m. motion is analytically solvable.

The equation of state of a homogeneous two-dimensional Bose gas is calculated using quantum Monte Carlo methods. The low-density universal behavior is investigated using different interatomic model potentials, both finite ranged and strictly repulsive and zero ranged, supporting a bound state. The condensate fraction and the pair distribution function are calculated as a function of the gas parameter, ranging from the dilute to the strongly correlated regime. In the case of the zero-range pseudopotential we discuss the stability of the gaslike state for large values of the two-dimensional scattering length, and we calculate the critical density where the system becomes unstable against cluster formation.

Single-photon-counting modules (SPCM’s), with their high quantum efficiency, have been widely used to investigate effectively the photon statistics of various light sources, such as the single-photon state and emission light from controlled molecules, atoms, and quantum dots. However, such SPCM’s cannot distinguish the arrivals of one photon and two (or more than two) photons at a moment, which makes measurement correction in real experiments. We analyze the effect of SPCM’s on photon statistics based on the Hanbury-Brown-Twiss configuration when the total efficiency and background are considered, and it shows that the measured second-order degree of coherence and Mandel $Q$ factor for different quantum states, including single-photon states and squeezed vacuum states, are corrected in different forms. A way of determining the squeezing of a squeezed vacuum state based on single-photon detection is presented.

The correspondence principle for atomic radiation is extended to all hydrogenic states $n$ and $l>0$. Lifetimes and branching ratios are obtained using analytic calculations of the classical radiated spectrum for the elliptical orbit corresponding to a particular quantum state. The polarization of the radiation is used to separate out the angular momentum decreasing and increasing transitions. The lifetimes show excellent agreement with quantum mechanics for all principal quantum numbers $n$ and $l⩾1$ (e.g., $<100\text{parts}\text{per}\text{million}$ for $l⩾30$, $<0.1\%$ for $l⩾9$, $<1\%$ for $l⩾3$). The calculated branching ratios are in reasonable agreement with quantum results for all $n^{\prime }$, $l^{\prime }$, $n$, and $l⩾1$.

A Bell inequality violation allowed by the two-mode squeezed state, whose Wigner function is nonnegative, is shown to hold only for correlations among dynamical variables that cannot be interpreted via a local hidden variable theory. Explicit calculations and interpretation are given for Bell’s suggestion that the EPR (Einstein, Podolsky, and Rosen) state will not allow violation of Bell’s inequality, in conjunction with its Wigner representative being nonnegative. It is argued that Bell’s theorem disallowing the violation of Bell’s inequality within a local hidden-variable theory depends on the dynamical variables having a definite value—assigned by the local hidden variables—even when they cannot be simultaneously measured. The analysis leads us to conclude that Bell’s inequality violation is to be associated with endowing these definite values to the dynamical variables, and not with their locality attributes.

We present numerical results on the capacities of two-qubit unitary operations for performing communication and creating entanglement. The capacities for communication considered are based upon the increase in Holevo information of an ensemble. Our results indicate that the capacity may be accurately estimated using ensemble sizes and ancilla dimensions of 4. In addition, the calculated values of these capacities were close to, and in some cases equal to, the similarly defined entangling capacities; this result indicates connections between these capacities.

We prove that sufficiently many copies of a bipartite entangled pure state can always be transformed into some copies of another one with certainty by local quantum operations and classical communication. The efficiency of such a transformation is characterized by deterministic entanglement exchange rate, and it is proved to be always positive and bounded from top by the infimum of the ratios of Renyi’s entropies of source state and target state. A careful analysis shows that the deterministic entanglement exchange rate cannot be increased even in the presence of catalysts. As an application, we show that there can be two incomparable states with deterministic entanglement exchange rate strictly exceeding 1.