This paper discusses the vacuum polarization in a Coulomb field $-Z\alpha /r$ when the electron momentum has been cut off at a given value $\Lambda .$ Radiative corrections are neglected. We carry out initially a first-order perturbative calculation when $|Z\alpha |$ is small and study the prerenormalization short-distance (i.e., $r\approx ħ/\Lambda )$ behavior of the induced charge-density distribution as $\Lambda$ goes to infinity. Then the perturbative results are compared with nonperturbative ones that are obtained by calculating numerically the set of eigenstates of a discretized Dirac equation in the Coulomb field. Our numerical investigations show that (i) when $|Z\alpha |<1\mathrm{}$ the nonperturbative results agree well with the first-order perturbative approximations; (ii) the inverse cubic law exhibited by the Uehling term of the induced charge density at distances $ħ/\Lambda <r\ll ħ{/m}_{0}c$ remains valid even for $|Z\alpha |\gg 1;$ (iii) the contribution to the induced charge density coming from extremely high energy states (i.e., the states just below the upper edge of the positive energy band and the states just above the lower edge of the negative energy band) is everywhere negative around a positively charged point source, while the contribution coming from all other states is everywhere positive. These two contributions cancel each other almost completely and result in a small negative term in the vicinity of the source.

We use the Liouville–von Neumann approach to study the dynamics and the adiabaticity of a time-dependent driven anharmonic oscillator as an example of nonequilibrium quantum dynamics. We show that the adiabaticity is minimally broken in the sense that a Gaussian wave packet at the past infinity evolves to coherent states; however slowly the potential changes, its coherence factor is of the order of the coupling. We also show that the dynamics are governed by an equation of motion similar to the Kepler motion, which satisfies angular momentum conservation.

A detailed study of a quantum free particle on a pointed plane is presented in this paper. In particular, some questions posed in the very recent paper by M. A. Cirone et al, Phys. Rev. A 65, 022101 (2002) are clarified. Namely, the topological effects related to extracting a point from a plane are indicated. The proposed results are introduced concerning self-adjoint extensions of operators describing the free particle on a pointed plane as well as the role played by discrete symmetries in the analysis of such extensions.

We work in the real Hilbert space ${\mathcal{H}}_s$ of Hermitian Hilbert-Schmidt operators and show that the entanglement witness which shows the maximal violation of a generalized Bell inequality (GBI) is a tangent functional to the convex set $S\subset {\mathcal{H}}_s$ of separable states. This violation equals the Euclidean distance in ${\mathcal{H}}_s$ of the entangled state to S and thus entanglement, GBI, and tangent functional are only different aspects of the same geometric picture. This is explicitly illustrated in the example of two spins, where also a comparison with familiar Bell inequalities is presented.

We investigate the differences between distributing entanglement using star- and ring-type network topologies. Assuming symmetrically distributed users, we assess the relative merits of the two network topologies as a function of the number of users when the amount of resources and the type of the quantum channel are kept fixed. For limited resources, we find that the topology better suited for entanglement distribution could differ from that which is more suitable for classical communications.

We derive the optimal exponent of the error probability of the quantum fixed-length pure-state source coding in both cases of blind coding and visible coding. The optimal exponent is universally attained by Jozsa et al.’s [Phys. Rev. Lett. 81, 1714 (1998)] universal code. In the direct part, a group representation theoretical type method is essential. In the converse part, Nielsen and Kempe’s [Phys. Rev. Lett. 86, 5184 (2001)] lemma is essential.

We present our calculations of the electric dipole and quadrupole matrix elements for transitions between low-lying bound states of ${\mathrm{Ba}}^{+}$ that are relevant for parity nonconservation studies using the relativistic coupled-cluster method. The results compare well with the experimental data. We have also computed the electric dipole transition matrix elements between many high-lying excited states.

Capture of negatively charged, heavy particles by hydrogen atoms, i.e., $X^{-}+\overrightarrow{H}{X}^{-}p+e,$ where $X^{-}=\overline{p}$ (antiproton), $K^{-}$ (kaon), and ${\mu }^{-}$ (muon), is investigated by carrying out a rigorous full quantum-mechanical (QM) wave-packet calculation and a semiclassical (SC) calculation. An empirical law for the capture probabilities, found by the present author [Phys. Rev. A 65, 012706 (2002)], is examined extensively by using the QM and SC results. The empirical law is useful to obtain reasonably accurate capture cross sections at center-of-mass translational energies less than 10 eV. Furthermore, a local-complex-potential (LCP) model is employed to discuss a quantum-mechanical effect of the relative motion at very low energies. The LCP calculation shows that a resonance structure is seen in the capture cross section.

We formulate a method to study two-body correlations in a system of N identical bosons interacting via central two-body potentials. We use the adiabatic hyperspherical approach and assume a Faddeev-like decomposition of the wave function. For a fixed hyperradius we derive variationally an optimal integro-differential equation for the hyperangular eigenvalue and wave function. This equation reduces substantially by assuming the interaction range much smaller than the size of the N-body system. At most, one-dimensional integrals then remain. We view a Bose-Einstein condensate pictorially as a structure in the landscape of the potential given as a function of the one-dimensional hyperradial coordinate. The quantum states of the condensate can be located in one of the two potential minima. We derive and discuss properties of the solutions and illustrate with numerical results. The correlations lower the interaction energy substantially. The new multibody Efimov states are solutions independent of details of the two-body potential. We compare with mean-field results and available experimental data.

The multiplet splittings resulting from Hund’s rules effects for open-shell atomic $d^n$ configurations are investigated within density-functional theory. The calculated results are compared to experiment, Hartree-Fock, and Slater-Condon-Racah fits. Marked systematic errors are found in the local-spin-density (LSDA) and generalized-gradient (GGA) results arising from the failure of the LSDA/GGA single-particle Hamiltonian to commute with L, $M_L,$ and S, which are good quantum numbers for the exact wave functions. The shortcomings of LSDA/GGA for the middle of the transition-metal row ions are more severe than those seen in previous work that concentrated on open p shells, even for multiplet levels with single-determinant wave functions. A number of issues confronting density-functional-based theories are addressed; in particular, it is demonstrated that any exchange-correlation functional that depends on the charge and spin densities alone is incapable of describing multiplet effects correctly.

Natural radiative lifetimes have been measured along the $6sns$ ${}^3{S}_1$ $(n=7\mathrm{}–10)$ and $6snd$ ${}^3{D}_1$ $(n=6\mathrm{}–11)$ Rydberg series of neutral mercury using time-resolved laser-induced fluorescence spectroscopy in a laser-produced mercury plasma. The states of Hg I investigated in the present work were populated from the ground state by a stepwise excitation process. Relativistic Hartree-Fock calculations, including intravalence interactions and core-polarization effects, have been performed and the theoretical lifetimes have been compared with the measurements.

Recent ab initio calculations of low-energy electron-${\mathrm{CO}}_2$ scattering [Rescigno et al., Phys. Rev. A $65,$ 032716 (2002)] are interpreted using an analytically solvable model. The model, which treats two partial-wave Hamiltonians with different l values coupled by a long-range ${(d/r}^2)$ interaction, is a generalization of similar single-channel models that have previously been used to interpret the low-energy behavior of electron scattering by polar diatomic molecules. The present model is used to track the pole trajectories of both resonances and virtual states, both of which figure prominently in low-energy electron-${\mathrm{CO}}_2$ scattering, in the plane of complex momentum. The connection between resonant and virtual states is found to display a different topology in the case of a polyatomic molecule than it does in diatomic molecules. In a polyatomic molecule, these states may have a conical intersection and consequently acquire a Berry phase along closed paths in two-dimensional vibrational motion. The analytic behavior of the S matrix is further modified by the presence of a geometry-dependent dipole moment.

A He plus electron scattering experiment by Gosselin and Marmet [Phys. Rev. A 41, 1335 (1990)] produced the previously known ${\mathrm{He}}^{-}$ ${2s2p}^2{}^{2}D$ resonance at $58.283\pm 0.003\mathrm{eV}$ with a width $\Gamma =59\mathrm{}\pm 4\mathrm{meV},$ and two new structures at $58.415\pm 0.005$ and $58.48\pm 0.02\mathrm{eV}$ with $\Gamma <2\mathrm{}\mathrm{meV}$ and $\Gamma =70\mathrm{}\pm 20\mathrm{meV},$ respectively. The nature of these last two structures has since remained unexplained. Heuristic analysis of the spectrum of the triply excited states (TES) of ${\mathrm{He}}^{-}$ and of conditions of electron correlation and possible localization, and application of the state-specific theory (SST) for the calculation of electronic structures and properties led to the determination of three resonance states of ${}^{2}D$ symmetry that explain quantitatively the experimental data. The implementation of the SST involved the combination of suitable choices of optimized orbitals, of nonorthonormal configuration interaction, and of mixing of bound with scattering configurations. The first two ${}^{2}D$ TES contain the ${2s2p}^2$ configuration as a major component, but strong radial correlation results in the spatial separation of the two p spin orbitals. The third TES, computed systematically with up to 996 optimized configurations, is an open-channel like localized wave packet.

Collisions between low-energy multiply charged ions and neutral metal clusters are an efficient method to investigate charge instabilities in finite systems. We study here the appearance size $n_{\mathrm{app}}\mathrm{}\left(q\right)\mathrm{}$ of multiply charged sodium clusters ${\mathrm{Na}}_n^{q+}$ with $q<~10,$ i.e., the smallest size of observation for q-fold charged clusters and its dependence on the collision parameters. The experimental results are compared with the energy transferred to the cluster during the collision, calculated with the semiclassical Vlasov equation within the jellium approximation. Experimental and theoretical data show similar trends with the collision parameters and evidence the importance of dynamical effects. These results guide further investigations for studying low excited multiply charged finite systems.

We examine, both numerically and analytically, the limits of controllability and the dynamics of population transfer in systems with degenerate target states embedded in a finite manifold of states. An analysis of the dressed eigenstates of coupled field-matter systems is combined with the theory of the controllability of invariant systems on Lie groups to show the existence of a control scheme using a pair of shaped laser pulses acting upon a four-state system with intermediate degenerate states and a diamond-shaped array of transition moments $({\mu }_{12},{\mu }_{24},{\mu }_{13},{\mu }_{34}\ne 0,{\mu }_{14},{\mu }_{23}=0).\mathrm{}$ The limits of the controllability of these systems are linked to the symmetry of the transition dipole moments connecting the states. A broken symmetry of the transition dipole moments $({\mu }_{12}/{\mu }_{24}\ne {\mu }_{13}/{\mu }_{34})$ permits complete population transfer to one of the pair of degenerate states. Numerical simulations of the optimized population transfer to one of a pair of degenerate states in the system agree quantitatively with the analytically predicted limits of population transfer in different regimes in the joint material-field characteristics of the system. The applicability of the four-state model to selective population transfer in vibrationally mediated photodissociation experiments is discussed.

Circularly polarized light propagating at an angle to the external magnetic field does not optically pump atoms to full transparency under conditions common to spin-exchange optical pumping experiments. This causes excess absorption of the pumping light that can significantly reduce the efficiency of the optical pumping process even for angles of a few degrees.

In this paper I investigate mean-field effects for a Bose gas harmonically trapped above the quantum transition temperature in the collisionless regime. I point out that these effects can play a role in low dimensional systems. My treatment relies on the Boltzmann equation with the inclusion of the mean-field term. I first discuss the equilibrium state then derive the dispersion relation for collective oscillations (monopole, quadrupole, and dipole modes) in D dimensions.

We propose a technique for generating momentum-squeezed states of optical pulses with a simple apparatus. An initial coherent state is launched into a dispersion-decreasing fiber, leading to pulse compression. The compressed pulse has a broader spectrum, but the average frequency of the pulse is fundamentally conserved by the Kerr effect. Although the momentum, or frequency, uncertainty of the pulse is not reduced, the final momentum uncertainty is below the coherent-state level with respect to the broadened output spectrum. The observable momentum uncertainty reflects photon correlations generated during the Kerr-effect scattering events. We discuss the basic characteristics of squeezing as well as the possibility of generating interesting quantum superposition states in an ideal lossless device.

We report on the observation of noise-correlated light beams emitted from a pair of spatially coupled microchip lasers. We study in particular, both experimentally and theoretically, the noise reduction induced in the intensity difference fluctuations, by examining the spectral density ratio between the difference and the sum of the two laser intensities in different frequency domains. The noise in the intensity difference is strongly reduced in the spectral domain of the relaxation oscillations of the coupled lasers. The agreement between experiment and the theoretical model findings is very good.

We analyze the two-photon linewidth of a recently proposed adiabatic transfer technique for “stopping” of light using electromagnetically induced transparency (EIT). We show that a successful and reliable transfer of excitation from light to atoms and back can be achieved if the spectrum of the input probe pulse lies within the initial transparency window of EIT, and the two-photon detuning $\delta$ is less than the collective coupling strength (collective vacuum Rabi frequency) $g\sqrt{N}$ divided by $\sqrt{\gamma T},$ with γ being the radiative decay rate, N being the effective number of atoms in the sample, and T being the pulse duration. Hence in an optically thick medium light “storage” and retrieval is possible with high fidelity even for systems with rather large two-photon detuning or inhomogeneous broadening.