Recently, Munro, Nemoto, and White (The Bell Inequality: A Measure of Entanglement?, quant-ph/0102119) tried to indicate that the reason behind a state $\rho$ having a higher amount of entanglement (as quantified by the entanglement of formation) than a state ${\rho }^{\prime },$ but producing the same amount of Bell violation, is due to the fact that the amount of mixedness (as quantified by the linearized entropy) in $\rho$ is higher than that in ${\rho }^{\prime }.$ We counter their argument with examples. We extend these considerations to the von Neumann entropy. Our results suggest that the reason as to why equal amount of Bell violation requires different amounts of entanglement cannot, at least, be explained by mixedness alone.

We report an experimental demonstration of photon switching by quantum interference in a four-level atomic system proposed by Harris and Yamamoto [Phys. Rev. Lett. 81, 3611 (1998)]. Quantum interference inhibits single-photon absorption but enhances third-order, two-photon-type absorption in the four-level system. We have observed greatly enhanced nonlinear absorption in the four-level system realized with cold ${}^{87}\mathrm{Rb}$ atoms and demonstrated fast switching of the nonlinear absorption with a pulsed pump laser.

We investigate theoretically the intensity and phase correlations in the quantum-noise-driven dynamics of two spatially coupled microchip lasers. These correlations induce noise reduction phenomena for which simple analytic expressions are derived. We predict a complete suppression of the dominant relaxation oscillation peaks in the intensity difference noise spectrum, as well as photon statistics approaching the standard quantum limit. The correlations and consequent noise reduction effects are robust against frequency detuning and persist for pump powers well above threshold.

A construction of Gaussian Klauder coherent states for systems with degenerate energy spectra is presented. Of special interest are the cases of truly accidental degeneracy that do not arise from a hidden or explicit symmetry. This is the case for a particle in a two-dimensional square box. In this case, the degeneracy results from the number of different ways an integer can be expressed as the sum of two squares. It is shown how to manage this situation and produce generalized coherent states that can mimic classical particle behavior for many collisions with the box walls.

We calculate the effect of an inhomogeneous magnetic field, which is invariably present in an experimental environment, on the exchange energy of a double-quantum-dot artificial molecule, projected to be used as a two-qubit quantum gate in the proposed quantum-dot quantum computer. We use two different theoretical methods to calculate the Hilbert space structure in the presence of the inhomogeneous field: the Heitler-London method, which is carried out analytically, and the molecular orbital method, which is done computationally. Within these approximations we show that the exchange energy J changes slowly when the coupled dots are subject to a magnetic field with a wide range of inhomogeneity, suggesting that swap operations can be performed in such an environment as long as quantum error correction is applied to account for the Zeeman term. We also point out the quantum interference nature of this slow variation in exchange.

We consider nonuniversal cloning maps, namely, cloning transformations that are covariant under a proper subgroup G of the universal unitary group $U\left(d\right),$ where d is the dimension of the Hilbert space $\mathcal{H}$ of the system to be cloned. We give a general method for optimizing cloning for any cost function. Examples of applications are given for phase-covariant cloning (cloning of equatorial qubits and qutrits) and for the Weyl-Heisenberg group (cloning of “continuous variables”).

A representation of the exact nonlocal exchange-potential operator is proposed and applied to study electron-impact vibrational excitation of ${\mathrm{H}}_2$ in the low- and intermediate-energy range. In our approach, a complete set of one-dimensional particle-in-box wave functions is used as expansion basis. This representation of the exchange operator is easy to program and the calculated cross sections converge rapidly with the number of basis functions. Excitation cross sections for the transitions $v^{\prime }=\overrightarrow{0}v=0,$ 1, 2, and 3 calculated in the 1.5–100-eV range are in general good agreement with the available experimental and theoretical data.

Electron attachment to sulfur hexafluoride is studied using a photoelectron source of ultralow-energy electrons with sub-meV resolution. Vacuum-ultraviolet laser radiation produced through nonlinear-optical techniques is used to photoionize xenon at and above its ${}^2{P}_{1/2}^o$ ionization limit. The resulting photoelectrons interact with sulfur hexafluoride admixed to the xenon. The electron energy is continuously scanned from 0 to 127 meV, with a resolution of 0.1 meV at threshold. Computational modeling indicates that the attachment cross section is well described by the Wigner threshold law at electron energies less than about 5 meV. Data at higher energies are best described by the Wigner s-wave form, or by a Klots form with $\beta =\mathrm{0.228.}\mathrm{}$ Cusps are observed at the ${\omega }_6,$ ${\omega }_1,$ and ${\omega }_3$ vibrational modes of ${\mathrm{SF}}_6.$ While the ${\omega }_1$ and ${\omega }_3$ cusps have their maxima at the spectroscopic energies of 97.1 and 117.6 meV, respectively, the ${\omega }_6$ cusp has its maximum at 46 meV, nearly 3 meV higher than its spectroscopic value of $43.2\pm 0.4\mathrm{meV}.$ Possible explanations are considered, such as a low-l angular-momentum barrier, an overtone mode of ${\mathrm{SF}}_6$ excited by the collision, or clustering. The definitive cause of this shift is not understood.

The $2p$ photoionization of free Cr atoms has been studied. Unpolarized as well as laser-aligned Cr atoms have been ionized with linearly polarized undulator radiation well above the $2p$ ionization thresholds. The investigation of the main and satellite $2p$ photoelectron lines and of the linear alignment dichroism allowed for a detailed characterization of the Cr $2p$ photoionization process. The spectra are compared to the predictions of the pure $\mathrm{jK}$ coupling model and to the results of intermediate coupling Hartree-Fock calculations. The importance of the investigations for the discussion of the $2p$ photoelectron spectra of bound $3d$ transition-metal atoms is pointed out.

Angular momentum is an important concept in physics, and its phase space properties are important in various applications. In this work a phase space analysis of angular momentum is made starting from its classical definition, and its quantum properties are obtained by imposing the uncertainty principle. The kinetic energy operator is derived, but its part have a different interpretation from that in the standard treatment. The rigid rotor is discussed and its phase space representation is shown. The true rigid rotor is defined and its phase space properties are also discussed.

Observed but unexplained features, namely, oscillations in the capture cross sections and an unexpected increase in the ionization cross sections at lower velocities, are discussed using classical trajectory Monte Carlo simulated results for ion–aligned-Rydberg-atom collisions. The initial alignment $(m=0,$ 1, and 2) dependence of the cross sections shows evidence of “capture through quasimolecular ion formation,” identified as the most likely cause for the oscillations. Spatial overlap, in addition to the velocity matching mechanism, is shown to play an important role in the collision process. The unexpected rise in the ionization cross section toward lower reduced velocities is explained qualitatively in terms of the multiple encounter model [Perumal and Tripathi, Nucl. Instrum. Methods B 143, 429 (1998)].

Based on the dielectric response theory, electronic stopping powers of solids for slow atoms have been studied. Using a local-field-correction dielectric function, we have calculated these stopping powers by including the correlation and exchange effects. The screening of shellwise electron charge densities of slow atoms by the conduction electrons in solids was estimated using a Thomas-Fermi screening model. In this model, atomic shellwise electron densities were constructed by a superposition of several Yukawa potentials. Stopping powers of Al, Ni, Ag, and Au were calculated for atoms with atomic number between 6 and 18. Calculated results showed that stopping powers oscillated with atomic number consistent with experimental data. Present results also indicated that our approach is much improved over other theoretical calculations. A comparison of presently calculated results with available theoretical and experimental data was made and discussed.

The lowest-energy structures and electronic properties of cadmium clusters are studied by density-functional theory with the generalized gradient approximation. The equilibrium structures of ${\mathrm{Cd}}_n$ $(n=2\mathrm{}–21)$ clusters are determined from a number of structural isomers, which are generated from genetic algorithm simulations with a tight-binding potential. Various close-packed structures are found for cadmium clusters. ${\mathrm{Cd}}_n$ clusters with $n=4,9,10,15,17,20\mathrm{}$ show relatively high stability, which can be related to the electron shell model, and agrees with experimental results. The density of states for the magic number clusters can also be associated with the electronic shell. The theoretical ionization potentials of ${\mathrm{Cd}}_n$ compare well with experimental values. The size evolution of electronic properties from van der Waals to covalent and bulk metallic behavior in Cd clusters is discussed.

We present a linear-least-squares-fitting method to solve the time-dependent Schrödinger equation of a one-dimensional model atom in an intense laser field in the Kramers-Henneberger frame. In comparison with calculations in the laboratory frame, it is shown that in the Kramers-Henneberger frame, the method is more stable and larger time steps in the propagation can be used. The fitting procedure also allows for easy change of basis functions during the time propagation. The method is applied to study the stabilization of a model atom in an intense laser field where the electron is bound initially by a one-dimensional soft Coulomb potential.

A powerful and accurate pseudostate method has been used to study two-photon ionization using elliptically polarized light. Calculations are made for ionization from the ground state as well as from the metastable $2s$ state of atomic hydrogen. The range of the wavelength chosen is such that it corresponds to two-photon ionization, i.e., 900–1700 Å for ionization from the ground state and 4500–7250 Å for ionization from the $2s$ state. It is found that at a given wavelength the ellipticity of the incident radiation modifies the ionization cross section substantially.

We consider a single-mode Bose-Einstein condensate with an arbitrary initial density matrix. This mode is coupled to another condensate mode via a quantized optical-field. We describe a method for transferring the diagonal elements of the initial density matrix in a number state basis to the optical-field’s density matrix.

The structure and stability of dilute degenerate Fermi gases trapped in an external potential is discussed with special emphasis on the influence of s- and p-wave interactions. In a first step an effective contact interaction for all partial waves is derived, which reproduces the energy spectrum of the full potential within a mean-field model space. Using the s- and p-wave part the energy density of the multicomponent Fermi gas is calculated in Thomas-Fermi approximation. On this basis the stability of the one- and two-component Fermi gas against mean-field induced collapse is investigated. Explicit stability conditions in terms of density and total particle number are given. For the single-component system attractive p-wave interactions limit the density of the gas. In the two-component case a subtle competition of s- and p-wave interactions occurs and gives rise to a rich variety of phenomena. A repulsive p-wave part, for example, can stabilize a two-component system that would otherwise collapse due to an attractive s-wave interaction. It is concluded that the p-wave interaction may have important influence on the structure of degenerate Fermi gases and should not be discarded from the outset.

The scattering of an incident electron by a pure Bose-Einstein condensate of alkali-metal atoms confined to a three-dimensional harmonic-oscillator potential is investigated to give the corresponding differential cross section. It is shown that for the elastic scattering process the differential cross section is proportional to the square of the number of condensed atoms, and hence can be called the “coherent scattering.” For the inelastic scattering process, the stopping power is obtained by considering the state of the center of mass and the internal electronic state of the condensed atom being excited separately and simultaneously, which is found to be proportional to the $\frac{7}{5}$ power of the number of condensed atoms when the binary collision interaction between atoms is taken into account.

We present an analysis of stimulated Raman scattering in nonlinear periodic structures such as fiber Bragg gratings. The interplay of Raman gain, Kerr nonlinearity, grating dispersion, and Bragg reflection leads to the formation of Raman gap solitons, enhanced Stokes pulse amplification, and distributed-feedback Raman oscillation.

We propose a scheme for nondistortion quantum interrogation defined as an interaction-free measurement that preserves the internal state of the object being detected. In our scheme, two Einstein-Podolsky-Rosen entangled photons are used as the probe and polarization-sensitive measurements are performed at the four ports of the Mach-Zehnder interferometer. In comparison with the previous single-photon scheme, it is shown that the two-photon approach has a higher probability of initial state preserving interrogation of an atom prepared in a quantum superposition. In the case that the presence of the atom is not successfully detected, the experiment can be repeated since the initial state of the atom is unperturbed.