In Kaszlikowski et al. [Phys. Rev. Lett. 85, 4418 (2000)], it has been shown numerically that the violation of local realism for two maximally entangled N-dimensional $(3\mathrm{}<~N)$ quantum objects is stronger than for two maximally entangled qubits and grows with N. In this paper, we present the analytical proof of this fact for $N=3.\mathrm{}$

We examine constraints on quantum operations imposed by relativistic causality. A bipartite superoperator is said to be localizable if it can be implemented by two parties (Alice and Bob) who share entanglement but do not communicate; it is causal if the superoperator does not convey information from Alice to Bob or from Bob to Alice. We characterize the general structure of causal complete-measurement superoperators, and exhibit examples that are causal but not localizable. We construct another class of causal bipartite superoperators that are not localizable by invoking bounds on the strength of correlations among the parts of a quantum system. A bipartite superoperator is said to be semilocalizable if it can be implemented with one-way quantum communication from Alice to Bob, and it is semicausal if it conveys no information from Bob to Alice. We show that all semicausal complete-measurement superoperators are semilocalizable, and we establish a general criterion for semicausality. In the multipartite case, we observe that a measurement superoperator that projects onto the eigenspaces of a stabilizer code is localizable.

The relation between the requirement of efficient implementability and the product-state representation of numbers is examined. Numbers are defined to be any model of the axioms of number theory or arithmetic. Efficient implementability (EI) means that the basic arithmetic operations are physically implementable and the space-time and thermodynamic resources needed to carry out the implementations are polynomial in the range of numbers considered. Different models of numbers are described to show the independence of both EI and the product-state representation from the axioms. The relation between EI and the product-state representation is examined. It is seen that the condition of a product-state representation does not imply EI. Arguments used to refute the converse implication, EI implies a product-state representation, seem reasonable; but they are not conclusive. Thus this implication remains an open question.

Since Kato proved his singularity condition for Coulomb potentials in 1957, there has been interest in the creation of wave functions that meet the prescriptions of the cusp conditions, necessary for high-precision quantum-mechanical calculations. It is well known, that wave-function expansions based on Slater determinants of one-electron functions are poorly convergent with respect to satisfying the electron-electron cusp condition. In this contribution we show that with the wavelet expansion of density operators even the local form of the electron-electron cusp condition is easily representable by Slater determinants of one-electron wavelet functions with a proper asymptotics of the expansion coefficients, which is explicitly calculated for Haar wavelets.

The stability of antimatter in contact with matter has been investigated. The interaction between hydrogen and antihydrogen is considered as the prototype reaction. We have focused interest on the rates for proton-antiproton and/or electron-positron annihilation during hydrogen-antihydrogen collisions at low energies. In particular, we have concentrated on the calculation of the rates for the rearrangement reaction leading to formation of protonium and positronium, ending inevitably in particle-antiparticle annihilation. The cross section for the rearrangement collision has been calculated in a fully quantum-mechanical treatment. Additionally, we have calculated cross sections for direct annihilation during the collision process, which was found to be comparable to the rearrangement cross section. The elastic cross section and its low-energy limit, given by the scattering length, have been calculated, allowing, by comparison to the inelastic processes, a prediction for the efficiency of cooling antihydrogen via collisions with ultracold hydrogen atoms.

We present the results of a series of model Monte Carlo calculations of the scattering of spin-polarized electrons from gold foil targets. Our calculations examine the behavior of the left-right scattering asymmetry A as a function of various parameters conventionally used in extrapolation of the left-right asymmetry to single-atom and/or elastic scattering conditions. These parameters include target thickness, scattered count rate, and the maximum energy that an electron can have lost in the target and still be detected. Data are obtained at incident electron energies of 10–120 keV, with detector-subtended half-cone angles of 5°, 10°, and 20°, and gold foils of average thickness varying from 3 to 1000Å. Both elastic and inelastic electron scattering effects have been considered. Comparisons of our results are made with existing measurements and theoretical models. We make recommendations concerning extrapolation algorithms and for future experiments to test the present Mott scattering Monte Carlo model.

After a slow ${\mathrm{Si}}^{3+}$ ion captures a single electron from a highly excited Rydberg target, the populations of individual low-L levels within the $n=29\mathrm{}$ level of ${\mathrm{Si}}^{2+}$ are measured by laser excitation, and compared with the population of the very-high-L $n=29\mathrm{}$ levels. The measurements confirm some unusual features of L distributions predicted by classical trajectory Monte Carlo methods.

Eigenchannel R-matrix calculation results are presented for the photodetachment of ${\mathrm{K}}^{-}$ in the energy region between the $\mathrm{K}\mathrm{}\left(5s\right)\mathrm{}$ and $\mathrm{K}\mathrm{}\left(7p\right)\mathrm{}$ thresholds. Present results are compared with prior experimental studies, including the recent relative $\mathrm{K}\mathrm{}\left(5s\right)\mathrm{}$ partial cross section measurements of Kiyan et al. [Phys. Rev. A 84, 5979 (2000)], and resonances observed in electron-potassium scattering. Detailed analyses and identifications of ${}^1{P}^o$ resonance structures are presented. Comparisons with ${\mathrm{H}}^{-}$ and other alkali-metal negative ions provide further information on the structure and dynamics of negative ions.

In order to explain the experimental observation of the magic ${\mathrm{Al}}_{13}^{+}{\mathrm{H}}_2\mathrm{O}$ cluster [T. P. Lippa et al., Chem. Phys. Lett. 305, 75, (1999)], first-principles calculations are performed, a new stable structure for ${\mathrm{Al}}_{13}^{+}$ is found, and its intrinsic stability is confirmed. The most preferable adsorption site for the water molecule is determined from the electronic structure, and the interaction mechanism is clarified: the $p_z$ lone electron pair in the ${\mathrm{H}}_2\mathrm{O}$ molecule dominates the interactions with ${\mathrm{Al}}_{13}^{+}$ over the $p_x$ lone electron pair. Due to the strong interaction of the lone electron pair of the water molecule with the ${\mathrm{Al}}_{13}^{+}$ cluster, the adsorption energy for this molecule is 1.77 eV, and the adsorption widens the highest occupied-lowest unoccupied molecular orbital (HOMO-LUMO) gap in ${\mathrm{Al}}_{13}^{+}{\mathrm{H}}_2\mathrm{O}$ to 1.63 eV, which contributes to the stability of this cluster.

We discuss the equivalence of two nonequilibrium kinetic theories that describe the evolution of a dilute, Bose-Einstein condensed atomic gas in a harmonic trap. The second-order kinetic equations of Walser et al. [Phys. Rev. A 63, 013607 (2001)] reduce to the Gross-Pitaevskii equation and the quantum Boltzmann equation in the low- and high-temperature limits, respectively. These kinetic equations thus describe the system in equilibrium (finite temperature) as well as in nonequilibrium (real time). We have found this theory to be equivalent to the nonequilibrium Green’s function approach originally proposed by Kadanoff and Baym and more recently applied to inhomogeneous trapped systems by Imamović-Tomasović and Griffin [in Progress in Nonequilibrium Green’s Functions, edited by M. Bonitz (World Scientific, Singapore, 2000), p. 404].

We investigate the feasibility of a particular scheme for generating macroscopic quantum superposition states in two-species dilute gas Bose-Einstein condensates. The scheme utilizes two-body interactions and Josephson coupling between the species. We report numerical studies that extend a previous two-mode model to include dissipation and extra modes.

Traveling-wave irradiation with a laser pulse of duration $\sim 1$ picosecond has been shown to achieve saturated operation of Ne- and Ni-like x-ray lasers. Gain at 196 Å was confirmed by observation of both forward and backward x-ray laser beams from a germanium plasma under ideal and nonideal traveling-wave conditions at a small signal gain of $>40\mathrm{}\hspace{0.5em}{\mathrm{cm}}^{-1}.$ Saturation was observed for targets $>4\mathrm{}$ mm long consistent with a model of laser amplification along the plasma medium and with the output of a detailed ray-tracing post-processor coupled to a hydrodynamic and atomic physics code. Ni-like samarium targets, pumped under ideal traveling-wave conditions exhibited a small signal gain of $\sim 19\hspace{0.5em}{\mathrm{cm}}^{-1}$ at 73 Å with saturation observed for targets 8 mm long.

The spatial and temporal evolution is studied of two powerful short laser pulses having different wavelengths and interacting with a dense three-level Λ-type optical medium under coherent population trapping. The general case of unequal oscillator strengths of the transitions is considered. The durations of the probe pulse and the coupling pulse $T_{1,2}\hspace{0.5em}{(T}_2>T_1)$ are assumed to be shorter than any of the relevant atomic relaxation times. We propose analytical and numerical solutions of a self-consistent set of coupled Schrödinger equations and reduced wave equations in the adiabatic limit taking account of the first nonadiabatic correction. The adiabaticity criterion is also discussed taking account of pulse propagation. The dynamics of propagation is found to be strongly dependent on the ratio of the transition oscillator strengths. It is shown that the envelopes of the pulses slightly change throughout the medium length in the initial stage of propagation. This distance can be large compared to the one-photon resonant absorption length. Eventually, the probe pulse is completely reemitted into the coupling pulse during propagation. An effect of localization of the atomic coherence was observed similar to the one predicted by Fleischhauer and Lukin [Phys. Rev. Lett. 84, 5094 (2000)].

Light-induced absorption with population inversion and amplification without population inversion in a coherently prepared closed three level V-type system are investigated. This study is performed from the point of view of a two color dressed-state basis. Both of these processes are possible due to atomic coherence and quantum interference contrary to simple intuitive predictions. Merely on a physical basis, one would expect a complementary process to the amplification without inversion. We believe that absorption in the presence of population inversion found in the dressed-state picture utilized in this study, constitutes such a process. We derive approximate analytic time-dependent solutions, for coherences and populations that are compared with full numerical solutions exhibiting good agreement. Steady-state quantities are also calculated, and the conditions under which the system exhibits absorption and gain with and without inversion, in the dressed-state representation are derived. It is found that for weak input probe-laser field absorption with inversion and amplification without inversion may occur, for a range of system parameters. These take place at resonance and the generalized Rabi ac Stark-shifted frequencies, in agreement with exprimental investigations, and at beat frequencies, depending on the relevant parameters.

This paper deals with non-Markovian behavior in atomic systems coupled to a structured reservoir of quantum electromagnetic field modes, with particular relevance to atoms interacting with the field in high-Q cavities or photonic band-gap materials. In cases such as the former, we show that the pseudomode theory for single-quantum reservoir excitations can be obtained by applying the Fano diagonalization method to a system in which the atomic transitions are coupled to a discrete set of (cavity) quasimodes, which in turn are coupled to a continuum set of (external) quasimodes with slowly varying coupling constants and continuum mode density. Each pseudomode can be identified with a discrete quasimode, which gives structure to the actual reservoir of true modes via the expressions for the equivalent atom-true mode coupling constants. The quasimode theory enables cases of multiple excitation of the reservoir to now be treated via Markovian master equations for the atom-discrete quasimode system. Applications of the theory to one, two, and many discrete quasimodes are made. For a simple photonic band-gap model, where the reservoir structure is associated with the true mode density rather than the coupling constants, the single quantum excitation case appears to be equivalent to a case with two discrete quasimodes.

Electron interference in mesoscopic devices irradiated by external monochromatic nonclassical microwaves is considered. The relative phase factor between two electron paths is a quantum mechanical operator whose expectation value with respect to the density matrix of the nonclassical microwaves is studied. It is shown that, due to both classical and quantum noise in the microwaves, the absolute value of the phase factor is less than $1,$ causing partial destruction of the interference. Separable and entangled two-mode nonclassical microwaves are also considered and their effect on the expectation value of the phase factor is studied.

We analyze the collective spin noise in interacting spin systems. General expressions are derived for the short-time behavior of spin systems with general spin-spin interactions, and we suggest optimum experimental conditions for the detection of spin squeezing. For Ising models with site-dependent nearest-neighbor interactions, general expressions are presented for the spin squeezing parameter for all times. The reduction of collective spin noise can be used to verify the entangling powers of quantum computer architectures based on interacting spins.

Resonant Auger spectra following the decay of doubly excited core states in ${\mathrm{N}}_2$ in the range 409–411 eV have previously been assigned to “atomic” lines indicating ultrafast dissociation. Using high-resolution synchrotron radiation electron spectroscopy from the MAX II facility in Sweden we have remeasured the resonant Auger spectrum of ${\mathrm{N}}_2$ in the vicinity of the N $1s$ threshold. Contrary to earlier studies, we find vibrational progressions that can be associated with the final $C{}^2{\Sigma }_u^{+}$ and $2{}^2{\Pi }_g$ states in ${\mathrm{N}}_2^{+}.$ We conclude that the decay leads entirely to molecular final states.

The neutralization of ${\mathrm{He}}^{+}$ ions at a solid ${\mathrm{CO}}_2$ surface is investigated by analyzing the energy distribution of electrons ejected from the surface and by use of spin-labeling techniques, specifically the use of electron-spin-polarized ${\mathrm{He}}^{+}$ ions coupled with energy-resolved measurements of the ejected-electron polarization. The data indicate that ion impact leads to efficient electron ejection through formation of an autoionizing collision complex comprised of the incident ion and two neighboring ${\mathrm{CO}}_2$ molecules in which a significant portion of the initial kinetic energy of the ion is converted to potential energy.

We study the collective Raman cooling of a polarized trapped Fermi gas in the festina lente regime, when the heating effects associated with photon reabsorptions are suppressed. We predict that by adjusting the spontaneous Raman emission rates and using appropriately designed anharmonic traps, temperatures of the order of $2.7\%$ of the Fermi temperature can be achieved in 3D.