In this paper, a system composed of two pairs of two-level atoms and a multimode-vacuum field is considered. In our model, either pair contains two atoms that are assumed to be set close. We propose a disentanglement-free state of the two pairs of two-level atoms. It is remarkable that when the two pairs, initially in such a state, fly apart an arbitrary distance, the state will undergo no decoherence. By means of such a state, we can prepare the perfect Einstein-Podolsky-Rosen pair shared by two “distant” parties and realize long-distance entanglement swapping. Finally, a method for preparing such a disentanglement-free state is presented.

Besides their use for efficient computation, quantum computers and quantum robots form a base for studying quantum systems that create valid physical theories using mathematics and physics. If quantum mechanics is universally applicable, then quantum mechanics must describe its own validation by these quantum systems. An essential part of this process is the development of a coherent theory of mathematics and quantum-mechanics together. It is expected that such a theory will include a coherent combination of mathematical logical concepts with quantum mechanics. That this might be possible is shown here by defining truth, validity, consistency, and completeness for a quantum-mechanical version of a simple (classical) expression enumeration machine described by Smullyan. Some of the expressions are chosen as sentences denoting the presence or absence of other expressions in the enumeration. Two of the sentences are self-referential. It is seen that, for an interpretation based on a Feynman path sum over expression paths, truth, consistency, and completeness for the quantum system have different properties than for the classical system. For instance, the truth of a sentence S is defined only on those paths containing S. It is undefined elsewhere. Also S and its negation can both be true provided they appear on separate paths. This satisfies the definition of consistency. The definitions of validity and completeness connect the dynamics of the system to the truth of the sentences. It is proved that validity implies consistency. It is seen that the requirements of validity and maximal completeness strongly restrict the allowable dynamics for the quantum system. Aspects of the existence of a valid, maximally complete dynamics are discussed. An exponentially efficient quantum computer is described that is also valid and complete for the set of sentences considered here.

All incoherent as well as 2- and 3-qubit coherent eavesdropping strategies on the six-state protocol of quantum cryptography are classified. For a disturbance of $1/6$, the optimal incoherent eavesdropping strategy reduces to the universal quantum cloning machine. Coherent eavesdropping cannot increase Eve’s Shannon information, neither on the entire string of bits, nor on the set of bits received undisturbed by Bob. However, coherent eavesdropping can increase as well Eve’s Renyi information as her probability of guessing correctly all bits. The case that Eve delays the measurement of her probe until after the public discussion on error correction and privacy amplification is also considered. It is argued that by doing so, Eve gains only negligibly small additional information.

We analyze the use of entangled states to perform quantum computations nonlocally among distant nodes in a quantum network. The complexity associated with the generation of multiparticle entangled states is quantified in terms of the concept of global cost. This parameter allows us to compare the use of physical resources in different schemes. We show that, for ideal channels and for a sufficiently large number of nodes, the use of maximally entangled states is advantageous over uncorrelated ones. For noisy channels, one has to use entanglement purification procedures in order to create entangled states of high fidelity. We show that under certain circumstances a quantum network supplied with a maximally entangled input still yields a smaller global cost, provided that n belongs to a given interval $n\in \left[n_{\min }{,n}_{\max }\right]$. The values of $n_{\min }$ and $n_{\max }$ crucially depend on the purification protocols used to establish the n processor entangled states, as well as on the presence of decoherence processes during the computation. The phase estimation problem has been used to illustrate this fact.

The atomic electron-electron counterbalance density $d\left(0\right)\mathrm{}$ represents the probability density of finding any two electrons exactly at mirror positions with respect to the nucleus. We have computed these densities from accurate configuration interaction and Hartree-Fock-like wave functions for the isoelectronic series of He and first-row atoms. Our calculations demonstrate that the electron correlation decreases the value of $d\left(0\right)\mathrm{}$, and thus indicate that the radial correlation effects dominate over the angular effects. We have also found that inclusion of dynamical correlation is crucial for a realistic description of the electron-electron counterbalance density.

Adapting an approach used by Feynman for the Lamb shift of an isolated atom, we obtain a nonperturbative expression for the Lamb shift of an atom in a dielectric medium, previously calculated perturbatively [P. W. Milonni, J. Mod. Opt. 42, 1191 (1995)]. The separation of the Lamb and Casimir components of the field energy is greatly simplified, and previous nonperturbative results for the Lamb shift [M. Schaden, L. Spruch, and F. Zhou, Phys. Rev. A 57, 1108 (1998)], based on the generalized argument theorem, are obtained much more easily and directly.

It is shown that one can stimulate, by using present day laboratory magnetic fields, transitions between the $\mathrm{lm}$ sublevels of fast $\mu {\mathrm{He}}^{+}$ ions formed in muon-catalyzed fusion. Strong fields also cause the self-ionization from highly excited states of such muonic ions. Both effects are the consequence of the interaction of the bound muon with the oscillating field of the Stark term coupling the center-of-mass and muon motions of the $\mu {\mathrm{He}}^{+}$ ion due to the nonseparability of the collective and internal variables in this system. The performed calculations show a possibility to drive the population of the $\mathrm{lm}$ sublevels by applying a field of a few tesla, which affects the reactivation rate and is especially important to the $K\alpha$ x-ray production in muon catalyzed fusion. It is also shown that the $2s-2p$ splitting in $\mu {\mathrm{He}}^{+}$ due to the vacuum polarization slightly decreases the stimulated transition rates.

Various geometrical and energetical properties in the symmetric muonic molecular ions $\mathrm{pp}\mu ,dd\mu ,tt\mu$, molecular ions $ppe,dde,tte$, and exotic system $\mu \mu e$ $\left({\mu }^{+}{\mu }^{+}{e}^{-}\right)$ are determined with high accuracy by using the two-stage strategy proposed by Frolov [Phys. Rev. A 57, 2436 (1998)]. The significant difference between bound-state spectra in muonic molecular ions $\mathrm{pp}\mu ,dd\mu ,tt\mu$ and molecular ions $ppe,dde,tte$ ions is explained by using the general theory of bound-state spectra in Coulomb three-body systems, which is closely related with the general theory of compact operators. In particular, the principal classification of the bound-state spectra in such systems can be made in the same manner as for compact operators. For instance, the discrete spectrum of a Coulomb three-body system may have the Hilbert-Schmidt, nuclear or finite-dimensional structure. Moreover, this structure can be changed by varying some of the physical parameters (e.g., masses or charges) of the system. The developed theory is applied to the case of symmetric Coulomb three-body systems with unit charges.

We show evidence of dissociation during resonant inelastic soft x-ray scattering. Carbon and oxygen K-shell and sulfur L-shell resonant and nonresonant x-ray emission spectra were measured using monochromatic synchrotron radiation for excitation and ionization. After sulfur $L_{2,3}\to {\pi }^{*},$ ${\sigma }^{*}$ excitation, atomic lines are observed in the emission spectra as a consequence of competition between de-excitation and dissociation. In contrast the carbon and oxygen spectra show weaker line-shape variations and no atomic lines. The spectra are compared to results from ab initio calculations. The discussion of the dissociation paths is based on calculated potential energy surfaces and atomic transition energies.

In this paper we present results of four-component relativistic density-functional calculations for diatomic molecules with heavy constituents. The fully relativistic treatment of the electron kinematics is used for a consistent examination of the importance of gradient and relativistic corrections to the exchange-correlation energy functional. In agreement with recent scalar relativistic calculations, we find that relativistic corrections to exchange-correlation functionals give no significant contribution to the binding properties of the investigated diatomic molecules. On the other hand, the effect of gradient terms is sizable, leading to a clear improvement of dissociation energies over the standard local-density approximation. The usefulness of gradient contributions in the high-$Z$ regime is nevertheless somewhat questioned by the fact that they overcorrect the small errors in bond lengths found with the local-density approximation.

The multiconfiguration Dirac-Fock (MCDF) model is employed to compute the hyperfine interaction constants of the ${3d}^{2}4s{\hspace{0.5em}}^2{D}_{3/2},$ ${3d}^{2}4s{\hspace{0.5em}}^2{D}_{5/2},$ ${3d}^3{\hspace{0.5em}}^2{G}_{7/2},$ ${3d}^3{\hspace{0.5em}}^2{G}_{9/2},$ and ${3d}^3{\hspace{0.5em}}^2{P}_{3/2}$ levels of titanium ion. The wave function expansions are obtained with the active space expansion method, where configuration state functions of a specific parity and J value are generated by substitutions from the reference configurations to an active set of orbitals. The active set is then increased in a systematic way, allowing the convergence of the expectation values to be achieved. The calculated electric quadrupole hyperfine constants are used to evaluate the nuclear electric quadrupole moment of isotope 49 of titanium, for which the value $Q=0.247\mathrm{}\left(11\right)\mathrm{}\mathrm{b}$ is found.

The cross sections, initial quantum numbers, and kinetic energies for pionic atoms formed by negative pion capture in mixtures of isotopic hydrogen molecules are calculated using the fermion-molecular-dynamics (FMD) method. With these cross sections, the reduced capture ratio for a ${\mathrm{H}}_2+{\mathrm{D}}_2$ mixture is found to be ${(P}_p^{\left({\mathrm{H}}_2{+\mathrm{D}}_2\right)}{/P}_d^{\left({\mathrm{H}}_2{+\mathrm{D}}_2\right)}{)/(c}_p{/c}_d)=1.204\mathrm{}$, and the capture ratio for HD is found to be $P_p^{\left(\mathrm{HD}\right)}{/P}_d^{\left(\mathrm{HD}\right)}=0.875\mathrm{}$. In light of these results, the p-to-$d$ pion transfer probabilities Q are reevaluated using prior experimental data and determined to be larger than previously thought: $Q=0.28\mathrm{}$ at deuterium fraction $c_d=0.5\mathrm{}$ and $Q=0.42\mathrm{}$ as $c_d\to 1$. The puzzling relationship of the experimental data for HD to that for ${\mathrm{H}}_2+{\mathrm{D}}_2$ mixtures is explained.

Potential-energy curves for the low-lying doublet and quartet states of various symmetries $({\Pi }_g,$ ${\Pi }_u,$ ${\Sigma }_g,$ and ${\Sigma }_u)$ of the triply charged ${\mathrm{N}}_2^{3+}$ molecular cation are studied using quantum ab initio methods. These states correlate asymptotically to the ${\mathrm{N}}^{2+}{+\mathrm{N}}^{+}$ atomic fragments. No stable (bound) states are found to occur in the midst of many Coulomb repulsive potentials. The potentials are shown to follow a pure Coulomb repulsion law at $R>~5\mathrm{bohr}.$ The most relevant configurations are enumerated for discussion of recent laser Coulomb explosion and imaging experiments.

We present an analytic calculation of the $O\left(m{\alpha }^6\right)$ recoil and radiative recoil corrections to energy levels of positronium $\mathrm{nS}$ states and their hyperfine splitting. A complete analytic formula valid to $O\left(m{\alpha }^6\right)$ is given for the spectrum of S states. Technical aspects of the calculation are discussed in detail. Theoretical predictions are given for various energy intervals and compared with experimental results.

The interaction of a plane monochromatic traveling wave with two-level particles suffering collisions with buffer-gas particles is considered. Collision rates are assumed to be velocity dependent. The collision integral is obtained on the basis of the strong-collision model, generalized to the case of velocity-dependent collision rates (the so-called “kangaroo” model). We obtained the exact analytical solution of the problem for arbitrary intensity of radiation, arbitrary ratio of homogeneous and Doppler widths of the absorption line, and arbitrary mass ratio between absorbing- and buffer-gas particles. The obtained analytical solutions of the quantum kinetic equations allowed us to analyze the spectral shape of the strong-field absorption line as well as the probe-field absorption line (the nonlinear part of the work done by the probe field) and the frequency dependence of the light-induced drift (LID) velocity. A comprehensive comparative analysis for the three- and one-dimensional versions of the model is given. On the basis of this analysis, we reach the conclusion that the one-dimensional quantum kinetic equation has quite a wide range of application. We also reveal the conditions for the strongest manifestation of the velocity dependence of the collision rates, which affects most strongly the anomalous LID.

We solve the Holstein equation describing radiation trapping in an atomic vapor by the geometric quantization technique. The treatment is based on studying the integral trapping equation as a wave equation for an associated quasiparticle with a complicated form of its dispersion law. The latter is determined by the spectral properties of the vapor medium. Extending our previous work, which dealt with one-dimensional (1D) geometries, we consider here more realistic two- and three-dimensional (2D and 3D) vapor cell geometries. For this, an explicit representation of the phase factors is derived when the quasiparticle is reflected under arbitrary angles from the surface of the cell confining the vapor. We give closed-form equations to obtain analytically the complete 3D spectrum of escape factors in finite cylinder, sphere, parallelepiped, and finite prismlike geometries for all practically occurring line shapes and opacities. In addition, the relevant semiclassical variational method is applied to develop a perturbation theory for the evaluation of escape factors in more complicated geometries that are sometimes adopted in experiments, including infinite (or finite) elliptical cylinders, prolate and oblate ellipsoids. Comparisons with numerical calculations show that results are accurate within $5\%$ for the ground modes and even better for higher-order modes.

We present a theory of resonant processes in a frozen gas of atoms interacting via dipole-dipole potentials that vary as $r^{-3}$, where r is the interatomic separation. We supply an exact result for a single atom in a given state interacting resonantly with a random gas of atoms in a different state. The time development of the transition process is calculated both on and off resonance, and the linewidth with respect to detuning is obtained as a function of time t. We introduce a random spin Hamiltonian to model a dense system of resonators, and show how it reduces to the previous model in the limit of a sparse system. We derive approximate equations for the average effective spin, and we use them to model the behavior seen in the experiments of Anderson, Veale, and Gallagher [Phys. Rev. Lett. 80, 249 (1998)] and Lowell and co-workers [Ph.D. dissertation, University of Virginia, 1998, and (unpublished)]. The approach to equilibrium is found to be proportional to $\exp \left(-\sqrt{{\gamma }_{\mathrm{eq}}t}\right)$, where the constant ${\gamma }_{\mathrm{eq}}$ is explicitly related to the system’s parameters.

The spectral dependence of the angular distributions of photoelectrons produced by the single-photon detachment of ${\mathrm{Ge}}^{-}$ ions have been measured at four discrete photon wavelengths ranging from 457.9 to 647.1 nm (2.71–1.92 eV) using a crossed laser-ion beams apparatus. Values of the fine-structure resolved asymmetry parameters have been determined by fits to the photoelectron yield as a function of the angle between the laser polarization vector and the linear momentum vector of the collected photoelectrons. The measured asymmetry parameters for ${\mathrm{Ge}}^{-}$ are compared to previous asymmetry parameter measurements for ${\mathrm{C}}^{-}$ and ${\mathrm{Si}}^{-}.$ The measurements were also fit to a previously reported model for photoelectron asymmetry parameters for photodetaching p-orbital electrons from negative ions.

Dissociative electron attachment (DA) to ${\mathrm{H}}_2$ has been studied by measuring the outgoing kinetic energies of the ${\mathrm{H}}^{\mathrm{-}}{(1s}^2),$ with $\mathrm{H}\mathrm{}\left(\mathrm{nl}\right)\mathrm{}$ in $n=1\mathrm{}$ and 2 exit channels. The electron energies $E_e$ studied are 3–16 eV. Effects of vibration-rotation population in ${\mathrm{H}}_2$ are seen, and the DA results herein are modeled in terms of known cross sections for attachment from ${\mathrm{H}}_2{(v}^{″}{,J}^{″}).\mathrm{}$ Use is made of magnetically confined electron and ion beams with trochoidal deflection to measure outgoing ion energies.

Data and analysis for the ratio of double to single ionization of ${\mathrm{H}}^{-}$ in collisions with ${\mathrm{Ar}}^{q+}$ and ${\mathrm{Xe}}^{q+}$ are presented for $q=1\mathrm{}–6$. Evidence is found for effects of electron screening in ${\mathrm{Ar}}^{+1\mathrm{}}$ and ${\mathrm{Xe}}^{+1\mathrm{}}$. The data are analyzed in terms of both a Volkov-Keldysh approximation where the projectile field is strong compared to the target and a Born expansion in the electron projectile interaction where the projectile field is weak. At small $q/v$ the ${\mathrm{H}}^{-}$ data are consistent with the Born expansion while at lower energies a Volkov-Keldysh calculation is in agreement with observation if in both analyses correction for electron screening is included.