The energies, effective quantum numbers, classifications, and configuration mixings of the triply excited states of lithium in the energy range of 140–160 eV above the ground state are described in detail based on calculations using the truncated diagonalization method. A total of 30 Rydberg series with symmetries ${}^2{S}^o,{\hspace{0.5em}}^2{S}^e,{\hspace{0.5em}}^2{P}^o,{\hspace{0.5em}}^2{P}^e,$ and ${}^2{D}^e$ are investigated. The perturbation of a Rydberg series by an isolated state, or by another series, is examined and discussed. Differences in the literature on the designation of certain states are pointed out, and our results are compared with recent theoretical and experimental data. We observe that the configuration interactions previously described for two-electron systems [i.e., the mixing of the ${\mathrm{}\left(2s\right)\mathrm{}}^2$ and ${\mathrm{}\left(2p\right)\mathrm{}}^2{}^1{S}^e$ states] remain when a third electron is added.

A a procedure is proposed by which, in the course of an iterative solution of the second-order contracted Schrödinger equation, The N representability of the second-order reduced density matrix can be tested with increasing stringency. This procedure was suggested by an extended study of the G conditions and from the contraction into the two-electron space of an N-fermion relation, expressing in matrix form the antisymmetry and normalization properties of the N-electron wave function. Several relations are reported.

Photoionization excitation of helium has been performed employing the R-matrix method with a 20-term target representation for incident photon energies between the $N=2\mathrm{}$ and $N=5\mathrm{}$ thresholds (69–76.8 eV) of the ${\mathrm{He}}^{+}$ ion. Partial differential cross sections for photoionization leaving the ${\mathrm{He}}^{+}$ ion in the $N=2,3,4\mathrm{}$ levels at emission angles $0°$ and in the $N=2\mathrm{}$ level $90°$ are provided. Our results to ${\mathrm{He}}^{+}$ in the $N=2\mathrm{}$ state give fairly good agreement with the available experimental data and theoretical calculations below the $N=3\mathrm{}$ threshold. Between the $N=3\mathrm{}$ and $N=5\mathrm{}$ thresholds of the ${\mathrm{He}}^{+}$ ion, our results for ${\mathrm{He}}^{+}$ in the $N=2,3,4\mathrm{}$ states still agree with experiment qualitatively.

The double-differential cross section $d^2\sigma /d\Omega \mathrm{dE}$ for Compton backscattering in germanium was measured at the photon energy of 86.5 keV. The experimental setup with two high-purity germanium detectors operating in the coincidence mode was applied. A multiline radioactive source of ${}_{63}^{155}\mathrm{Eu}$ was used as the source of photons. The Compton spectrum with a very small background was obtained. A fast cascade was found to little influence the data due to the 86.5 keV crossover transition. The contribution of a group of processes, which is described as double cross talk between the two detectors, was also studied and results of calculations show their weak intensity. The calculations of other processes were made as in our earlier papers. The values of $d^2\sigma /d\Omega \mathrm{dE}$ were determined to an accuracy of better than 4% on an absolute scale in a broad energy region. The calculated values using the impulse approximation with hydrogenlike wave functions do not reproduce well the cross sections in some energy regions.

We consider the quantized motion of neutral atoms at very low temperature in a two-dimensional magnetic quadrupole structure formed, for example, by four current-carrying wires along the z direction. The magnetic field $\mathbf{B}$ in the guide is proportional to the vector $(x,-y).\mathrm{}$ We show that this field can be used to make a single-mode atomic de Broglie waveguide which has bound states of low angular momentum, even though the field at the center of the guide goes to zero. We investigate the spectrum and decay rate of the transverse modes for spin-1/2 and spin-1 atoms.

We present an experimental and theoretical investigation of the quantum control of ground-state rotational coherence in a linear molecule. A sequence of two temporally separated laser pulses creates a rotational superposition state in ${\mathrm{CO}}_2$ whose evolution is monitored through a polarization technique. We study the influence of the phase difference between the two pulses. We show that the overlapping of the two wave packets, produced by each pulse, gives rise to quantum interference that affects the orientational anisotropy of the sample. Because of the large number of coherently excited levels, the interference produces well-separated temporal structures, whose magnitude can be controlled through the relative delay of the two pulses.

A linear stability analysis of the Lorenz-laser equations taking into account the local field correction is presented. It is demonstrated that this correction lowers the second laser threshold for negative detunings.

We compare the time evolution of the quantum-mechanical spatial probability density obtained by solving the time-dependent Dirac equation with its classical counterpart obtained from the relativistic Liouville equation for the phase-space density in a regime in which the dynamics is essentially relativistic. For a resonantly driven one-dimensional harmonic oscillator, the simplest nontrivial model system to perform this comparison, we find that, despite the nonlinearity induced by relativity, the classical ensemble description matches the quantum evolution remarkably well.

Exact analytic solutions of the time-dependent Schrödinger equation are produced that exhibit a variety of vortex structures. The qualitative analysis of the motion of vortex lines is presented and various types of vortex behavior are identified. Vortex creation and annihilation and vortex interactions are illustrated in the special cases of the free motion, the motion in the harmonic potential, and in the constant magnetic field. Similar analysis of the vortex motions is carried out also for a relativistic wave equation.

I construct a secure multiparty scheme to compute a classical function by a succinct use of a specially designed fault-tolerant random polynomial quantum error correction code. This scheme is secure provided that (asymptotically) strictly more than five-sixths of the players are honest. Moreover, the security of this scheme follows directly from the theory of quantum error correcting code, and hence is valid without any computational assumption. I also discuss the quantum-classical complexity-security tradeoff in secure multiparty computation schemes and argue why a full-blown quantum code is necessary in my scheme.

We demonstrate superadditivity in the communication capacity of a binary alphabet consisting of two nonorthogonal quantum states. For this scheme, collective decoding is performed two transmissions at a time. This improves upon the previous schemes of Sasaki et al. [Phys. Rev. A 58, 146 (1998)] where superadditivity was not achieved until a decoding of three or more transmissions at a time. This places superadditivity within the regime of a near-term laboratory demonstration. We propose an experimental test based upon an alphabet of low photon-number coherent states where the signal decoding is done with atomic state measurements on a single atom in a high-finesse optical cavity.

One limit to the fidelity of quantum logic operations on trapped ions arises from heating of the ions’ collective modes of motion. Sympathetic cooling of the ions during the logic operations may eliminate this source of errors. We discuss the benefits and drawbacks of this proposal, and describe possible experimental implementations. We also present an overview of trapped-ion dynamics in this scheme.

We present a generalization of quantum teleportation that distributes quantum information from a sender’s d-level particle to $N_o$ particles held by remote receivers via an initially shared multiparticle entangled state. This entangled state functions as a multiparty quantum information distribution channel between the sender and the receivers. The structure of the distribution channel determines how quantum information is processed. Our generalized teleportation scheme allows multiple receivers at arbitrary locations, and can be used for applications such as optimal quantum information broadcasting, asymmetric telecloning, and quantum error correction.

We present a general method which expresses a unitary operator by the product of operators allowed by the Hamiltonian of spin-1/2 systems. In this method, the generator of an operator is found first, and then the generator is expanded by the base operators of the product operator formalism. Finally, the base operators disallowed by the Hamiltonian, including more than two-body interaction operators, are replaced by allowed ones by the axes transformation and coupling order reduction technique. This method directly provides pulse sequences for the nuclear magnetic resonance quantum computer, and can be generally applied to other systems.

For the rearrangement process $d\mu {(n}_i)+\overrightarrow{t}d+t\mu {(n}_f),$ results of high-precision numerical calculations for the zero total orbital momentum of the system are compared with those obtained from the analytical Demkov model. The latter is widely used in atomic collision theory to describe rearrangement processes with small energy defects. A specific feature of the studied system is that the energy defect has a purely isotopic nature. Muon transfer within the $n_i{=n}_f=1\mathrm{}$ and $n_i{=n}_f=2\mathrm{}$ manifolds is analyzed. In the latter case the natural reaction channels correspond to Stark states in the limit of separated atoms. Efficient transitions occur between Stark states with the muon cloud stretched toward (opposite to) the collision partner both in the initial and final states. An overall good agreement with accurate results sustains the relevance of the Demkov model for the studied process, and clarifies the reaction mechanisms. The interference effects strongly suppress the reaction probability within the $n_i{=n}_f=1\mathrm{}$ manifold, and enhance it for $n_i{=n}_f=2.\mathrm{}$ Some intriguing although yet unexplained features of the interference phases are revealed and discussed: they are almost energy independent and close to integer multiples of $\frac{1}{2}\pi .$

Accurate measurements, within 2%, of K radiation emission cross sections were carried out on thick foils of ${}^{64}\mathrm{Gd},$ ${}^{66}\mathrm{Dy},$ and ${}^{68}\mathrm{Er}$ stimulated by 59.54-keV photons, i.e., an energy close to the K thresholds of the target atoms. The results obtained provide a good global reference test for the relativistic quantum-mechanic models used in the calculations of K fluorescence yields and K vacancy creation cross sections.

The scattering cross section associated with a two-dimensional δ function has recently been the object of considerable study. It is shown here that this problem can be put into a field theoretical framework by the construction of an appropriate Galilean covariant theory. The Lee model with a standard Yukawa interaction is shown to provide such a realization. The usual results for δ-function scattering are then obtained in the case that a stable particle exists in the scattering channel provided that a certain limit is taken in the relevant parameter space. In the more general case in which no such limit is taken finite corrections to the cross section are obtained which (unlike the pure δ function case) depend on the coupling constant of the model.

An approach to bound and resonant states in scattering by a central potential $\mathrm{gV}\left(r\right),\hspace{0.5em}g\in C,$ based on a global analysis of S-matrix poles, is presented. The global method involves the construction of the Riemann surface $R_g^{\mathrm{}\left(l\right)\mathrm{}}$ over the g plane on which the pole function ${k=k}^{\mathrm{}\left(l\right)\mathrm{}}\mathrm{}\left(g\right)\mathrm{}$ is single valued and analytic. This implies the division of the Riemann surface $R_g^{\mathrm{}\left(l\right)\mathrm{}}$ into sheets and the construction of the Riemann sheets images in the k plane. By keeping the sheets of the Riemann surface apart, the single pole laying on each sheet image in the k plane is identified. With each state $\mathrm{}(l,n)\mathrm{}$ of the quantum system one associates a sheet ${\Sigma }_n^{\mathrm{}\left(l\right)\mathrm{}}$ of the Riemann surface $R_g^{\mathrm{}\left(l\right)\mathrm{}}.$ A new quantum number n with a topological meaning is introduced in order to label a pole and the corresponding state $\mathrm{}(l,n).$ All S-matrix poles for a central rectangular potential $\mathrm{gV}\left(r\right),$ with $l=0,$ 1, 2, 3, and 4, are analyzed by using the global method. A new class of resonant state poles, having unusual properties, is identified. The properties of these resonant state poles (exotic poles) and of the corresponding resonant states are studied. A new type of resonance in the cross section, associated with the cooperative contribution from three adjacent partial waves and due to the local degeneracy with respect to l, is discussed.

The emergent-angle-dependent charge-state fractions of 2-MeV ${}^4\mathrm{He}$ transmitted in a carbon foil of 2.5 μ${\mathrm{g}/\mathrm{c}\mathrm{m}}^2$ in thickness have been measured in the range from 0 to 8 mrad. The angular distribution due to multiple scattering has been also obtained for each outgoing charge state. Up to the angle of ∼4 mrad, both the neutral and singly charged fractions increase with increasing the emergent angle. This trend is more remarkable in the neutral fraction. At the larger angles, these fractions reach saturated values. The observed behavior can be explained qualitatively by the impact parameter dependence of the charge-exchange probabilities. Although a Monte Carlo simulation can reproduce the obtained angle-dependent charge-state fractions, it gives a slightly narrower angular distribution due to multiple scattering for each outgoing charge state.

The mechanisms of neutral dissociation of oxygen molecules in the excitation energy range 15–25 eV have been studied in a dispersed fluorescence experiment. By detecting the fluorescence from excited oxygen atoms, we find that neutral superexcited ${\mathrm{O}}_2$ states below 20 eV dissociate into $\mathrm{O}(\mathrm{g}.\mathrm{s}.\mathrm{})\mathrm{}+\mathrm{O}\mathrm{}(3s,3p).$ At higher excitation energies $(\mathrm{h}\nu =20\mathrm{}–25\mathrm{eV})$ the curve-crossing interactions following excitations to members of the Rydberg $c{}^4{\Sigma }_u^{-}$ series also yield atoms in Rydberg states $(nl,n>~4).$ The experimental data are analyzed on the ground of many-body perturbation theory, calculations which indicate the structure of the predissociating states converging to the experimentally observed ones.