Adopting an approach similar to that of Zukowski [Phys. Rev. A 62, 032101 (2000)], we investigate connections between teleportation and nonlocality. We derive a Bell-type inequality pertaining to the teleportation scenario and show that it is violated in the case of teleportation using a perfect singlet. We also investigate teleportation using “Werner states” of the form $\alpha P_s+\left(1\mathrm{}-\alpha \right)I/4,$ where $P_s$ is the projector corresponding to a singlet state and $I$ is the identity. We find that our inequality is violated, implying nonlocality, if $\alpha >1/\sqrt{2}.$ In addition, we extend Werner’s local hidden variable model to simulation of teleportation with the $\alpha =\frac{1}{2}$ Werner state. Thus teleportation using this state does not involve nonlocality even though the fidelity achieved is $\frac{3}{4},$ which is greater than the “classical limit” of $\frac{2}{3}.$ Finally, we comment on a result of Gisin’s and offer some philosophical remarks on teleportation and nonlocality generally.

Bernstein and Varizani have given the first quantum algorithm to solve the parity problem in which a strong violation of the classical information theoretic bound comes about. In this paper we refine this algorithm with fewer resources and implement a two-qubit algorithm in a single query on an ensemble quantum computer.

The Hamiltonian for an arbitrary Coulomb three-body system is written in closed form in terms of nine generators of three independent o(2,1) algebras and its six physical parameters (i.e., three masses and three charges). Moreover, it is shown that such a Hamiltonian can also be written in the second quantized form by using six pairs of creation and annihilation (boson) operators. The obtained finite-term representation of the Coulomb three-body Hamiltonian in the second quantized form is exact, i.e., it is not based on any approximation. In particular, this means that the original Coulomb three-body problem can be reduced to the equivalent problem of three interacting, complex (i.e., charged) boson fields. The developed procedure opens new avenues in obtaining analytical and semianalytical (or highly accurate) solutions for various Coulomb three-body problems.

The photoionization cross sections of N-like Al VII are calculated from the first ionization threshold to 140 Ry using the R-matrix method. 14 target states (including 4 K-shell excited states) of Al VIII are included in the close-coupling calculation. The detailed structure and resonances of the cross sections across the L-shell and K-shell thresholds is described. The resonance energies and widths of some of the autoionization states are determined by analyzing the resonance structures. The results show that the autoionization width of the K-shell excited state of a $1s$ electron being excited into $2p$ orbital is the largest among all of the autoionization states. It is also larger than Doppler and Stark widths under a typical plasma condition. This result shows that the autoionization widths will have essential influence in simulating the x-ray transmission spectrum of Al plasma.

Optical parametric amplification is a process that leads to the generation of quantum states of light. In the limit of low single-pass gain, this process is often referred to as parametric down conversion, and produces entangled two-photon states. Such states have played a key role in recent studies of quantum optical effects such as quantum teleportation. As the gain of the parametric amplification process is increased, the generated light field still possesses strong quantum correlations, but not of the sort associated with two-photon states. Here we present an analysis of the output state of a parametric amplifier as a function of the single-pass gain, and we find certain signatures of quantum light (such as the vanishing of the coincidence rate in a Hong-Ou-Mandel interferometer) disappear in the high-gain limit, whereas others (such as the existence of two-photon interference fringes) remain. Consequently, the intense light field generated by a high-gain parametric amplifier can be utilized in such applications of quantum optics.

The time-resolved reflectivity of optical phase conjugation by stimulated Brillouin scattering (SBS) is investigated both theoretically and experimentally. A three-dimensional and transient model of SBS is developed to compare the experimental and theoretical results. Noise initiation of the SBS process is included in the model to simulate the shot-to-shot variation in the reflectivity and the Stokes temporal profile.

Starting from an expression for the critical temperature of a Bose gas trapped in power-law potentials in any-dimensional space, we obtain analytic expressions for the allowed maximum extensions of Bose-Einstein condensates in reduced space dimensions. It is shown that the allowed maximum thickness in two-dimensional space and the allowed maximum radius in one-dimensional space are both proportional to $1/\sqrt{m}.$

We show that a central ${1/r}^n$ singular potential (with $n>~2)$ is renormalized by a one-parameter square-well counterterm; low-energy observables are made independent of the square-well width by adjusting the square-well strength. We find a closed form expression for the renormalization-group evolution of the square-well counterterm.

We consider several problems that involve finding the eigenvalues and generating the eigenstates of unknown unitary gates. We first examine controlled-$U$ gates that act on qubits and assume that we know the eigenvalues. It is then shown how to use singlet states to produce qubits in the eigenstates of the gate. We then remove the assumption that we know the eigenvalues and show how to both find the eigenvalues and produce qubits in the eigenstates. Finally, we look at the case where the unitary operation acts on qutrits and it has two eigenvalues of $1$ and one of $-1.$ We are able to use a singlet state to produce a qutrit in the eigenstate corresponding to the $-1$ eigenvalue.

The quantum analogues of classical variable-length codes are indeterminate-length quantum codes, in which code words may exist in superpositions of different lengths. This paper explores some of their properties. The length observable for such codes is governed by a quantum version of the Kraft–McMillan inequality. Indeterminate-length quantum codes also provide an alternate approach to quantum data compression.

The central premise of density functional methods is that functionals of the electron density describe the properties of many-electron systems, including quantum effects such as electron exchange and correlation. In practice, such methods have demonstrated accuracies comparable to those of more computationally intensive quantum methods; however, they are limited by their demand of computational power. In this report we describe an alternative approach to constructing the initial electron density that serves as the starting point for density functional methods. In our method, the total density is constructed piecewise from fragments. Assuming that fragment densities can be computed efficiently, this leads to significant improvements in the overall calculation effort. We report results of calculations in several model systems.

A Hilbert-space multireference perturbation theory is presented to treat spin-dependent operators, and specifically formalism is derived for spin-orbit coupling. The zeroth-order states are obtained by diagonalizing the spin-free portion of the full Hamiltonian within a complete active space (CAS). The perturbation contains an additional spin-dependent term. A subset of the CAS self-consistent-field (CASSCF) states are permitted to mix via an effective Hamiltonian that is computed through the second order. The efficiency of the theory in capturing electron correlation and relativistic contributions is tested on a variety of systems, including atoms (C,Si,Ge,Os) and diatomic molecules (NiCl, PdCl, PtCl). The results are found to be very satisfactory. For example, the Os results reproduce the experimental results for the lowest levels within 1000 ${\mathrm{cm}}^{-1}$ and consistently good results for higher excited states.

We have performed an experiment in which a polarized electron beam ionizes an orbitally oriented and/or spin-polarized valence electron of sodium. The cross section for this reaction is measured for well-resolved vector momenta of the two electrons in the final channel. In order to study the transfer of the initial spin and orbital orientation from the electron-atom system to the final-state correlated electron pair, we develop a tensorial recoupling scheme in which the measured quantities are expressed in terms of independent, irreducible spherical tensor components. By this procedure the cross section is separated into terms characterized by their specific rotational transformation properties, decoupling of geometrical effects due to initial-state preparation from effects associated with details of the scattering dynamics is achieved, and exchange and orbital angular momentum transfer effects are disentangled. For a comparison with experiment we performed numerical ionization-cross section calculations within the distorted wave Born approximation and the dynamically screened three Coulomb waves theory. For some tensorial parameters significant discrepancies between theory and experiment are observed that underline the importance of the state-specific measurements as stringent tests of scattering theories.

The quenching processes of the thermalized orthopositronium $(o-\mathrm{Ps})$ on an oxygen molecule have been studied by the positron annihilation age-momentum correlation technique. The Doppler-broadening spectrum of the 511-kev $\gamma$ rays from the $2\gamma$ annihilation of $o-\mathrm{Ps}$ in ${\mathrm{O}}_2$ has been measured as a function of the $o-\mathrm{Ps}$ age. The rate of the quenching, consisting of the pickoff and the spin conversion, is estimated from the positron lifetime spectrum. The ratio of the pickoff quenching rate to the spin-conversion rate is deduced from the Doppler broadening of the 511-kev $\gamma$ rays from the annihilation of the $o-\mathrm{Ps}.$ The pickoff parameter ${}^1{Z}_{\mathrm{eff}},$ the effective number of the electrons per molecule that contribute to the pickoff quenching, for ${\mathrm{O}}_2$ is determined to be $0.6\pm \mathrm{0.4.}$ The cross section for the elastic spin-conversion quenching is determined to be $(1.16\mathrm{}\pm 0.01)\times {10}^{-19}\hspace{0.5em}{\mathrm{cm}}^2.$

The restriction imposed on the J-matrix method of using specific $L^2$ bases is lifted without compromising any of the advantages that it offers. This opens the door to a wider range of application of the method to physical problems beyond the restrictive SO(2,1) dynamical symmetry. The numerical scheme developed to achieve this objective projects the J-matrix formalism in terms of the eigenvalues of a finite-Hamiltonian matrix and its submatrices in any convenient $L^2$ basis. Numerical stability and convergence of the original analytic J-matrix method is still maintained in the proposed scheme, which can be applied to multichannel nonrelativistic as well as relativistic scattering problems.

Equilibrium geometric structures of ${\mathrm{Na}}_n\mathrm{Au}$ and ${\mathrm{Na}}_n\mathrm{Ag}$ $(n<~10)$ clusters are obtained by a pseudopotential approach within spin-polarized density-functional theory using the Becke-Perdew-Wang 1991 (BPW91) generalized gradient approximation for the exchange-correlation energy functional. The stability of these clusters is examined via the the analysis of the binding energy (BE) and second difference of energy. Properties related to the electronic structure such as the vertical ionization potential, electron affinity, energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, and the hardness are also determined. The BE is largest for the dimer in the ${\mathrm{Na}}_n\mathrm{Au}$ series and also has peaks for ${\mathrm{Na}}_7\mathrm{Au}$ and ${\mathrm{Na}}_9\mathrm{Au}.$ The NaAg dimer, ${\mathrm{Na}}_7\mathrm{Ag},$ and ${\mathrm{Na}}_9\mathrm{Ag}$ are also found to be more stable in the ${\mathrm{Na}}_n\mathrm{Ag}$ series. The vertical ionization potentials of ${\mathrm{Na}}_n\mathrm{Au}$ clusters are in good agreement with the available experimental data. The electronic structure of ${\mathrm{Na}}_n\mathrm{Au}$ clusters for $n=1,$ 7, and 9 shows that electronic shell closures are responsible for the high stability of these clusters.

The coupled dynamics of electrons and ions in sodium clusters under irradiation by strong femtosecond laser pulses is investigated within numerical simulations. Electrons are described with the self-consistent semiclassical Vlasov equation and ions are treated classically. The interplay between Coulomb forces and kinetic pressure in the dissociation process is analyzed. The transfer of energy from the electron to the ion system is also analyzed. We compare the ionization/excitation balance with that in peripheral collisions of clusters with highly charged ions.

Energy levels of the ${1s2l2l}^{\prime }{}^2{S}^e$ and ${}^{2,4}{P}^{e,o}$ states of the helium negative ion in magnetic-field strengths up to $4.7011\times {10}^4$ T are calculated by using the multiconfiguration interaction approach. The extended full core plus correlation (FCPC) method and the saddle-point technique are used to construct the nonrelativistic wave functions. We have observed that the field effects on the states considered are quite unusual. In the presence of a magnetic field, three previously unobserved stable states associated with the helium $1s2p{}^{1}P$ and $1s2s{}^{3}S$ thresholds are predicted. The possibility of attracting an extra electron by the parent ${1s}^2$ state is also analyzed in the low and medium regime $(\beta <~0.1$ a.u.). The opening of new decay channels of the ${1s2s}^2{}^{2}S$ resonance state connected with the higher threshold due to field effects is analyzed. Two significantly different resonance mechanisms for the ${1s2s}^2$ state are proposed and discussed briefly.

We study theoretically a generation of vortices by phase imprinting in trapped Bose-Einstein condensates. Phase imprinting is achieved by passing a short off-resonance laser pulse through an appropriately designed absorption plate, and impinging it on a condensate. We answer the fundamental question how the circulation and the vortex are introduced into the system. We discuss the possibility of multiple vortex arrays creation. Using multiple absorption plates we show that genuine vortex arrays and vortex-antivortex configurations can be created in a controlled way. We discuss vortex dynamics and interactions in such configurations. Various methods of vortex detection based on interference combined with Bragg scattering technique are also analyzed.