We introduce the entanglement gauge describing the combined effects of local operations and nonlocal unitary transformations on bipartite quantum systems. The entanglement gauge exploits the invariance of nonlocal properties for bipartite systems under local (gauge) transformations. This new formalism yields observable effects arising from the gauge geometry of the bipartite system. In particular, we propose a non-Abelian gauge theory realized via two separated spatial modes of the quantized electromagnetic field manipulated by linear optics. In this linear optical realization, a bipartite state of two separated spatial modes can acquire a non-Abelian geometric phase.

We study the phase-covariant quantum cloning machine for qudits, i.e., the input states in a d-level quantum system have complex coefficients with arbitrary phase but constant module. A cloning unitary transformation is proposed. After optimizing the fidelity between input state and single qudit reduced density operator of output state, we obtain the optimal fidelity for 1 to 2 phase-covariant quantum cloning of qudits and the corresponding cloning transformation.

Several teleportation protocols, namely those using entangled coherent states, entangled squeezed states, and the single-photon Einstein-Podolsky-Rosen state, are all shown to be particular instances of a more general scheme that relies on the detection of an odd number of photons.

We propose an experimentally feasible scheme to achieve quantum computation based on a pair of orthogonal cyclic states. In this scheme, quantum gates can be implemented based on the total phase accumulated in cyclic evolutions. In particular, geometric quantum computation may be achieved by eliminating the dynamic phase accumulated in the whole evolution. Therefore, both dynamic and geometric operations for quantum computation are workable in the present theory. Physical implementation of this set of gates is designed for NMR systems. Also interestingly, we show that a set of universal geometric quantum gates in NMR systems may be realized in one cycle by simply choosing specific parameters of the external rotating magnetic fields. In addition, we demonstrate explicitly a multiloop method to remove the dynamic phase in geometric quantum gates.

We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.

The formation and subsequent thermalization of positronium (Ps) produced at a few eV in gases are investigated using time-resolved Doppler-broadening measurements of the annihilation photons. A static magnetic field quenches the Ps enabling Doppler energy measurements from 25 to 70 ns after the Ps is formed. Varying the gas density permits a significant range of the thermalization process to be observed. Seven different gases are studied, He, Ne, Ar, ${\mathrm{H}}_2,$ ${\mathrm{N}}_2,$ isobutane, and neopentane. A classical elastic scattering model fits all the gas data reasonably well. For each gas, an elastic scattering cross section and an average Ps formation energy are determined from the classical model fit. When comparisons can be made, these cross sections are often significantly smaller than most quantum-mechanical-theory predictions and most previous experimental results obtained using the angular correlation technique. Various systematic tests have been applied to the apparatus and the analysis, reinforcing the discrepancy with previous works.

Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a three-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of ${}^4\mathrm{He}$ atoms. We also extend Efimov’s theory to include the effects of deep two-body bound states, which give widths to the Efimov states.

The most probable structure of protonated acetylene ${\mathrm{C}}_2{\mathrm{H}}_3^{+}$ (the “vinyl cation”) is inferred from both Coulomb-explosion experiments and finite-temperature ab initio quantum simulations followed by simulations of foil effects. It is found that ${\mathrm{C}}_2{\mathrm{H}}_3^{+}$ features significant deviations from the planar bridged equilibrium structure as well as from the planar Y-shaped local minimum structure, which are known from static electronic structure calculations. In particular, the “axial protons” feature a significant out-of-plane trans-bending due to fluctuation effects. This implies that the nonplanarity has to be taken into account in theoretical treatments that aim at describing this fluxional molecule.

In this paper, we introduce a finite-space integration method to shed physical insight into the interactions of a Rydberg electron with a molecular ion core, as sampled by the potential-energy curves (PECs) of various electronic states of LiH. We postulate that these interactions are dominated by two independent electron-atom processes: (1) scattering of the Rydberg electron at negative energy solely off of the lithium atomic core and (2) a transition from the lithium scattering state to the lithium valence orbital necessarily accompanied by an excitation of the hydrogen atom. It is shown that the ratio of the amplitudes for the occurrences of these two processes can be obtained by means of bounded integrations inside a small region of space where the electron-electron repulsion term in the Hamiltonian is dominant. Our theory and approximations are verified by a comparison of derived potential-energy curves with those produced by ab initio calculations as well as another empirical model that uses the Fermi approximation. It is observed that the complicated features of the PECs, which reflect the nodal structure of the Rydberg orbitals, are reproduced well within our treatment.

The ionization energy of ${}^{160}\mathrm{Gd}$ has been determined using high-resolution laser excitation on an effusive Gd atomic beam. Even-parity $J=5,6\mathrm{}\mathrm{Rydberg}$ series were excited by three single-frequency lasers. Despite the complex electronic structure of Gd, sequences of relatively unperturbed levels were observed in the ranges $n=50\mathrm{}–79$ and 87–120. After correcting for weak perturbations, the convergence of several Rydberg series has an uncertainty of $6\times {10}^{-4}{\mathrm{cm}}^{-1}.$ The final value of $49601.5142\left(8\right)\mathrm{}{\mathrm{cm}}^{-1}$ includes cumulative uncertainty in absolute laser wave numbers for the ladder of transitions coupling the Rydberg spectrum to the $J=2\mathrm{}$ ground state.

Moshinsky introduced an exactly soluble model of a two-electron atom consisting of two spin-$\frac{1}{2}$ particles interacting via harmonic forces and moving in a harmonic-oscillator potential. Here, the exact ground-state density $\rho \mathrm{}\left(r\right)\mathrm{}$ is related to the (also analytically known) Hartree-Fock density ${\rho }_{\mathrm{HF}}\mathrm{}\left(r\right).$ The generalization to the off-diagonal matrix $\gamma (\mathbf{r},{\mathbf{r}}^{\prime })$ is then effected, this being related to the idempotent ${\gamma }_{\mathrm{HF}}(\mathbf{r},{\mathbf{r}}^{\prime })/2.\mathrm{}$ This exact information on this “model atom” prompts us to propose an approximate form of $\gamma (\mathbf{r},{\mathbf{r}}^{\prime })$ for the He-like ions, the ${\mathrm{H}}_2$ molecule and, in general, all two-electron systems. $\gamma (\mathbf{r},{\mathbf{r}}^{\prime })$ is constructed solely from the exact $\rho \left(\mathbf{r}\right)$ and its Hartree-Fock counterpart. Some detailed treatment of the two-electron Hookean atom with spring constant $k=1/4\mathrm{}$ (atomic units) is also presented.

The variation with excitation energy of the line shapes of the Cu $K{\alpha }_{1,2}$ x-ray spectrum was measured with high energy resolution near the K-shell threshold. Fits with ab initio Dirac-Fock calculated spectra allow us to estimate separately the magnitudes and energy variations of the $3d$ electron shakeup and shakeoff probabilities from threshold to saturation. The Thomas model is found to account well for the intensity evolution, in contrast with shakeoff from deeper shells. A suggested, yet unexplained, strong dependence of the shakeoff intensity saturation range on the shell number is confirmed.

We analyzed radial and angular correlations of 50 ${2l2l}^{\prime }{3l}^{″}$ triply excited states of atoms. Using hyperspherical coordinates, we examined channel wave functions in the body-fixed frame to identify elementary normal modes of the correlated motion of the three electrons. For these states, we showed that the bending vibrational modes characterizing the angular correlations are the same as those in ${2l2l}^{\prime }{2l}^{″}$ and ${3l3l}^{\prime }{3l}^{″}$ intrashell states, but additional “$+$” or “$-$” quantum numbers are needed to distinguish the symmetric or antisymmetric stretch of the outer electron with respect to the two inner ones for the ${2l2l}^{\prime }{3l}^{″}$ intershell states.

The radiative correction to hyperfine splitting in hydrogen is dominated by the Schwinger term, $\alpha /2\mathrm{}\pi E_F,$ where $E_F$ is the lowest-order hyperfine splitting. Binding corrections to this term, which enter as powers and logarithms of $Z\alpha ,$ can be expected to be increasingly important in atoms with higher nuclear charge Z. Methods that include all orders of $Z\alpha ,$ developed first to study highly charged ions, are adapted to the study of the neutral alkali metals, lithium through francium. It is shown that the use of the Schwinger term alone to account for radiative corrections to hyperfine splittings becomes qualitatively incorrect for the heavier alkali metals.

We describe single and double photoionization of two-electron atoms by photoabsorption at high incident photon energies $\omega$ (but still $\omega \ll {\mathrm{mc}}^2)$ using a unified approach based on asymptotic Fourier transform (AFT) theory modified by Coulombic interactions. Within this approach the matrix elements for photoabsorption processes at high energies can be understood in terms of the singularities of the many-body Coulomb potential. These singularities $(e-e$ and $e-N)$ result in the singularities of the wave functions and the singularities of the $e-\gamma$ interaction, which determine the asymptotic behavior of the matrix element. Within our unified approach we explain the dominant contributions, including both the dominant contributions to the total cross section for single ionization and for ionization with excitation, and the dominant contributions to the double ionization spectrum, as a Fourier transform asymptotic in a single large momentum (dependent on the process and the region of the spectrum). These dominant contributions are connected, through AFT, with either the $e-N$ singularity or the $e-e$ singularity. The AFT results are modified by Coulombic interactions. We include these modifications, for the cases of single ionization and of double ionization in the shake-off region at high energies, and extract a slowly convergent factor (Stobbe factor). In this way we obtain rapid convergence of the cross sections to their high-energy behaviors. This also allows us to discuss the convergence of ratios of cross sections.

We describe single photoionization of excited states of two-electron atoms by photoabsorption at high incident photon energies $\omega$ (but still $\omega \ll m).\mathrm{}$ Our description of photoionization from excited states of the simplest many-body system is also, however, applicable for the characterization of high-energy photoionization of a many-electron atom from any subshell. We are using an approach [Surić et al., Phys. Rev. A 67, 022709 (2003)] based on asymptotic Fourier-transform (AFT) theory, in which the matrix elements for photoabsorption processes at high energies are understood in terms of the singularities of the many-body Coulomb potential. We obtain the dependence of the total cross section for single ionization of a two-electron atom in any initial state on photon energy. This energy dependence, for a general initial two-electron state, is generally different from the predictions of independent-particle approximation, and it is in qualitative agreement with recent experimental observations of L-shell photoionization in Ne and M-shell ionization in Ar. As in ground-state ionization, the energy dependence of the dominant contribution to the matrix element is connected, through AFT, with the $e-N$ singularity; and it is determined by the amplitude of the lowest angular momentum $l_{\min }$ with which one electron can approach the $e-N$ singularity. When $l_{\min }=0,$ as in the cases considered experimentally, this gives a factor for the dominant part of the total cross section, which is the same as for the ground state, $(1/{\omega }^{7/2}).\mathrm{}$ The final state interaction reduces this energy dependence by just one additional factor of $1/\omega .$

Inverting experimental data provides a powerful technique for obtaining information about molecular Hamiltonians. However, rigorously quantifying how laboratory error propagates through the inversion algorithm has always presented a challenge. In this paper, we develop an inversion algorithm that realistically treats experimental error. It propagates the distribution of observed laboratory measurements into a family of Hamiltonians that are statistically consistent with the distribution of the data. This algorithm is built upon the formalism of map-facilitated inversion to alleviate computational expense and permit the use of powerful nonlinear optimization algorithms. Its capabilities are demonstrated by identifying inversion families for the $X{}^1{\Sigma }_g^{+}$ and $a{}^3{\Sigma }_u^{+}$ states of ${\mathrm{Na}}_2$ that are consistent with the laboratory data.

The single ionization of helium by antiproton impact has been studied utilizing a fully correlated, planar model in which the time-dependent Schrödinger equation was solved on a four-dimensional (4D) Cartesian lattice. The choice of a “softcore” Coulomb potential was shown to enable approximate reproduction of the full six-dimensional $\overline{p}\mathrm{He}$ adiabatic electronic eigenenergy curves in the dynamically important region of the 4D space, thus providing a reasonable model to treat $\overline{p}+\mathrm{He}$ collisions. In addition, the applicability of this approach was demonstrated by favorable comparison of analogous two-dimensional lattice solutions for ionization of atomic hydrogen by antiprotons with previously computed three-dimensional lattice results. The present work aids in the interpretation of existing theoretical and experimental studies considering the low-energy behavior of the single-ionization cross section for antiproton impact of few-electron targets and explores the applicability of the planar model in describing correlated two-electron systems.

An interference quenching of the $m=1\mathrm{}$ final state vibrational line in the resonant Auger decay of $N1\overrightarrow{s}{\pi }^{*}$ core-excited $N_2$ is observed and analyzed. The intensity ratio between the $m=1\mathrm{}$ and $m=0\mathrm{}$ vibrational levels of the $X{}^2{\Sigma }_g^{+}$ final state shows a surprising nonmonotonic variation as a function of frequency detuning, going through a minimum with a complete suppression of $m=1.\mathrm{}$ We have developed a simple model which indicates a linear relation between the value of the detuning frequency for this minimum and the equilibrium bond distance of the core-excited state. This implies the possibility of determining the equilibrium bond distances for core-excited states to a high degree of accuracy. Simultaneously with the simple model we present a strict theory of the studied effect. This strict theory allows us to explore the accuracy of determining the bond length of the core-excited state from resonant Auger spectra. We obtain a weak influence of the core-hole lifetime on the determined bond length, whereas the number of intermediate vibrational states accounted for in the numerical simulations seems to be quite important.

Different lifetime broadenings in molecular-field-split $2p$ core levels in ${\mathrm{H}}_2\mathrm{S}$ are predicted theoretically and are identified in an experimental investigation of the $\mathrm{S}2p$ Auger electron spectrum. The measurements were performed for the transition to the vibrationally resolved $X^1{A}_1$ ground state of ${\mathrm{H}}_2{\mathrm{S}}^{2+}.$ The lifetimes of the ${3e}_{1/2}$ and ${5e}_{1/2}$ levels of the $2p$ ionized molecule are found to be 64 and 74 meV, respectively. This unambiguous determination of the lifetime difference of $10\pm 1\mathrm{meV}$ is only possible as the ${4e}_{1/2}\to X^1{A}_1{(2b}_1^{-2})$ decay channel that overlaps the ${5e}_{1/2}\to X^1{A}_1{(2b}_1^{-2})$ channel is practically suppressed in Auger decay in ${\mathrm{H}}_2\mathrm{S}.$ The lifetime difference is confirmed by ab initio calculations. A theoretical analysis shows that it results from the mutual orientation of the core hole in the intermediate states and the valence electron density in the sulfur $3p$ orbitals. Both are strongly influenced by the chemical bond. Thus the observed effect is the direct result of a fundamental property of molecular electronic structure.