Motivated by the ideas of using cold alkaline-earth atoms trapped in an optical lattice for realization of optical atomic clocks, we investigate theoretically the perturbative effects of atom-atom interactions on a clock transition frequency. These interactions are mediated by the dipole fields associated with the optically excited atoms. We predict resonancelike features in the frequency shifts when constructive interference among atomic dipoles occur. We theoretically demonstrate that by fine tuning the coherent dipole-dipole couplings in appropriately designed lattice geometries, the undesirable frequency shifts can be greatly suppressed.

In this paper, a four-photon entangled state obtained directly from the down-conversion of a two-crystal geometry is analyzed. These two identically cut type-I crystals are oriented with their optic axes aligned in perpendicular planes. The applications of this kind of four-photon entangled state are also discussed.

The magnetic moment of a particle orbiting a straight current-carrying wire may precess rapidly enough in the wire’s magnetic field to justify an adiabatic approximation, eliminating the rapid time dependence of the magnetic moment and leaving only the particle position as a slow degree of freedom. To zeroth order in the adiabatic expansion, the orbits of the particle in the plane perpendicular to the wire are Keplerian ellipses. Higher-order postadiabatic corrections make the orbits precess, but recent analysis of this “vector Kepler problem” has shown that the effective Hamiltonian incorporating a postadiabatic scalar potential (“geometric electromagnetism”) fails to predict the precession correctly, while a heuristic alternative succeeds. In this paper we resolve the apparent failure of the postadiabatic approximation, by pointing out that the correct second-order analysis produces a third Hamiltonian, in which geometric electromagnetism is supplemented by a tensor potential. The heuristic Hamiltonian of Schmiedmayer and Scrinzi is then shown to be a canonical transformation of the correct adiabatic Hamiltonian, to second order. The transformation has the important advantage of removing a ${1/r}^3$ singularity which is an artifact of the adiabatic approximation.

The quantitative formulation of Bohr’s complementarity proposed by Greenberger and Yasin is applied to some physical situations for which analytical expressions are available. This includes a variety of conventional double-slit experiments, but also particle oscillations, as in the case of the neutral-kaon system, and Mott scattering of identical nuclei. For all these cases, a unified description can be achieved including a new parameter $\nu ,$ which quantifies the effective number of fringes one can observe in each specific interferometric setup.

Radiative corrections to the decay rate of $n=2\mathrm{}$ states of hydrogenic ions are calculated. The transitions considered are the $M1\mathrm{}$ decay of the $2s$ state to the ground state and the $E1\mathrm{}\left(M2\mathrm{}\right)\mathrm{}$ decays of the ${2p}_{1/2}$ and ${2p}_{3/2}$ states to the ground state. The radiative corrections start in order $\alpha (Z\alpha {)}^2,$ but the method used sums all orders of $Z\alpha .$ The leading $\alpha (Z\alpha {)}^2$ correction for the $E1\mathrm{}$ decays is calculated and compared with the exact result. The extension of the calculational method to parity nonconserving transitions in neutral atoms is discussed.

For one-qubit systems, we present a short, elementary argument characterizing unital quantum operators in terms of their action on Bloch vectors. We then show how our approach generalizes to multiqubit systems, obtaining inequalities that govern when a “diagonal” superoperator on the Bloch region is a quantum operator. These inequalities are the n-qubit analog of the Algoet-Fujiwara conditions. Our work is facilitated by an analysis of operator-sum decompositions in which negative summands are allowed.

Optimized probabilistic teleportation and remote symmetric entangling of an arbitrary logical qubit are studied using particular forms of W-type entangled coherent states. Of interest is the fact that, while the teleportation can alternatively be performed by the GHZ-type entangled coherent states, the remote symmetric entangling strictly requires those of the W type.

A finite-field scaling method is applied to evaluate the Lennard-Jones interaction constant $C_3$ for alkali-metal atoms. The calculations are based on the relativistic single-double approximation in which single and double excitations of Dirac-Hartree-Fock wave functions are included to all orders in perturbation theory.

Absolute doubly differential cross sections for the ionization of atomic hydrogen by electron impact have been measured at energies ranging from near threshold to intermediate values. The measurements are normalized to the accurate differential cross section for the electron-impact excitation of the H $1{}^2\overrightarrow{S}2{}^{2}S+2\mathrm{}{}^{2}P$ transition. These measurements were made possible through the use of a moveable target source which enables the collection of hydrogen energy loss spectra free of all backgrounds. The measurements cover the incident electron energy range of 14.6–40 eV and scattering angles from $12°$ to $127°,$ and are in very good agreement with the results of the latest theoretical models—the convergent close-coupling model and the exterior complex scaling model.

We present measurements of differential cross sections for elastic electron scattering from atomic hydrogen at 20 eV and 40 eV incident electron energies and ratios of differential cross sections for electron-impact excitation of atomic hydrogen to the $n=2,$ 3, and 4 levels at incident electron energies of 14.6 eV, 15.6 eV, 17.6 eV, 20 eV, 25 eV, and 40 eV with scattering angles ranging from $10°$ to $130°.$ We compare our results to available experimental measurements and recent convergent close-coupling calculations. Our results resolve significant discrepancies that existed between theory and past experiments.

We consider several observers who monitor different parts of the environment of a single quantum system and use their data to deduce its state. We derive a set of conditional stochastic master equations that describe the evolution of the density matrices each observer ascribes to the system under the Markov approximation, and show that this problem can be reduced to the case of a single “superobserver,” who has access to all the acquired data. The key problem—consistency of the sets of data acquired by different observers—is then reduced to the probability that a given combination of data sets will be ever detected by the superobserver. The resulting conditional master equations are applied to several physical examples: homodyne detection of phonons in quantum Brownian motion, photodetection and homodyne detection of resonance fluorescence from a two-level atom. We introduce relative purity to quantify the correlations between the information about the system gathered by different observers from their measurements of the environment. We find that observers gain the most information about the state of the system and they agree the most about it when they measure the environment observables with eigenstates most closely correlated with the optimally predictable pointer basis of the system.

A geometrical method to calculate the Maslov index, which is an important part of the quantum phase, is proposed. This method is particularly useful for the recently proposed amplitude-free quasicorrelation function approach for the quantization of chaos [K. Hotta and K. Takatsuka, J. Phys. A 36, 4785 (2003)]. In this theory the Maslov index is involved with no need to calculate the amplitude factor, which is usually obtained through integration of the stability matrix. Since this matrix constitutes the major origin of difficulty in semiclassical quantization of chaos and since its integration is time consuming, the present method, which avoids the stability matrix, should assist in opening a gate for practical semiclassical quantization of chaos in a large molecular system.

We present many ensembles of states that can be remotely prepared by using minimum classical bits from Alice to Bob and their previously shared entangled state and prove that we have found all the ensembles in two-dimensional case. Furthermore we show that any pure quantum state can be remotely and faithfully prepared by using finite classical bits from Alice to Bob and their previously shared nonmaximally entangled state though no faithful quantum teleportation protocols can be achieved by using a nonmaximally entangled state.

Entanglement sharing among pairs of spins in Heisenberg antiferromagnets is investigated using the concurrence measure. For a nondegenerate $S=0\mathrm{}$ ground state, a simple formula relates the concurrence to the diagonal correlation function. The concurrence length is seen to be extremely short. Various finite clusters are studied numerically, to see the trend in two dimensions. It is argued that the concurrences vanish between pairs of spins which are not nearest neighbors for the linear-chain and square-lattice antiferromagnet ground states. For the triangular lattice and Kagome’ lattice, nearest-neighbor concurrences also vanish. The concurrences in the maximal-spin states are explicitly calculated, where the concurrence averaged over all pairs is larger than the $S=0\mathrm{}$ states.

Motivated by the Peres-Horodecki criterion and the realignment criterion we develop a more powerful method to identify entangled states for any bipartite system through a universal construction of the witness operator. The method also gives a new family of positive but noncompletely positive maps of arbitrary high dimensions, which provide a much better test than the witness operators themselves. Moreover, we find that there are two types of positive maps that can detect $2\times N$ and $4\times N$ bound entangled states. Since entanglement witnesses are physical observables and may be measured locally our construction could be of great significance for future experiments.

We describe a broad dynamical-algebraic framework for analyzing the quantum control properties of a set of naturally available interactions. General conditions under which universal control is achieved over a set of subspaces/subsystems are found in terms of the representation theory of the group ${\mathcal{U}}_A$ of allowed quantum evolutions. In some cases universal control can be achieved in all the state-space sectors carrying an irreducible action of ${\mathcal{U}}_A.$ All known physical examples of universal control on subspaces/systems are related to the framework developed here. Implications for quantum-information processing are discussed.

An experiment has been performed at the Gesellschaft für Schwerionenforschung accelerator facility using a beam-foil time-of-flight technique with a newly developed chemical vapor deposition diamond particle detector to measure the lifetime of the $2{}^3{P}_0$ state, $\tau \left(2\mathrm{}{}^3{P}_0\right),$ of the two-electron ion ${}^{197}{\mathrm{Au}}^{77+}$ (He-like gold) with the result $\tau \left(2\mathrm{}{}^3{P}_0\right)=22.16\mathrm{}\left(0.81\right)\mathrm{}$ ps. The mechanism for the decay of this state is by a hyperfine-induced radiative transition to the $1{}^1{S}_0$ ground state (hyperfine quenching). The lifetime is therefore determined by a number of fundamental atomic and nuclear parameters not normally involved in radiative decay of allowed transitions. The experimental result is compared to several theoretical calculations.

The correction of order $1/\omega$ to the high-energy total $e^{+}{e}^{-}$ photoproduction cross section in the electric field of a heavy atom is derived with the exact account of this field; $\omega$ is the photon energy. The consideration is based on the use of the quasiclassical electron Green’s function in an external electric field. The next-to-leading correction to the cross section is discussed. The influence of screening on the Coulomb corrections is examined in the leading approximation. It turns out that the corresponding correction to the high-energy total cross section is $\omega$ independent. In the region where both produced particles are relativistic, the corrections to the high-energy asymptotics of the electron (positron) spectrum are derived. Our results for the total cross section are in good agreement with experimental data for photon energies down to a few MeV. In addition, the corrections to the bremsstrahlung spectrum are obtained from the corresponding results for pair production.

Local quantities which describe correlations in position and momentum and also uncertainties (noise) in position and momentum are introduced. They obey uncertainty relations, which forbid both local correlations and local uncertainties to be small at the same time. Examples which elucidate the meaning of these quantities are discussed.

We have found conditions required to achieve complete population transfer, via coherent population trapping, from an initial state to a designated final state at a designated time in a degenerate three-state atom, where transitions are caused by an external interaction. Complete population transfer from an initially occupied state one to a designated state two occurs under two conditions. First, there is a constraint on the ratios of the transition matrix elements of the external interaction. Second, there is a constraint on the action integral over the interaction, or “area,” corresponding to the phase shift induced by the external interaction. Both conditions may be expressed in terms of simple odd integers. Some specific examples are discussed.