We introduce an efficient, quasideterministic scheme to generate maximally entangled states of two atomic ensembles. The scheme is based on quantum nondemolition measurements of total atomic populations and on adiabatic quantum feedback conditioned by the measurements outputs. The high efficiency of the scheme is tested and confirmed numerically for ideal photodetection as well as in the presence of losses.

Recently, quantum random walks (QRWs) have been thoroughly studied in order to develop new quantum algorithms. In this paper we propose scalable quantum networks for discrete QRWs on circles, lines, and also in higher dimensions. In our method the information about the position of the walker is stored in a quantum register and the network consists of only one-qubit rotation and ${\left(\text{controlled}\right)}^n\text{−}\mathrm{NOT}$ gates, therefore it is purely computational and independent of the physical implementation. As an example, we describe the experimental realization in an ion-trap system.

We apply our recent technique of using a Rb-stabilized ring-cavity resonator to measure the absolute frequencies of various isotopic components in the $399\text{−}\mathrm{nm}$ ${}^{1}S_0\to {}^{1}P_1$ line of Yb. For the transition in ${}^{174}\mathrm{Yb}$, we obtain a value of $751525987.761\left(60\right)\mathrm{MHz}$, representing a relative uncertainty of $0.08\mathrm{ppb}$. We also obtain the isotope shifts and hyperfine structure with $50\mathrm{kHz}$ precision, an order-of-magnitude improvement over our earlier measurements on this line. Our earlier work had helped in resolving some discrepancies among previous measurements, and the present work further confirms those results.

We report the results of our calculations of the magnetic dipole hyperfine constants for the ground and low-lying excited states of ${\mathrm{Pb}}^{+}$ using the relativistic coupled-cluster theory. The spectacular role of correlation effects particularly for the $6p_{3∕2}$ state is highlighted. The relative importance of core polarization and pair correlation effects have been studied and the result obtained for the ground state is different from that of ${\mathrm{Ba}}^{+}$, which has a single $s$ valence electron.

Multielectron giant dipole resonances of atoms in crossed electric and magnetic fields are investigated. Stationary configurations corresponding to a highly symmetric arrangement of the electrons on a decentered circle are derived, and a normal-mode and stability analysis are performed. A classification of the various modes, which are dominated by the magnetic field or the Coulomb interactions, is provided. Based on the MCTDH approach, we carry out a six-dimensional wave-packet dynamical study for the two-electron resonances, yielding in particular lifetimes of more than $0.1\mu \mathrm{s}$ for strong electric fields.

We discuss localized ground states of Bose-Einstein condensates (BEC’s) in optical lattices with attractive and repulsive three-body interactions in the framework of a quintic nonlinear Schrödinger equation which extends the Gross-Pitaevskii equation to the one-dimensional case. We use both a variational method and a self-consistent approach to show the existence of unstable localized excitations which are similar to Townes solitons of the cubic nonlinear Schrödinger equation in two dimensions. These solutions are shown to be located in the forbidden zones of the band structure, very close to the band edges, separating decaying states from stable localized ones (gap solitons) fully characterizing their delocalizing transition. In this context the usual gap solitons appear as a mechanism for arresting the collapse in low-dimensional BEC’s in optical lattices with an attractive real three-body interaction. The influence of the imaginary part of the three-body interaction, leading to dissipative effects in gap solitons, and the effect of atoms feeding from the thermal cloud are also discussed. These results may be of interest for both BEC’s in atomic chips and Tonks-Girardeau gas in optical lattices.

We consider the collision of a dark soliton with an obstacle in a quasi-one-dimensional Bose condensate. We show that in many respects the soliton behaves as an effective classical particle of mass twice the mass of a bare particle, evolving in an effective potential which is a convolution of the actual potential describing the obstacle. Radiative effects beyond this approximation are also taken into account. The emitted waves are shown to form two counterpropagating wave packets, both moving at the speed of sound. We determine, at leading order, the total amount of radiation emitted during the collision and compute the acceleration of the soliton due to the collisional process. It is found that the radiative process is quenched when the velocity of the soliton reaches the velocity of sound in the system.

We propose a scheme for the conditional generation of arbitrary finite superpositions of Fock states in a single mode of a traveling optical field. The setup requires a source of squeezed vacuum states, beam splitters, strong coherent beams, photodetectors with single-photon sensitivity, and a final squeezer. If we want to generate a squeezed superposition of Fock states, which is sufficient in several applications, then the last squeezer is not even needed. The thrust of this method is that it achieves a high fidelity without requiring photodetectors with a high efficiency or a single-photon resolution. The possibility to improve its scaling by using a quantum memory is also discussed.

We discuss a parity nonconserving asymmetry in the cross section of $KLL$ dielectronic recombination of polarized electrons on the hydrogenlike ions with $Z\lesssim 60$. This effect is strongly enhanced because of the near degeneracy of doubly excited $2l2l^{\prime }$ states of opposite parity in He-like ions. For ions with $Z\sim 30$ the asymmetry is of the order of ${10}^{-9}$. For $Z\approx 48$ a level crossing takes place, leading to the PNC asymmetry of $-1.3\times {10}^{-8}$, which is ${10}^8$ times greater than the basic strength of the weak interaction in atoms.

Spontaneous emission of a photon by an atom is described theoretically in three dimensions with the initial wave function of a finite-mass atom taken in the form of a finite-size wave packet. Recoil and wave-packet spreading are taken into account. The total atom-photon wave function is found in the momentum and coordinate representations as the solution of an initial-value problem. The atom-photon entanglement arising in such a process is shown to be closely related to the structure of atom and photon wave packets which can be measured in the coincidence and single-particle schemes of measurements. Two predicted effects, arising under the conditions of high entanglement, are anomalous narrowing of the coincidence wave packets and, under different conditions, anomalous broadening of the single-particle wave packets. Fundamental symmetry relations between the photon and atom single-particle and coincidence wave-packet widths are established. The relationship with the famous scenario of Einstein-Podolsky-Rosen is discussed.

We describe an implementation of Grover’s fixed-point quantum search algorithm on a nuclear magnetic resonance quantum computer, searching for either one or two matching items in an unsorted database of four items. In this algorithm the target state (an equally weighted superposition of the matching states) is a fixed point of the recursive search operator, so that the algorithm always moves towards the desired state. The effects of systematic errors in the implementation are briefly explored.

We investigate the von Neumann entanglement entropy as function of the size of a subsystem for permutation invariant ground states in models with finite number of states per site, e.g., in quantum spin models. We demonstrate that the entanglement entropy of $n$ sites in a system of length $L$ generically grows as $\sigma {\log }_2[2\pi en(L-n)∕L]+C$, where $\sigma$ is the on-site spin and $C$ is a function depending only on magnetization.

Three approximate exchange potentials of high accuracy $v_{\mathrm{x}}^{\mathrm{Y}}\left(\mathbf{r}\right)$, $\mathrm{Y}=\mathrm{A}$,B,C, for the density-functional theory applications are obtained by replacing the matrix elements of the exact potential between the Kohn-Sham (KS) orbitals with such elements of the Fock exchange operator (within the virtual-occupied subset only) in three representations found for any local potential. A common identity is the base of these representations. The potential $v_{\mathrm{x}}^{\mathrm{C}}$ happens to be the same as that derived by Harbola and Sahni, and $v_{\mathrm{x}}^{\mathrm{A}}$ as that derived by Gritsenko and Baerends, and Della Sala and Görling. The potentials obtained can be expressed in terms of occupied KS orbitals only. At large $r$, their asymptotic form $-1∕r$ is the same as that of the exact potential. The high quality of these three approximations is demonstrated by direct comparison with the exact potential and using various consistency tests. A common root established for the three approximations could be helpful in finding new and better approximations via modification of identities employed in the present investigation.

In a recent paper [Phys. Rev. Lett. 93, 130401 (2004)], we proposed the idea of expanding the space of variations in variational calculations of the energy by considering the approximate wave function $\psi$ to be a functional of functions $\chi$, $\psi =\psi \left[\chi \right]$, rather than a function. A constrained search is first performed over all functions $\chi$ such that the wave-function functional $\psi \left[\chi \right]$ satisfies a physical constraint or leads to the known value of an observable. A rigorous upper bound to the energy is then obtained via the variational principle. In this paper we generalize the constrained-search variational method, applicable to both ground and excited states, to the determination of arbitrary Hermitian single-particle operators as applied to two-electron atomic and ionic systems. We construct analytical three-parameter ground-state functionals for the ${\mathrm{H}}^{-}$ ion and the He atom through the constraint of normalization. We present the results for the total energy $E$, the expectations of the single-particle operators $W={\sum }_i{r}_i^n$, $n=-2,-1,1,2$, $W={\sum }_i\delta \left({\mathbf{r}}_i\right)$, and $W={\sum }_i\delta ({\mathbf{r}}_i-\mathbf{r})$, the structure of the nonlocal Coulomb hole charge ${\rho }_c\left(\mathbf{r}{\mathbf{r}}^{\prime }\right)$, and the expectations of the two particle operators $u^2,u,1∕u,1∕u^2$, where $u=\mid {\mathbf{r}}_i-{\mathbf{r}}_j\mid$. The results for all the expectation values are remarkably accurate when compared with the 1078-parameter wave function of Pekeris, and other wave functions that are not functionals. We conclude by describing our current work on how the constrained-search variational method in conjunction with quantal density-functional theory is being applied to the many-electron case.

High-resolution spectroscopy of a hot tokamak plasma seeded with argon ions and interacting with an energetic, short-pulse neutral hydrogen beam was used to obtain a high-resolution $K$-shell x-ray spectrum formed solely by charge exchange. The observed $K$-shell emission of ${\mathrm{Ar}}^{16+}$ is dominated by the intercombination and forbidden lines, providing clear signatures of charge exchange. Results from an ab initio atomic cascade model provide excellent agreement, validating a semiclassical approach for calculating charge-exchange cross sections.

We investigate the dynamics of matter-wave solitons in the presence of a spatially varying atomic scattering length and nonlinearity. The dynamics of bright and dark solitary waves is studied using the corresponding Gross-Pitaevskii equation. The numerical results are shown to be in very good agreement with the predictions of the effective equations of motion derived by adiabatic perturbation theory. The spatially dependent nonlinearity is found to lead to a gravitational potential, as well as to a renormalization of the parabolic potential coefficient. This feature allows one to influence the motion of fundamental as well as higher-order solitons.

The mean-field dynamics of Bose-Einstein condensates loaded in an optical lattice, confined by a parabolic potential, and subjected to a change of scattering length by means of the Feshbach resonance is considered. The system is described by the Gross-Pitaevskii (GP) equation with varying nonlinearity, which in a number of cases is reduced to one-dimensional (1D) perturbed nonlinear Schrödinger (NLS) equations, the particular form of which depends on the relation among the parameters of the problem. We analytically describe the adiabatic dynamics of periodic solutions of the respective NLS equations, provide a numerical study of 1D models confined by a parabolic trap, and carry out numerical simulations of the matter-wave dynamics within the framework of the radially symmetric 3D GP equation. Special attention is paid to processes of generation of trains of bright and dark matter solitons from initially periodic waves. The results of the 1D approximation are compared with direct numerical simulation of the original 3D GP eqation, showing remarkable coincidence for definite regions of parameters.

We discuss interacting and noninteracting one dimensional atomic systems trapped in an optical lattice plus a parabolic potential. We show that, in the tight-binding approximation, the noninteracting problem is exactly solvable in terms of Mathieu functions. We use the analytic solutions to study the collective oscillations of ideal bosonic and fermionic ensembles induced by small displacements of the parabolic potential. We treat the interacting boson problem by numerical diagonalization of the Bose-Hubbard Hamiltonian. From analysis of the dependence upon lattice depth of the low-energy excitation spectrum of the interacting system, we consider the problems of “fermionization” of a Bose gas, and the superfluid-Mott insulator transition. The spectrum of the noninteracting system turns out to provide a useful guide to understanding the collective oscillations of the interacting system, throughout a large and experimentally relevant parameter regime.

In this paper we study the nondegenerate optical parametric oscillator with injected signal, both analytically and numerically. We develop a perturbation approach which allows us to find approximate analytical solutions, starting from the full equations of motion in the positive-$P$ representation. We demonstrate the regimes of validity of our approximations via comparison with the full stochastic results. We find that, with reasonably low levels of injected signal, the system allows for demonstrations of quantum entanglement and the Einstein-Podolsky-Rosen paradox. In contrast to the normal optical parametric oscillator operating below threshold, these features are demonstrated with relatively intense fields.

We study theoretically the optical properties of a finite inverted-opal photonic crystal. The light-matter interaction is strongly affected by the presence of the three-dimensional photonic crystal and the alterations of the light emission and absorption processes can be used to suppress or enhance the thermal emissivity and absorptivity of the dielectric structure. We investigate the influence of the absorption present in the system on the relevant band edge frequencies that control the optical response of the photonic crystal. Our study reveals that the absorption processes cause spectral broadening and shifting of the band edge optical resonances, and determine a strong reduction of the photonic band gap spectral range. Using the angular and spectral dependence of the band edge frequencies for stop bands along different directions, we argue that by matching the blackbody emission spectrum peak with a prescribed maximum of the absorption coefficient, it is possible to achieve an angle-sensitive enhancement of the thermal emission/absorption of radiation. This result opens a way to realize a frequency-sensitive and angle-sensitive photonic crystal absorbers/emitters.