We find a coupling-strength configuration for a linear chain of $N$ spins which gives rise to simultaneous multiple Bell states. We suggest a way such an interesting entanglement pattern can be used in order to distribute maximally entangled channels to remote locations and generate multipartite entanglement with a minimum-control approach. Our proposal thus provides a way to achieve the core resources in distributed information processing. The schemes we describe can be efficiently tested in chains of coupled cavities interacting with three-level atoms.

We propose an architecture and methodology for large-scale quantum simulations using hyperfine states of trapped ions in an arbitrary-layout microtrap array with laserless interactions. An ion is trapped at each site, and the electrode structure provides for the application of single and pairwise evolution operators using only locally created microwave and radio-frequency fields. The avoidance of short-lived atomic levels during evolution effectively eliminates errors due to spontaneous scattering; this may allow scaling of quantum simulators based on trapped ions to much larger systems than currently estimated. Such a configuration may also be particularly appropriate for one-way quantum computing with trapped-ion cluster states.

A method is developed to derive algebraic equations for the geometric measure of entanglement of three-qubit pure states. The equations are derived explicitly and solved in the cases of most interest. These equations allow one to derive analytic expressions of the geometric entanglement measure in a wide range of three-qubit systems, including the general class of W states and states which are symmetric under the permutation of two qubits. The nearest separable states are not necessarily unique, and highly entangled states are surrounded by a one-parametric set of equally distant separable states. A possibility for physical applications of the various three-qubit states to quantum teleportation and superdense coding is suggested from the aspect of entanglement.

The equilibrium geometries, vibrational frequencies, dissociation energies, and populations of the title species were studied at Hartree-Fock (HF), second-order Møller-Plesset (MP2), and coupled-cluster singles-doubles (triples) [CCSD(T)] levels. The electron correlation effects and relativistic effects on the geometry and stability were investigated at the CCSD(T) level. Both effects stabilize title species. The populations analyses show that $M\text{-Xe}$ bonding is dominated by electrostatic interactions and the best theoretical estimate of the dissociation energies are 1.104 and 2.260 eV for ${\text{AuXe}}^{+}$ and ${\text{AuXe}}_2^{+}$, respectively. The Cu and Ag are weakly bonded to Xe compared to Au.

The nonrelativistic analytical structure of the doubly differential cross section of the contact inelastic scattering of an x-ray photon by a free atom is determined by means of the irreducible tensor operator theory outside the frame of the impulse approximation. For the neon atom in the vicinity of the 1$s$ shell ionization threshold our theory predicts the existence of the distinct fine structure of the cross section caused by transitions of the atomic core electrons into the excited discrete spectrum states. The results of our calculations with inclusion of the effects of radial relaxation, inelastic scattering through the intermediate states, and elastic Rayleigh scattering, are predictions, while at the $22\mathrm{keV}$ incident photons they compare well with the synchrotron experiment by Jung et al. [Phys. Rev. Lett. 81, 1596 (1998)].

We report on the observation of long range interaction in the second-harmonic generation from rubidium Rydberg atoms. The asymmetric spectral broadening of the resonant lines provides evidence of the van der Waals interaction between pairs of Rydberg atoms. This effect is investigated when the two-photon transition is resonant with $nd$ levels for $n\approx 13$.

Population transfer in three-level atomic systems with high efficiency and selectivity is desirable for practical applications in laser spectroscopy, trace analysis, and isotope separation. The effective excitation method for achieving this population transfer in three-level atomic systems using coherent two-photon excitation with two optimally detuned counterpropagating pulsed lasers, initially investigated analytically assuming monochromatic lasers and Doppler-free systems, is studied numerically by solving the density matrix equations incorporating finite laser linewidth and effective Doppler width. A three-level Yb system is chosen for illustration of numerical results. The effects of laser linewidth and effective Doppler width on the values of optimal detunings and maximum third-level population are discussed.

It was recently demonstrated that wire-guide roughness can be suppressed by modulating the wire currents so that the atoms experience a time-averaged potential without roughness [Trebbia et al., Phys. Rev. Lett. 98, 263201 (2007)]. In this paper, we theoretically study the limitations of this technique. At low modulation frequency, we show that the longitudinal potential modulation produces heating of the cloud, and we compute the heating rate. We also give a quantum derivation of the rough conservative potential associated with the micromotion of the atoms. At large modulation frequency, we compute the loss rate due to nonadiabatic spin flip and show that it presents resonances at multiple modulation frequencies. These studies show that the modulation technique works for a wide range of experimental parameters. We also give conditions to realize radio-frequency evaporative cooling in such a modulated trap.

Starting from the spectrum of the radially symmetric quantum harmonic oscillator in two dimensions, we create a large set of nonlinear solutions. The relevant three principal branches, with $n_r=0,1$, and 2 radial nodes, respectively, are systematically continued as a function of the chemical potential and their linear stability is analyzed in detail, in the absence as well as in the presence of topological charge $m$, i.e., vorticity. It is found that for repulsive interatomic interactions only the ground state is linearly stable throughout the parameter range examined. Furthermore, this is true for topological charges $m=0$ or 1; solutions with higher topological charge can be unstable even in that case. All higher excited states are found to be unstable in a wide parametric regime. However, for the focusing (attractive) case the ground state with $n_r=0$ and $m=0$ can only be stable for a sufficiently low number of atoms. Once again, excited states are found to be generically unstable. For unstable profiles, the dynamical evolution of the corresponding branches is also followed to monitor the temporal development of the instability.

Lorentz transformation of the three-qubit Greenberger-Horne-Zeilinger (GHZ) state is studied. Also we obtain the relativistic spin joint measurement for the transformed state. Using these results it is shown that Bell’s inequality is maximally violated for the three-qubit GHZ state in the relativistic regime. For ultrarelativistic particles we obtain the critical value for boost speed, which Bell’s inequality is not violated for velocities smaller than this value. We also show that in the ultrarelativistic limit Bell’s inequality is maximally violated for the GHZ state.

A formulation for evaluating the performance of quantum error correcting codes for a general error model is presented. In this formulation, the correlation between errors is quantified by a Hamiltonian description of the noise process. We classify correlated errors using the system-bath interaction: local versus nonlocal and two-body versus many-body interactions. In particular, we consider Calderbank-Shor-Steane codes and observe a better performance in the presence of correlated errors depending on the timing of the error recovery. We also find this timing to be an important factor in the design of a coding system for achieving higher fidelities.

We use Jost functions to determine the leading and next-to-leading terms of the phase shifts ${\delta }_l\left(k\right)$ in the case of homogeneous attractive singular potentials $-1/r^{\alpha }$, $\alpha >2$, for arbitrary angular momentum $l$ with incoming boundary conditions at small distances. The Jost solutions are obtained by solving a Volterra equation and a more general ansatz is used to fit the Jost solutions to the WKB waves in the inner region, where the WKB approximation is accurate. A connection between the phase shifts of attractive and repulsive homogeneous singular potentials is presented. Finally, an alternative formulation of the effective range theory for arbitrary $l$ is proposed, where both, the scattering length and the effective range have the dimension of a length. The ratio of effective range and scattering length is then the same for attractive and repulsive potentials.

We quantify interference effects on radiation by calculating the angle- and energy-resolved Larmor radiation from atomic ionization in the focus of ultraintense field. Our calculations use a Monte Carlo classical and semiclassical tunneling probability current models of ionization for intensities in the range of ${10}^{16}\text{to}{10}^{20}\mathrm{W}∕{\mathrm{cm}}^2$. For nonrelativistic intensities, whether the radiation from the photoionization is treated coherently or incoherently, classically or semiclassically, leads to a negligible effect on radiation. For relativistic intensities, coherently summing across the tunneling ionization probability current decreases the radiation by an order of magnitude when compared to classical ionization or incoherent summation of the radiation from the tunneling ionization probability current. The interference effect is most pronounced for high-energy photons since ionization and the electron quiver may be $1\mu \mathrm{m}$ and extends over multiple radiation wavelengths.

Matter-light quantum interface and quantum memory for light are important ingredients of quantum information protocols, such as quantum networks, distributed quantum computation, etc. [P. Zoller et al., Eur. Phys. J. D 36, 203 (2005)]. In this paper we present a spatially multimode scheme for quantum memory for light, which we call a quantum hologram. Our approach uses a multiatom ensemble which has been shown to be efficient for a single spatial mode quantum memory. Due to the multiatom nature of the ensemble and to the optical parallelism it is capable of storing many spatial modes, a feature critical for the present proposal. A quantum hologram with the fidelity exceeding that of classical hologram will be able to store quantum features of an image, such as multimode superposition and entangled quantum states, something that a standard hologram is unable to achieve.

We report on the characterization of long-range surface plasmon waveguide bends at telecom wavelengths $(\lambda =1550\mathrm{nm})$. The structures consist of a thin Au stripe embedded in a transparent polymer film. When the polymer thickness is larger than the lateral extension of the plasmon, the stripe sustains a conventional long-range mode; in the opposite case, the mode is hybrid because its field distribution is confined by total internal reflection in the dielectric cladding. This hybridization increases the damping by absorption but dramatically reduces the radiation loss that occurs for curved geometries, such as bends. Our results are supported quantitatively by full-wave finite-element simulations.

We construct a large class of bipartite $M\otimes N$ quantum states which defines a proper subset of states with positive partial transposes (PPTs). Any state from this class has PPT but the positivity of its partial transposition is recognized with respect to canonical factorization of the original density operator. We propose to call elements from this class states with strong positive partial transposes (SPPTs). We conjecture that all SPPT states are separable.

Recent years have seen increased interest in complexified Bohmian mechanical trajectory calculations for quantum systems as both a pedagogical and computational tool. In the latter context, it is essential that trajectories satisfy probability conservation to ensure they are always guided to where they are most needed. We consider probability conservation for complexified Bohmian trajectories. The analysis relies on time-reversal symmetry considerations, leading to a generalized expression for the conjugation of wave functions of complexified variables. This in turn enables meaningful discussion of complexified flux continuity, which turns out not to be satisfied in general, though a related property is found to be true. The main conclusion, though, is that even under a weak interpretation, probability is not conserved along complex Bohmian trajectories.

We propose that the entanglement of mixed states is characterized properly in terms of a probability density function ${\mathcal{P}}_{\rho }\left(\mathcal{E}\right)$. There is a need for such a measure since the prevalent measures (such as concurrence and negativity) for two-qubit systems are rough benchmarks and not monotones of each other. Focusing on the two-qubit states, we provide an explicit construction of ${\mathcal{P}}_{\rho }\left(\mathcal{E}\right)$ and show that it is characterized by a set of parameters of which concurrence is but one particular combination. ${\mathcal{P}}_{\rho }\left(\mathcal{E}\right)$ is manifestly invariant under $\text{SU}\left(2\right)\times \text{SU}\left(2\right)$ transformations. It can, in fact, reconstruct the state up to local operations—with the specification of at most four additional parameters. Finally, the measure resolves the controversy regarding the role of entanglement in quantum computation in NMR systems.

We report the implementation of the complete set of the lowest-order relativistic corrections of the order of ${\alpha }^2$ (where $\alpha$ is the fine structure constant) for calculating vibrational states of diatomic molecular systems within the framework that does not assume the Born-Oppenheimer approximation. To test the accuracy of the approach we have performed calculations for all rotationless vibrational states (also called pure vibrational states or $S$ states) of the ${\text{HeH}}^{+}$ ion in the ground electronic state. For the lowest transitions, where very precise experimental results are available, an excellent agreement with the experimental values has been achieved.

From the work by W. Perrie et al. [Phys. Rev. Lett. 54, 1790 (1985)], it is known that the photon pairs that are emitted in the $2s_{1∕2}\to 1s_{1∕2}$ (two-photon) decay of atomic hydrogen are quantum mechanically correlated, i.e., entangled. However, less information is available about the degree of polarization entanglement between the two photons if an arbitrary geometry is considered for collecting the photons. In this paper, we study the effect of the decay geometry on the degree of polarization entanglement between the two emitted photons. Results are shown for the $2s_{1∕2}\to 1s_{1∕2}$ and $3d_{5∕2}\to 1s_{1∕2}$ two-photon transitions of atomic hydrogen. The outlined theory is general and can be applied also to heavier elements. To demonstrate the influence of relativistic and multipole effects, results are also shown for the $3d_{5∕2}\to 1s_{1∕2}$ transition of hydrogenlike uranium.