We show the series of Greenberger-Horne-Zeilinger-like paradoxes for N maximally entangled N-dimensional quantum systems. The hypothesis of local hidden variables leads to a prediction of perfect correlations that do not appear for the quantum systems.

We discuss the entropic criterion for separability of compound quantum systems for general nonadditive entropic forms based on arbitrary concave functions f. For any separable state, the generalized entropy of the whole system is shown to be not smaller than that of the subsystems, for any choice of f, providing thus a necessary criterion for separability. Nevertheless, the criterion is not sufficient and examples of entangled states with the same property are provided. This entails, in particular, that the conjecture about the positivity of the conditional Tsallis entropy for all q, a more stringent requirement than the positivity of the conditional von Neumann entropy, is actually a necessary but not sufficient condition for separability in general. The direct relation between the entropic criterion and the largest eigenvalues of the full and reduced density operators of the system is also discussed.

Two-mode cavities can be prepared in quantum states which represent symmetric multiqubit states. However, the qubits are impossible to address individually and as such cannot be independently measured or otherwise manipulated. We propose two related schemes to coherently transfer the qubits that the cavity state represents onto individual atoms, so that the qubits can then be processed individually. In particular, our scheme can be combined with the quantum cloning scheme of Simon and co-workers [C. Simon et al., Phys. Rev. Lett. 84, 2993 (2000)] to allow the optimal clones that their scheme produces to be spatially separated and individually utilized.

Quantum state discrimination for two coherent states with opposite phases as measured relative to a reference pulse is analyzed as functions of the intensities of both the signal states and of the reference pulse. This problem is relevant for quantum key distribution with phase encoding. We consider both the optimum measurements and simple measurements that require only beam splitters and photodetectors.

A QED recoil correction of order $(\mu /M){\alpha }^5{\mathrm{mc}}^2$ recently derived by Pachucki [J. Phys. B 31, 5123 (1998)] is evaluated for lithium in the ${1s}^2{2s}^2{S}_{1/2},$ ${1s}^2{3s}^2{S}_{1/2},$ and ${1s}^2{2p}^{2}P$ states, and its contribution to the isotope shift is calculated. The new term is shown to be equivalent to the recoil term included in our previous work in a hydrogenic approximation. Total energies are calculated for each of the states in question, including screening corrections to the Bethe logarithm estimated from the two-particle parent states. The results for the total transition frequencies are shown to be in good agreement with experiment, but there are surprisingly large discrepancies between theory and experiment for the isotope shift in the fine structure splitting (SIS) for the ${1s}^2{2p}^{2}P$ state. The ionization potential of ${}^7\mathrm{Li}$ is calculated to be $43487.1520\left(40\right)\mathrm{}{\mathrm{cm}}^{-1}.$ The estimated accuracy is about the same as the experimental value. A recent measurement of the ${}^7\mathrm{Li}{–}^6\mathrm{Li}$ isotope shift for the $2^2{P}_{1/2}-2^2{S}_{1/2}$ transition determines the difference of the squares of the nuclear radii to be $0.84\left(6\right)\mathrm{}{\mathrm{fm}}^2,$ which is a factor of 4 more accurate than the value $0.79\left(25\right)\mathrm{}{\mathrm{fm}}^2$ derived from nuclear scattering data.

The forward scattering amplitude for electron-hydrogen scattering is expected to be an analytic function of the energy. However, when calculated within the framework of nonrelativistic quantum mechanics and the Born approximation, the exchange part has double and triple left-hand poles. From the viewpoint of field theory, such higher-order singularities are unexpected: One normally encounters only simple poles and branch points. A simple nonrelativistic model, which interpolates between binding by short-range and long-range forces, is used to show that these singularities are a direct consequence of the fact that the target system is bound by Coulomb forces: If the binding is by short-range forces there is only a simple pole. The double and triple poles emerge from a coalescence of simple poles and logarithmic branch points, in the limit of long-range binding. In the same framework, the direct amplitude has both simple and double poles, regarded as a function of the squared momentum transfer. Now even the simple pole is unexpected because the H atom is neutral. Again, the existence of these singularities is shown to be a consequence of Coulomb binding. The singularities are then studied within the framework of field theory. I show that if the H atom is treated as if it were an elementary particle, described by a field ${\phi }_{\mathrm{H}}$ coupled to electron and proton fields ${\phi }_e$ and ${\phi }_p$ by a Lagrangian density $L_I=-G_0({\phi }_e{\phi }_p{)}^{†}{\phi }_{\mathrm{H}}+\mathrm{H}.\mathrm{c}.\mathrm{},$ the location of the singularity of the exchange amplitude is immediately obtained from a tree diagram, without the need to carry out any integrations. However, the nature of the singularity found does not agree with the nonrelativistic theory: There is no free lunch. Further analysis indicates that in full-fledged quantum electrodynamics, the vertex function Γ which describes the virtual decomposition of the H atom into its constituents must itself be singular when all particles are on the mass shell.

We have computed the single-differential and total ionization cross sections for the proton-hydrogen collision system at low-energy range (0.1–10 keV/amu), using the electron translation factor corrected close-coupling method. Full convergence of ionization cross sections as a function of ${\mathrm{H}}_2^{+}$ molecular basis size was achieved by including up to ten bound states and 11 continuum partial waves. The present results are compared with the available experimental data and various theoretical models. Our calculated cross sections are in an excellent agreement with the recent experiments of Shah et al. [J. Phys. B. 31, L757 (1998)], but decrease more rapidly than the cross sections measured by Pieksma et al. [Phys. Rev. Lett. 73, 46 (1994)] with decreasing energy. We have found that the $1s{\sigma }_g$ electron ionization is a rather higher-level ladder climbing process than a direct mechanism; the $2p{\sigma }_u$ electron, on the contrary, is ionized directly and the higher levels act as a temporary trap.

An ultracold Bose gas of two-level atoms can be thought of as a spin-1/2 Bose gas. It supports spin-wave collective modes due to the exchange mean field. Such collective spin oscillations have been observed in recent experiments at JILA with ${}^{87}\mathrm{Rb}$ atoms confined in a harmonic trap. We present a theory of the spin-wave collective modes based on the moment method for trapped gases. In the collisionless and hydrodynamic limits, we derive analytic expressions for the frequencies and damping rates of modes with dipole and quadrupole symmetry. We find that the frequency for a given mode is given by a temperature-independent function of the peak density n, and falls off as $1/n.$ We also find that, to a very good approximation, excitations in the radial and axial directions are decoupled. We compare our model to the numerical integration of a one-dimensional version of the kinetic equation and find very good qualitative agreement. The damping rates, however, show the largest deviation for intermediate densities, where one expects Landau damping—which is unaccounted for in our moment approach—to play a significant role.

The work in this article extends the optimal control framework of variational calculus to optimize the conversion of a Bose-Einstein condensate of atoms to one of molecules. It represents the derivation of the closed form optimal control equations for a system governed by a nonlinear Schrödinger equation and its successful application. It was necessary to derive a density matrix formulation of the coupled Gross-Pitaevskii equations to optimize STIRAP-like Raman light fields, to overcome dissipation.

We study the crossover between the mean-field and critical behavior of the two-dimensional Bose gas throughout the fluctuation region of the Berezinskii-Kosterlitz-Thouless phase transition point. We argue that this crossover is described by universal (for all weakly interacting $|\psi {|}^4$ models) relations between thermodynamic parameters of the system, including superfluid and quasicondensate densities. We establish these relations with high-precision Monte Carlo simulations of the classical $|\psi {|}^4$ model on a lattice, and check their asymptotic forms against analytic expressions derived on the basis of the mean-field theory.

We report on experimental and theoretical studies of a photorefractive ring resonator pumped by a 1.06 μm beam and injected with a weak, external, seeding beam. The competition between the two dominant gratings that form inside the photorefractive crystal leads to characteristic periodic oscillations in the intensity of the resonating beam, which originate from the frequency difference between the pump beam and the unidirectional oscillation beam. We show that such a system can be treated as a driven nonlinear oscillator.

We explain the “hidden symmetries” observed in wave functions of deformed microwave resonators in recent experiments. We also predict that other such symmetries can be seen in microwave resonators.

The scalar Aharonov-Bohm effect with a time-dependent magnetic field was investigated for ultracold sodium atoms using the time-domain atom interferometer. The 38 interference fringes with almost the same amplitude verified the nondispersivity of this effect. The measured phase shift as a function of the strength of the applied magnetic field agreed with the predicted one within an accuracy of 3%. With a weak magnetic field orthogonal to the quantization axis, the phase shift was in proportion to the variation of the strength of the resultant magnetic field.

We describe the results of a parametric down-conversion experiment in which the detection of one photon of a pair causes the other photon to be switched into a storage loop. The stored photon can then be switched out of the loop at a later time chosen by the user, providing a single photon for potential use in a variety of quantum information processing applications. Although the stored single photon is only available at periodic time intervals, those times can be chosen to match the cycle time of a quantum computer by using pulsed down-conversion. The potential use of the storage loop as a photonic quantum memory device is also discussed.

We present a criterion for estimation of the quality of state-dependent $\overrightarrow{N}L$ cloning. We call this criterion the relative error because one compares the errors in copies with contiguous size, which is not independent of the closeness of the states to be copied. First, we prove several useful statements that maintain the interpretation for the proposed measure. The tightest lower bound on the relative error is then derived. We describe the optimal asymmetric state-dependent cloner that minimizes the relative error.

The Brüschweiler quantum search [Phys. Rev. Lett. 85, 4815 (2000)] offers an exponential speedup over the corresponding classical search. In the Brüschweiler search, the data bits and measurement bit (the ancillary bit) are different bits. We propose a modified method, in which no ancillary bit is needed to reach exponential speedup. The modified Brüschweiler search can be easier to design and realize. We also demonstrate the modified search in a three-qubit molecular system using nuclear magnetic resonance.

The $B{}^1{\Sigma }_{\mathrm{u}}^{+}\to X{}^1{\Sigma }_{\mathrm{g}}^{+}$ system in ${}^{40}{\mathrm{Ca}}_2$ was studied by Fourier-transform spectroscopy. Transitions to 730 ground-state levels were induced by the blue-green lines of an ${\mathrm{Ar}}^{+}$ radiation and the single-mode radiation of a frequency-doubled continuous-wave Nd:YAG yttrium aluminum garnet laser. An accurate potential-energy curve, which covers 99.8% of the well depth, was derived directly from the experimentally observed differences between ground-state levels. Long-range analysis led to a revised value of the ground-state dissociation energy, $1102.08\left(9\right)\mathrm{}{\mathrm{cm}}^{-1},$ which differs by more than $7{\mathrm{cm}}^{-1}$ from the previous experimental determination [C. R. Vidal, J. Chem. Phys. 72, 1864 (1980)]. A first estimate of the s-wave scattering length is reported.

The quantum localization of the periodically kicked Rydberg atom in the limit of high frequencies $\nu$ is studied. We show that the quantum suppression of fast chaotic ionization as predicted by classical dynamics persists as $\overrightarrow{\nu }\infty .$ Properties of localization in the regime of strong coupling to the continuum due to one-photon transitions are discussed. For the unidirectionally kicked atom, the high-frequency limit of localization is determined by the zero-frequency Stark Hamiltonian. The persistence of quantum localization due to interference of classical trajectories can be understood in terms of smearing out of the instabilities at finite $ħ.$ Unstable trajectories whose action differs from each other and from Stark orbits in less than $ħ$ contribute to quantum localization rather than to chaotic ionization.

In the optical Stern-Gerlach effect, the interaction of a traveling two-level atom with the electromagnetic field of an optical cavity causes a splitting of the atomic trajectory. One may ask if it is possible to single out particular initial configurations of the system that will lead to selective scattering, in which the atoms follow only one trajectory. We show that these configurations consist of a coherent superposition of the atomic internal states, and of a field phase state or a field coherent state, with a precise phase relation between the two subsystems: The same configurations which produce the so-called atomic coherent trapping in the Jaynes-Cummings model.

Photoionization of a cold atomic sample offers intriguing possibilities for observing collective effects at extremely low temperatures. Irradiation of a rubidium condensate and of cold rubidium atoms within a magneto-optical trap (MOT) with laser pulses ionizing through one-photon and two-photon absorption processes was performed. Losses and modifications in the density profile of the remaining trapped cold cloud or the remaining condensate sample were examined as functions of the ionizing laser parameters. Ionization cross sections were measured for atoms in a MOT, while in magnetic traps losses larger than those expected for ionization process were measured.