We report on experimental and theoretical studies on recently introduced entanglement measures which use a sum of spin-variance criteria for two spin-$1∕2$ particles. Three inequalities are explored which exhibit useful concatenating properties. They are each shown to have greater sensitivities than a Bell’s measurement, while each requiring fewer measurements than a Bell’s measurement to obtain. The simplest inequality, requiring just four measurements, is shown to be efficient at testing for entanglement in down-conversion sources which naturally exhibit maximally polarized noise. The most complex inequality, requiring just 12 measurements, is shown to have a sensitivity equal to that of the Peres separability criterion for maximally polarized and Werner noise. This increased sensitivity implies optimality of the measure.

A systematic analysis of the behavior of the quantum Markovian master equation driven by coherent control fields is proposed. Its irreversible character is formalized using control-theoretic notions and the sets of states that can be reached via coherent controls are described. The analysis suggests to what extent (and how) it is possible to counteract the effect of dissipation.

The quantum clock synchronization (QCS) algorithm proposed by Chuang [Phys. Rev. Lett. 85, 2006 (2000)] has been implemented in a three qubit nuclear magnetic resonance quantum system. The time difference between two separated clocks can be determined by measuring the output states. The experimental realization of the QCS algorithm also demonstrates an application of the quantum phase estimation.

$L$-subshell ionization cross sections are extracted from measured $L\alpha$, $L\beta$, $L\gamma$, $L{\gamma }_1$, $L{\gamma }_{23}$, and $L{\gamma }_{44}$ x-ray production cross sections in thin targets of ${}_{75}\mathrm{Re}$, ${}_{78}\mathrm{Pt}$, and ${}_{79}\mathrm{Au}$ bombarded by $4–8\mathrm{MeV}$ ${\mathrm{C}}^{3+}$ ions. For each projectile energy, using the fluorescence and Coster-Kronig yields recently recommended by Campbell with an amendment for multiple ionization effects, a mutually consistent set of ionization cross sections is extracted from $L\alpha$ and six pairs of other $L$-line x-ray production cross sections. Extracted $L_1$-, $L_2$-, $L_3$-ionization cross sections are compared with the predictions of the ECPSSR theory—which accounts for the energy $\left(E\right)$ loss and Coulomb $\left(C\right)$ deflection of the projectile as well as for perturbed-stationary state (PSS) and relativistic $\left(R\right)$ nature of $L$ subshells—and its modification, ECUSAR-IS. In the ECUSAR-IS theory, the PSS effect is calculated with a united and separated atom (USA) treatment and the intrashell (IS) coupling is accounted for by multiplicative factors of Sarkadi and Mukoyama normalized so that the sum of $L$-subshell ECUSAR-IS cross sections equals ECUSAR $L$-shell ionization cross section without the IS correction. Further improvement of this theory to account for better wave functions in its evaluation is made by scaling it with ratios of Dirac-Hartree-Slater cross sections to the screened hydrogenic formulas used in the ECPSSR theory. Very good agreement is obtained with $L_2$ and $L_3$ ionization data. For the $L_1$ subshell, the data are in good agreement with the ECPSSR theory but are by factors of 2 to 3 above the results of its modifications.

An eigenchannel method for nonrelativistic quantum scattering from an arbitrary system of zero-range potentials is presented. Eigenchannel vectors are defined as characteristic vectors of an auxiliary Hermitian matrix spectral problem with a positive semidefinite weight; real eigenvalues to this problem are the negative cotangents of eigenphase shifts. The eigenchannel vectors and the eigenphase shifts are used to construct particular solutions, called eigenchannels, of the pertinent Schrödinger equation. Analysis of the asymptotics of the eigenchannels in the far zone leads to a definition of eigenchannel harmonics, which for the problem at hand play the role analogous to that played by spherical harmonics for scattering in a central field. Representations of a far-field amplitude (for scattering of particles emitted from a point source) as well as a scattering amplitude, a scattering kernel, total, and total averaged cross sections (for scattering of a parallel beam of projectiles) in terms of the eigenphase shifts and the eigenchannel harmonics are derived. As an illustrative example, scattering of a plane wave from a system of four identical zero-range potentials, located in vertices of a regular tetrahedron, is worked out in detail.

The satellite and hypersatellite $K$ x-ray emission of a thin Mg foil and thick polycrystalline Si target bombarded by $34\text{‐}\mathrm{MeV}$ C and $50\text{‐}\mathrm{MeV}$ Ne ions was measured using high-resolution crystal diffractometry. The corresponding projectile reduced velocities $v∕v_K$ were 1.09 and 0.92 for C ions and 1.02, 0.86 for Ne ions in case of Mg and Si targets, respectively. An energy resolution of approximately $0.5\mathrm{eV}$ enabled separation of contributions corresponding to states with different numbers of $K$- and $L$-shell vacancies. The relative intensities of satellite and hypersatellite lines were determined by fitting the measured spectra with line shapes calculated using the GRASP92 computer code. To determine the production yields of initial states from the measured x-ray yields, the total decay schemes of initial states were considered. The decay schemes were also used to determine the relative intensities of components contributing to the observed $K\alpha$ satellites and hypersatellites and $K\beta$ satellite intensities. Including theoretical predictions in the fitted model is crucial to analyze properly the $K\alpha$ hypersatellite region which overlaps the $K\beta$ satellites. The initial-state production yields were then used to determine the $L$-shell ionization probabilities and the double- to single-$K$-shell ionization ratio corresponding to the four investigated collisions. The experimental values were compared to the theoretical predictions obtained within the independent electron model using single-electron ionization probabilities calculated by the three-body classical trajectory Monte Carlo (CTMC) method. Since the targets used were thick enough, the equilibrium projectile charge-state distributions in the solid media were assumed. While for the double- to single-$K$-shell ionization ratios a satisfactory agreement was observed between the CTMC predictions and our experimental results, the $L$-shell ionization probabilities were found to be overestimated by the CTMC calculations by a factor of about 2.

A quantum-mechanical (QM) and semiclassical (SC) study of inelastic collisions in collinear three-body Coulomb systems below the three-body disintegration threshold is presented. The QM results are obtained by solving the stationary Schrödinger equation in hyperspherical coordinates using the slow/smooth variable discretization method. After appropriate rescaling of the hyperspherical coordinates, an asymptotic parameter $0⩽h⩽1$ that depends only on the masses of particles and has the meaning of an effective Planck’s constant for the motion in hyperradius emerges. The SC results are obtained in the leading order approximation of the asymptotic expansion in $h$. The main attention is paid to investigating how the SC and QM results converge as $h\to 0$. It is shown that the overall agreement for a wide spectrum of systems and processes is surprisingly good even for $h\sim 1$. However, because of interference effects the convergence is not monotonic, and the SC results may be grossly in error in the situations where a destructive interference occurs. The analysis of hidden crossings clarifies mechanisms of the nonadiabatic transitions. It is shown that if the oppositely charged particle is located between the two others, the nonadiabatic transitions occur near the top of the potential barrier via the well-known $T$ series of hidden crossings. If it is located on one end of the system, then there is no potential barrier for real values of the angular variable, but there still exists an extremum in the complex plane; the mechanism of nonadiabatic transitions in this case is called the complex $T$ series of hidden crossings.

Narrow line laser cooling is advancing the frontier for experiments ranging from studies of fundamental atomic physics to high precision optical frequency standards. In this paper, we present an extensive description of the systems and techniques necessary to realize $689\mathrm{nm}$ ${}^{1}S_0\text{−}{}^{3}P_1$ narrow line cooling of atomic ${}^{88}\mathrm{Sr}$. Narrow line cooling and trapping dynamics are also studied in detail. By controlling the relative size of the power broadened transition linewidth and the single-photon recoil frequency shift, we show that it is possible to smoothly bridge the gap between semiclassical and quantum mechanical cooling. Novel semiclassical cooling processes, some of which explicitly depend on the relative size of gravity and the radiative force, are also explored. Moreover, for laser frequencies tuned above the atomic resonance, we demonstrate momentum-space crystals containing up to 26 well defined lattice points. Gravitationally assisted cooling is also achieved with blue-detuned light. Theoretically, we find the blue detuned dynamics are universal to Doppler limited systems. This paper offers the most comprehensive study of narrow line laser cooling to date.

The influence of dynamical medium depletion in high-order above-threshold ionization (ATI) in left/right asymmetry of photoelectron energy spectra is analyzed. Based on a classical analysis of high-order ATI electrons produced by few-cycle laser pulses, calculated asymmetry maps of electron spectra reproduce very well the experimental results reported in Lindner et al. [Phys. Rev. Lett. 92, 113001 (2004)], utilized for determining the Guoy phase shift of few-cycle laser pulses. The anomalous behavior of the high-energy part of the ATI electron spectra is, then, fully understood in terms of earlier medium depletion occurring in the leading edge of the laser pulse. In order to correctly reproduce the experimental findings a physical temporal envelope of the laser pulse, which only vanishes at the infinity, plays a crucial role.

Motivated by its relation to an $\mathcal{NP}$-hard problem, we analyze the ground-state properties of antiferromagnetic Ising-spin networks embedded on planar cubic lattices, under the action of homogeneous transverse and longitudinal magnetic fields. This model exhibits a quantum phase transition at critical values of the magnetic field, which can be identified by the entanglement behavior, as well as by a majorization analysis. The scaling of the entanglement in the critical region is in agreement with the area law, indicating that even simple systems can support large amounts of quantum correlations. We study the scaling behavior of low-lying energy gaps for a restricted set of geometries, and find that even in this simplified case, it is impossible to predict the asymptotic behavior, with the data allowing equally good fits to exponential and power-law decays. We can therefore draw no conclusion as to the algorithmic complexity of a quantum adiabatic ground-state search for the system.

The ultrafast control of large polyatomic molecules in the gas and condensed phases entails working with a randomly oriented ensemble. During the short control period, little reorientation may occur, especially for cases in the condensed phases. This paper addresses the degree to which all members of the ensemble may be simultaneously controlled with respect to their internal motion by a single laser pulse. It is shown that all members of the ensemble are fully controllable if any one member is. Numerical optimal control simulations also show that excellent quality full ensemble control can be achieved even with reasonable constraints placed on the control fields. Although the full ensemble may be controlled to a high degree, the control mechanism is likely to differ for each ensemble member.

We study vortices in a radially inhomogeneous superfluid, as realized by a trapped degenerate Bose gas in a uniaxially symmetric potential. We show that, in contrast to a homogeneous superfluid, an off-axis vortex corresponds to an anisotropic superflow whose profile strongly depends on the distance to the trap axis. One consequence of this superflow anisotropy is vortex precession about the trap axis in the absence of an imposed rotation. In the complementary regime of a finite prescribed rotation, we compute the minimum-energy vortex density, showing that in the rapid-rotation limit it is extremely uniform, despite a strongly inhomogeneous (nearly) Thomas-Fermi condensate density ${\rho }_s\left(r\right)$. The weak radially dependent contribution $[\propto {\nabla }^2\ln {\rho }_s\left(r\right)]$ to the vortex distribution, that vanishes with the number of vortices $N_v$ as $1∕N_v$, arises from the interplay between vortex quantum discreteness (namely their inability to faithfully support the imposed rigid-body rotation) and the inhomogeneous superfluid density. This leads to an enhancement of the vortex density at the center of a typical concave trap, a prediction that is in quantitative agreement with recent experiments. One striking consequence of the inhomogeneous vortex distribution is an azimuthally directed, radially shearing superflow.

We discuss a simple search problem which can be pursued with different methods, either on a classical or on a quantum basis. The system is represented by a chain of trapped ions. The ion to be searched for is a member of that chain, consisting, however, of an isotopic species different from the others. It is shown that classical imaging may lead to the final result as fast as quantum imaging. However, for the discussed case the quantum method gives more flexibility and higher precision when the number of ions considered in the chain increases. In addition, interferences are observable even when the distances between the ions are smaller than half a wavelength of the incident light.

The possibility of using strongly and continuously interacting spins for quantum computation has recently been discussed. Here we present a simple optical scheme that achieves this goal while avoiding the drawbacks of earlier proposals. We employ a third state, accessed by a classical laser field, to create an effective barrier to information transfer. The mechanism proves to be highly efficient both for continuous and pulsed laser modes; moreover, it is very robust, tolerating high decay rates for the excited states. The approach is applicable to a broad range of systems, in particular, dense structures such as solid-state self-assembled (e.g., molecular) devices. Importantly, there are existing structures upon which “first-step” experiments could be immediately performed.

The zero-temperature phase diagram of a Bose-Einstein condensate confined in realistic one-dimensional $\mathit{\ell }$-periodic optical superlattices is investigated. The system of interacting bosons is modeled in terms of a Bose-Hubbard Hamiltonian whose site-dependent local potentials and hopping amplitudes reflect the periodicity of the lattice partition in $\mathit{\ell }$-site cells. Relying on the exact mapping between the hardcore limit of the boson Hamiltonian and the model of spinless noninteracting fermions, incompressible insulator domains are shown to exist for rational fillings that are predicted to be compressible in the atomic limit. The corresponding boundaries, qualitatively described in a multiple-site mean-field approach, are shown to exhibit an unusual loophole shape. A more quantitative description of the loophole domain boundaries at half filling for the special case $\mathit{\ell }=2$ is supplied in terms of analytic strong-coupling expansions and quantum Monte Carlo simulations.

We propose a physical mechanism that leads to the emergence of secondary threshold laws in processes of multiple ionization of atoms. We argue that the removal of $n$ electrons $(n>2)$ from a many-electron atom may proceed via intermediate resonant states of the corresponding doubly charged ion. For atoms such as rare gases, the density of such resonances in the vicinity of subsequent ionization thresholds is high. As a result, the appearance energies for multiply charged ions are close to these thresholds, while the effective power indices $\mu$ in the near-threshold energy dependence of the cross section, $\sigma \propto E^{\mu }$, are lower compared to those from the Wannier theory. This provides a possible explanation of the recent experimental results of B. Gstir et al. [Nucl. Instrum. Methods Phys. Res. B 205, 413 (2003)].

We emulate the ground state and the single-vortex state of a Bose-Einstein condensate in an isotropic harmonic trap by constructing analytic simulacra of the wave functions in the regions around the origin and far from the origin. These simulacra are generalizations of asymptotic solutions of the nonlinear Schrodinger equation and they are matched by requiring continuity not only of the wave function and of its slope, but of its curvature as well. The resulting piecewise analytic simulacra coincide almost perfectly with the numerically obtained solutions. Analytic expressions are obtained for the kinetic energy and the number of atoms, and they too are in very good agreement with the corresponding numerical results.

The cross sections for the ionization $\overline{p}+\mathrm{H}\to \overline{p}+p+e$ at low collision energies are computed with a complete quantum-mechanical method of time-dependent wave-packet propagation, which was applied to the protonium formation $(\to \overline{p}p+e)$ by the present author [Phys. Rev. A 65, 012706 (2002)]. The ionization process shows very large cross sections even near threshold energy. An impact-parameter semiclassical method, in which the trajectory bending is taken into account by the introduction of the adiabatic potential, is also examined for the calculation of the ionization cross section. The semiclassical results are in good agreement with the quantum-mechanical results.