The meta-generalized-gradient-approximation (meta-GGA) for the exchange-correlation energy, as constructed by Tao, Perdew, Staroverov, and Scuseria (TPSS) [Phys. Rev. Lett. 91, 146401 (2003)], has achieved usefully consistent accuracy for diverse systems and is the most reliable nonempirical density functional (and the most reliable nonhybrid) in common use. We present here an optimized version of this TPSS functional obtained by empirically fitting a single free parameter that controls the approach of the exchange enhancement factor to its rapidly-varying-density limit, while preserving all the exact constraints that the original TPSS functional satisfies. We find that molecular atomization energies are significantly improved with the optimized version and are even better than those obtained with the best hybrid functionals employing a fraction of exact exchange (e.g., the TPSS hybrid), while energy barrier heights are slightly improved; jellium surface energies remain accurate and almost unchanged. The one-parameter freedom of the TPSS functional may be useful even beyond the meta-GGA level, since the TPSS approximation is a natural starting point for the higher-level hyper-GGA.

Within the framework of a model of a hollow atom as a hydrogenlike multicharged ion located at the center of a spherical shell formed by highly excited electrons, the photoionization cross sections of the inner $1s$ level of the ion have been calculated. The results show that the existence of the outer electronic shell of the hollow atom results in oscillations in the energy dependence of the photoionization cross section. It has been demonstrated also that the photoionization cross section as a function of photon energy is extremely sensitive to the magnitude of the discontinuity of the electric field at the surface of the outer electronic shell.

We have investigated the intermediate stages of electron capture into Rydberg states of multiply charged ions (core charge $Z\gg 1$, principal quantum number $n_A\gg 1$) escaping solid surfaces at low velocity. The time-symmetrized, two-state vector model of the process is proposed by using both initial and final states of the ion-surface system. The two conditions determine two wave functions and both are used to describe the system at intermediate stages. The appropriate probabilities and rates are defined and calculated from the corresponding mixed flux. Taking into account both the surface polarization and the polarization of the electronic cloud of the ionic core, the probabilities and rates are obtained in a simple analytical form; the population of the Rydberg levels of the ions $\mathrm{Ar}\mathrm{VIII}$, $\mathrm{Kr}\mathrm{VIII}$, and $\mathrm{Xe}\mathrm{VIII}$ interacting with an Al surface is considered as an example. The quasiresonant character of the process is demonstrated, as well as the complementarity of the neutralization and ionization processes for the $A^{Z+}$ ions escaping the surface and the $A^{(Z-1)+}$ ions approaching the surface, respectively. The neutralization distances for the ions finally detected in a given Rydberg state are obtained from the calculated rates. Although defined under different physical conditions, the results obtained are in agreement with the coupled-angular-mode theoretical predictions.

We perform a detailed analysis of high-order harmonic generation in diatomic molecules within the strong-field approximation (SFA), with emphasis on quantum-interference effects. Specifically, we investigate how the different types of electron orbits, involving one or two centers, affect the interference patterns in the spectra. We also briefly address the influence of the choice of gauge and of the initial and final electronic bound states on such patterns. For the length-gauge SFA and undressed bound states, there exist additional terms, which can be interpreted as potential energy shifts. If, on the one hand, such shifts alter the potential barriers through which the electron initially tunnels, and may lead to a questionable physical interpretation of the features encountered, on the other hand, they seem to be necessary in order to reproduce the overall maxima and minima in the spectra. Indeed, for dressed electronic bound states in the length gauge, or undressed bound states in the velocity gauge, for which such shifts are absent, there is a breakdown of the interference patterns. In order to avoid such a problem, we provide an alternative pathway for the electron to reach the continuum, by means of an additional attosecond-pulse train. A comparison of the purely monochromatic case with the situation for which the attosecond pulses are present suggests that the patterns are due to the interference between the electron orbits which finish at different centers, regardless of whether one or two centers are involved.

In the field of optical trapping and micromanipulation it is well known that linearly polarized Gaussian beams, which possess no inherent angular momentum, can exert an orienting torque on optically or geometrically anisotropic particles. Conservation of angular momentum requires that the application of such a torque be compensated for by an equivalent, and opposite, angular momentum flux in the beam. In the following paper we analyze this effect in terms of both the scattered field, and the mechanical torque experienced by the particle. It is demonstrated that, in general, the scattered field has a complicated form, carrying both spin and orbital angular momentum. However, we show that the variation of torque with rotation angle is identically equal to $A+B\sin (2\alpha +\beta )$ for arbitrarily shaped particles, where $A$, $B$, and $\beta$ are constants and $\alpha$ is the angular displacement of the major axis of the particle from the polarization direction. The scattered field, and the mechanical torque, are seen to reduce to qualitatively distinct forms that depend on the symmetry group of the scattering particle. Our findings are verified and illustrated by a series of numerical calculations of the forces and torques experienced by arbitrarily shaped particles trapped in linearly polarized Gaussian beams.

In this paper, we present a detailed investigation of the laser cooling and trapping of the Zn atom, and various schemes employing the ${{}^{1}S}_0\text{−}{{}^{3}P}_0$ transition, induced by nuclear magnetic moment or applied fields, as the clock transition. Using numerical simulations, the deceleration of Zn by a Zeeman slower and its capture by a magneto-optical trap (MOT) are analyzed, and the corresponding parameters are determined. The linear loss rate and the coefficient for two-body collisional loss in the MOT are discussed. To prove the feasibility of the intercombination line cooling, one-dimensional semiclassical Monte Carlo simulations are performed. Multiconfiguration Hartree-Fock and multiconfiguration Dirac-Fock approaches are employed to calculate the hyperfine-induced ${{}^{1}S}_0\text{−}{{}^{3}P}_0$ transition. Up to now, various schemes inducing the ${{}^{1}S}_0\text{−}{{}^{3}P}_0$ transition in bosonic isotopes have been proposed for alkaline-earth-metal atoms and Yb. Their applicability for Zn are investigated, and the corresponding parameters of Zn are calculated. Our results show that the Zn atom, either fermionic or bosonic, is a potential candidate for the quantum absorber used in laser-cooled neutral atomic optical frequency standard.

We consider a trapped Bose-Einstein condensate (BEC) with a highly quantized vortex. For the BEC with a doubly, triply, or quadruply quantized vortex, the numerical calculations have shown that the Bogoliubov-de Gennes equations, which describe the fluctuation of the condensate, have complex eigenvalues. In this paper, we obtain the analytic expression of the condition for the existence of complex modes, using the method developed by Rossignoli and Kowalski [R. Rossignoli and A. M. Kowalski, Phys. Rev. A 72, 032101 (2005)] for the small coupling constant. To derive it, we make the two-mode approximation. With the derived analytic formula, we can identify the quantum numbers of the complex modes for each winding number of the vortex. Our result is consistent with those obtained by the numerical calculation in the case that the winding number is two, three, or four. We prove that the complex modes always exist when the condensate has a highly quantized vortex.

We study the reduced single-particle density matrix (RSPDM), the momentum distribution, and natural orbitals and their occupancies of dark “soliton” (DS) states in a Tonks-Girardeau gas. DS states are specially tailored excited many-body eigenstates, which have a dark solitonic notch in their single-particle density. The momentum distribution of DS states has a characteristic shape with two sharp spikes. We find that the two spikes arise due to the high degree of correlation observed within the RSPDM between the mirror points ($x$ and $-x$) with respect to the dark notch at $x=0$; the correlations oscillate rather than decay as the points $x$ and $-x$ are being separated.

Joint signal-idler photoelectron distributions of twin beams containing several tens of photons per mode have been measured recently. Exploiting a microscopic quantum theory for joint quasidistributions in parametric down-conversion developed earlier we characterize properties of twin beams in terms of quasidistributions using experimental data. Negative values as well as oscillating behavior in the quantum region are characteristic for the subsequently determined joint signal-idler quasidistributions of integrated intensities. Also the conditional and difference photon-number distributions are shown to be sub-Poissonian and sub-shot-noise, respectively.

We propose an experimental setup to probe the low-lying excitation modes of a parametrically oscillating planar cavity, in particular the soft Goldstone mode which appears as a consequence of the spontaneously broken $\text{U}\left(1\right)$ symmetry of signal-idler phase rotations. A strong and narrow peak corresponding to the Goldstone mode is identified in the transmission spectrum of a weak probe beam incident on the cavity. When the $\text{U}\left(1\right)$ symmetry is explicitly broken by an additional laser beam pinning the signal-idler phase, a gap opens in the dispersion and the Goldstone peak is dramatically suppressed. Quantitative predictions are given for the case of semiconductor planar cavities in the strong exciton-photon coupling regime.

By introducing a quantitative “degree of commutativity” in terms of the angle between spin observables we present two tight quantitative trade-off relations in the case of two qubits. First, for entangled states, between the degree of commutativity of local observables and the maximal amount of violation of the Bell inequality: if both local angles increase from zero to $\pi ∕2$ (i.e., the degree of local commutativity decreases), the maximum violation of the Bell inequality increases. Secondly, a converse trade-off relation holds for separable states: if both local angles approach $\pi ∕2$ the maximal value obtainable for the correlations in the Bell inequality decreases and thus the non-violation increases. As expected, the extremes of these relations are found in the case of anticommuting local observables where, respectively, the bounds of $2\sqrt{2}$ and $\sqrt{2}$ hold for the expectation value of the Bell operator. The trade-off relations show that noncommmutativity gives “a more than classical result” for entangled states, whereas “a less than classical result” is obtained for separable states. The experimental relevance of the trade-off relation for separable states is that it provides an experimental test for two qubit entanglement. Its advantages are twofold: in comparison to violations of Bell inequalities it is a stronger criterion and in comparison to entanglement witnesses it needs to make less strong assumptions about the observables implemented in the experiment.

An exactly solvable model for the decoherence of one and two-qubit states interacting with a spin bath, in the presence of a time-dependent magnetic field is studied. The magnetic field is static along $\widehat{z}$ direction and oscillatory in the transverse plane. The transition probability and Rabi oscillations between the spin states of a single qubit is shown to depend on the size of bath, the distribution of qubit-bath couplings, and the initial bath polarization. In contrast to the fast Gaussian decay for short times, the polarization of the qubit shows an oscillatory power-law decay for long times. The loss of entanglement for the maximally entangled two-qubit states can be controlled by tuning the frequency of the rotating field. The decay rates of entanglement and purity for all the Bell states are the same when the qubits are noninteracting, and different when they are interacting.

We study entanglement dynamics between four qubits interacting through two isolated Jaynes-Cummings Hamiltonians, via an entanglement measure based on the wedge product. We compare the results with similar results obtained using bipartite concurrence resulting in what is referred to as “entanglement sudden death.” We find a natural entanglement invariant under evolution, demonstrating that entanglement spreads out over all of the system’s degrees of freedom that become entangled through the interaction. We also provide an analysis of why certain initial states lose all their entanglement in a finite time, although their excitation and coherence vanish only asymptotically with time.

We study fluorescence x rays emitted from multiply inner-shell excited states produced by high-brightness x-ray absorption. The pulses of the fluorescence x rays from the multiply inner-shell excited states are shorter than that of the original x-ray source. As the pulse of x-ray sources becomes shorter, hollow atoms are produced more efficiently.

A theoretical study on electron collisions with $\mathrm{SiF}$ and ${\mathrm{SiF}}_2$ radicals in the low- and intermediate-energy range is reported. More specifically, calculated elastic differential, integral, and momentum transfer cross sections as well as total and total absorption cross sections are presented in the $1–1000\text{−}\mathrm{eV}$ energy range. A complex optical potential is used to represent the electron-radical interaction dynamics, whereas the iterative Schwinger variational method combined with the distorted-wave approximation is used to solve the scattering equations. Comparison of the present results with the available theoretical and experimental results in the literature is made.

The cathodoluminescence spectra of free xenon clusters produced by condensation of xenon-argon gas mixtures in supersonic jets expanding into vacuum were studied. By varying the initial experimental parameters, including the xenon concentration, we could obtain clusters with a xenon core (300–3500 atoms) covered by an argon outer shell as well as shell-free xenon clusters ($\approx 1500$ atoms). The cluster size and temperature ($\approx 40\mathrm{K}$ for both cases) were measured electronographically. Luminescence bands evidencing the existence of bulk and surface excitons were detected for shell-free xenon clusters. The emission from bulk excitons in small clusters is supposed to be due to processes of their multiple elastic reflections from the xenon-vacuum interface. The presence of an argon shell causes extinction of the excitonic bands. In addition, some bands were found which have no analogs for bulk xenon cryosamples.

We propose that micrometer-sized atom traps can be created using the optical dipole force between the ends of two single-mode optical fibers carrying counterpropagating light beams of two different wavelengths from both fibers. The traps have a simple design that is feasible to implement with commercially available products. They can be used as a flexible “atom tweezer” to manipulate atoms in free space without the need for traditional focused laser beams. A particularly interesting feature is the formation of a static ring-shaped trap for properly chosen beam parameters. Furthermore, this ring can be split into two longitudinally adjacent rings. Microscopic ring traps such as this could have important applications in atom interferometry and fundamental investigations of Bose-Einstein condensates.

We have developed an ab initio $R$-matrix-based approach for the time-dependent description of the multielectron response of complex atoms irradiated by intense ultrashort laser pulses. Ionization rates for Ar irradiated by intense $390\mathrm{nm}$ laser light are in excellent agreement with the most accurate rates available. The present approach shows how complex atomic structure affects the atomic response in the time domain. The approach extends the range of intensities, for which accurate ionization rates can be obtained for complex multielectron atoms, and the amount of atomic structure that can be included at high intensities, compared to the $R$-matrix Floquet approach. Because of these advantages, the approach is highly promising for the ab initio investigation of the multielectron response to intense ultrashort light pulses.

Doppler cooling on narrow transitions has become a crucial technique for preparing ultracold samples of alkaline-earth-metal and alkaline-earth-metal-like atoms. For lighter species, such as calcium and magnesium, this technique relies on artificial broadening (quenching) of the upper level of the narrow line. We report on quenching experiments on a ${}^{24}\mathrm{Mg}$ atomic beam. The branching ratio of the ${\left(3s4s\right)}^1{S}_0$ state was determined to be $\beta =(1.33\pm 0.53)\times {10}^{-5}$ from the measured quenching efficiency. The branching ratio combined with the known linewidth of this state yields a transition rate for ${\left(3s3p\right)}^3{P}_1\to {\left(3s4s\right)}^1{S}_0$ of ${\Gamma }_{23}=283\pm 114{\mathrm{s}}^{-1}$, i.e., one order of magnitude smaller than estimated from semiempirical data. We have applied different numerical approaches, including ab initio relativistic many-body calculations, to compute the transition probabilities of the ${\left(3s3p\right)}^3{P}_1\to {\left(3s4s\right)}^1{S}_0$ and ${\left(3s3p\right)}^1{P}_1\to {\left(3s4s\right)}^1{S}_0$ transitions. The results are in good agreement with our experimental observation. With the measured branching ratio, we expect a transfer efficiency of Doppler-cooled atoms into a quench magneto-optical trap (QuenchMOT) of approximately 1% for our experimental parameters. According to our simulations, the transfer efficiency can be increased by one order of magnitude for lower ensemble temperatures as recently demonstrated by two-photon cooling in our uv MOT.

We study a Bose-Einstein condensate of a dilute gas with dipolar interactions, at finite temperature, using the Hartree-Fock-Bogoliubov theory within the Popov approximation. An additional approximation involving the dipolar exchange interaction is made to facilitate the computation. We calculate the temperature dependence of the condensate fraction of a condensate confined in a cylindrically symmetric harmonic trap. We show that the biconcave-shaped condensates found in [Ronen et al. Phys. Rev. Lett. 98, 30406 (2007)] in certain pancake traps at zero temperature are also stable at finite temperature. Surprisingly, the dip in the central density of these structured condensates is actually enhanced at low finite temperatures. We explain this effect.