Experimental 2$p$ x-ray-absorption spectra of 3$d$ transition-metal cations in their electronic ground states were obtained in photoion-yield detection. Individual transitions are assigned within the $Z+1$ approximation and Hartree-Fock calculations, which reproduce the experimental spectra with good agreement. For 3$d$ transition metals, 2$p$ x-ray-absorption spectra are nearly identical for atoms and cations with equal 3$d$ electron configurations. The oscillator strengths of $2p\to 3d$ transitions in 3$d$ transition-metal cations are proportional to the number of unoccupied 3$d$ states in accordance with bulk data. The “continuum step” does not coincide with the direct 2$p$ photoionization threshold but is related to resonant transitions into Rydberg states. For nickel cations, a 2$p$ core-hole lifetime of $1.6\pm 0.1$ fs is derived from the natural linewidth, which is $0.1$–$0.2$ eV smaller than for nickel adatoms and bulk because of the absence of inhomogeneous broadening.

The most challenging scenario for Kohn-Sham density-functional theory, that is, when the electrons move relatively slowly trying to avoid each other as much as possible because of their repulsion (strong-interaction limit), is reformulated here as an optimal transport (or mass transportation theory) problem, a well-established field of mathematics and economics. In practice, we show that to solve the problem of finding the minimum possible internal repulsion energy for $N$ electrons in a given density $\rho \left(\mathbf{r}\right)$ is equivalent to find the optimal way of transporting $N-1$ times the density $\rho$ into itself, with the cost function given by the Coulomb repulsion. We use this link to set the strong-interaction limit of density-functional theory on firm ground and to discuss the potential practical aspects of this reformulation.

We propose a concrete experiment to probe the nonequilibrium local dynamics of the one-dimensional Bose-Hubbard model using a trapped ion system consisting of a linear chain of few ions prepared in a state of transverse motional mode which corresponds to a fixed number of phonons per ion. These phonons are well known to be described by an effective Bose-Hubbard model. We propose a protocol which leads to a sudden local sign reversal of the on-site interaction strength of this Hubbard model at one of the sites and demonstrate that the subsequent nonequilibrium dynamics of the model can be experimentally probed by measuring the time-dependent phonon number in a specific motional state of the ions. We back our experimental proposal with exact numerical calculation of the dynamics of a Bose-Hubbard model subsequent to a local quench.

Experimental investigation of laser-induced quadrupole-quadrupole collisional energy transfer between Xe and Kr is reported in this paper. The excitation spectrum of laser-induced collisional energy transfer (LICET) is characterized by a slowly decreasing tail on the blue side of the peak and a width of ∼30 cm${}^{-1}$. The experimental evidence shows that in the quasistatic wing the quadrupole-quadrupole LICET spectrum follows a power law that is different from the dipole-dipole LICET line shape and the profile of the quadrupole-quadrupole LICET decreases more slowly than the dipole-dipole LICET profile. The results indicate that the laser-induced quadrupole-quadrupole collision can be considered as a practical process to transfer energy selectively from a storage state making a parity-nonallowed transition to a target state making a parity-allowed transition.

We suggest that Bose-Einstein condensates in optical lattices subjected to ac forcing with a smooth envelope may provide detailed experimental access to multiphotonlike transitions between ac-Stark-shifted Bloch bands. Such transitions correspond to resonances described theoretically by avoided quasienergy crossings. We show that the width of such anticrossings can be inferred from measurements involving asymmetric pulses. We also introduce a pulse tracking strategy for locating the particular driving amplitudes for which resonances occur. Our numerical calculations refer to a currently existing experimental setup [E. Haller, R. Hart, M. J. Mark, J. G. Danzl, L. Reichsöllner, and H.-C. Nägerl, Phys. Rev. Lett. 104, 200403 (2010)].

We study the quantum phase transition from a superfluid to a Mott insulator in optical lattices using a Bose-Hubbard Hamiltonian. For this purpose we develop a field theoretical approach in terms of path integral formalism to calculate the second-order quantum corrections to the energy density as well as to the superfluid fraction in cubic optical lattices. Using the present approach, the condensate fraction and ground-state energy are calculated as functions of the $s$-wave scattering length. In contrast to the Bogoliubov model, which is, technically speaking, a one-loop approximation, we carry the calculation up to two loops and improve the result further by variational perturbation theory. The result suggests that the quantum phase transition exists.

We investigate static properties of laser-driven ultracold Rydberg atoms confined to one- and two-dimensional uniform lattices in the limit of vanishing laser coupling. The spectral structure of square lattices is compared to those of linear chains, and similarities as well as differences are pointed out. Furthermore, we employ a method based on elements of graph theory to numerically determine the laser-detuning-dependent ground states of various lattice geometries. Ground states for chains as well as square and rectangular lattices are provided and are discussed.

We demonstrate an effective mechanism for gain-controlled soliton routing in dissipative optical lattices. An effective particle model reveals the essential features of soliton dynamics in such structures. The results presented are directly applicable to general inhomogeneous systems where interplay between gain and loss mechanisms occurs. Focusing on the complexity of soliton dynamics rather than on the complexity of their profiles we have analyzed scenarios that are promising for all-optical control concepts and applications.

We present the results of an operational use of experimentally measured optical tomograms to determine state characteristics (purity) avoiding any reconstruction of quasiprobabilities. We also develop a natural way how to estimate the errors (including both statistical and systematic ones) by an analysis of the experimental data themselves. Precision of the experiment can be increased by postselecting the data with minimal (systematic) errors. We demonstrate those techniques by considering coherent and photon-added coherent states measured via the time-domain improved homodyne detection. The operational use and precision of the data allowed us to check purity-dependent uncertainty relations and uncertainty relations for Shannon and Rényi entropies.

We analyze spin dynamics in the tunneling decay of a metastable localized state in the presence of spin-orbit coupling. We find that the spin polarization at short-time scale is affected by the initial state, while at long-time scale both the probability and the spin density exhibit diffraction-in-time phenomenon. We find that in addition to the tunneling time the tunneling in general can be characterized by a new parameter, the tunneling length. Although the tunneling length is independent of the spin-orbit coupling, it can be accessed by the spin rotation measurement.

We examine the validity of the harmonic approximation, where the radio-frequency ion trap is treated as a harmonic trap, in the problem regarding the controlled collision of a trapped atom and a single trapped ion. This is equivalent to studying the effect of the micromotion since this motion must be neglected for the trapped ion to be considered as a harmonic oscillator. By applying the transformation of Cook and Shankland we find that the micromotion can be represented by two periodically oscillating operators. In order to investigate the effect of the micromotion on the dynamics of a trapped atom-ion system, we calculate (i) the coupling strengths of the micromotion operators by numerical integration and (ii) the quasienergies of the system by applying the Floquet formalism, a useful framework for studying periodic systems. It turns out that the micromotion is not negligible when the distance between the atom and the ion traps is shorter than a characteristic distance. Within this range the energy diagram of the system changes remarkably when the micromotion is taken into account, which leads to undesirable consequences for applications that are based on an adiabatic process of the trapped atom-ion system. We suggest a simple scheme for bypassing the micromotion effect in order to successfully implement a quantum controlled phase gate proposed previously and create an atom-ion macromolecule. The methods presented here are not restricted to trapped atom-ion systems and can be readily applied to studying the micromotion effect in any system involving a single trapped ion.

We present experimental measurements and theoretical calculations of photoionization time delays from the $3s$ and $3p$ shells in Ar in the photon energy range of 32–42 eV. The experimental measurements are performed by interferometry using attosecond pulse trains and the infrared laser used for their generation. The theoretical approach includes intershell correlation effects between the $3s$ and $3p$ shells within the framework of the random-phase approximation with exchange. The connection between single-photon ionization and the two-color two-photon ionization process used in the measurement is established using the recently developed asymptotic approximation for the complex transition amplitudes of laser-assisted photoionization. We compare and discuss the theoretical and experimental results, especially in the region where strong intershell correlations in the $3s\to kp$ channel lead to an induced “Cooper” minimum in the 3s ionization cross section.

We study the problem of high-temperature Bose-Einstein condensation (BEC) of atom-light polaritons in a waveguide cavity appearing due to the interaction of two-level atoms with (nonresonant) quantized optical radiation in the strong-coupling regime and in the presence of optical collisions (OCs) with buffer-gas particles. Specifically, we propose a special biconical waveguide cavity (BWC), permitting localization and trapping of low-branch (LB) polaritons imposed by the variation of the waveguide radius in longitudinal direction. We have shown that the critical temperature of BEC occurring in the system can be high enough—a few hundred kelvins; it is connected with the photonlike character of LB polaritons and strongly depends on waveguide-cavity parameters. In the case of a linear trapping potential we obtain an Airy-shaped polariton condensate wave function which, when disturbed out of equilibrium, exhibits small-amplitude oscillations with the characteristic period in the picosecond domain.

We express the optical properties of multilayered hyperbolic metamaterials (HMMs) in terms of the Fresnel reflection coefficients at the boundary between the metamaterial and the ambient medium. Formation of a band of bulk propagating modes in HMMs located far outside the lightcone of homogeneous isotropic media is demonstrated. Exotic behavior of HMMs, such as the broadband Purcell effect and suppressed outward scattering, is reproduced. Conditions under which a metal-dielectric multilayer can be approximated by a homogeneous effective medium with extreme anisotropy (indefinite medium) are derived. It is shown that real multilayer HMMs usually have a smaller Purcell factor than the corresponding effective medium; however, the reverse scenario is shown to be possible due to an intermediary role of short-range surface plasmon excitations in the outermost metal layer in a metal-dielectric multilayer.

We demonstrate optical bistability in a ${\chi }^{\left(2\right)}$-nonlinear plasmonic nanocavity. The nanocavity is made from a metal-insulator-metal waveguide possessing stubs as realistic mirrors. The design of the nanocavity is sufficiently flexible to allow for resonances at both the fundamental and the second-harmonic frequency and a phase-matched nonlinear interaction. By using rigorous diffraction theory and a mean-field approach, we establish the conditions required to observe optical bistability and present optimal configurations with regard to a minimum pump power. This work might be useful for employing plasmonic nanocircuits in optical computing schemes.

We study two-species fermion gases with attractive interaction in two-dimensional optical lattices, producing an array of elongated tube confinements. Focusing on the interplay of Cooper pairing, spin imbalance (or magnetization), and intertube tunneling, we find the pairing gap can exhibit oscillatory behavior both along and across the tubes, reminiscent of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We obtain a Bose-Hubbard-like phase diagram that shows that the magnetization of the system undergoes an incompressible-compressible transition as a function of magnetic field and intertube tunneling strength. We find the parity of tube-filling imbalance in incompressible states is protected by that of the oscillatory pairing gap. Finally, we discuss signatures of this transition and thus (indirectly) of the FFLO pairing in cold-atom experiments.

Entanglement and violation of Bell inequalities are aspects of quantum nonlocality that have been often confused in the past. It is now known that this equivalence is only true for pure states. Even though almost all the studies of quantum correlations at quantum phase transitions deal only with entanglement, we here argue that Bell inequalities can also reveal a general quantum phase transition. This is also shown for a particular case of two spin-$\frac{1}{2}$ particles in an infinite one-dimensional chain described by the XXZ model. In this case, the Bell inequality is able to signal not only the first-order phase transition, but also the infinite-order Kosterlitz-Thouless quantum phase transition, which cannot be revealed either by the energy of the system nor by the bipartite entanglement. We also show that although the nearest-neighbor spins are entangled, they, unexpectedly, never violate the Bell inequality. This indicates that the type of entanglement which is relevant for quantum phase transition is not trivial, i.e., it cannot be revealed by the Bell inequality.

We study a class of nonlinear waveguide arrays in which the waveguides are endowed with ${\chi }^{\left(2\right)}$ nonlinearity and coupled through the evanescent overlap of the guided modes. We investigate the viability of such an array as a platform for generating both bipartite and tripartite continuous-variable entanglement. We explicitly address the effect of realistic losses on the entanglement produced, discuss the possible types of nonlinear materials that could be used, and suggest solutions for the possible phase matching issues in the waveguides. The simultaneous generation and manipulation of the light on a single waveguide chip circumvents the usual bandwidth problems associated with the use of external bulky optical elements and makes this avenue promising for further investigation.

We study the relation between the electromagnetic vacuum energy of a random medium and its optical response. The medium is modeled by a collection of molecular electric dipoles. First, we evaluate the contribution of statistical fluctuations to the average total vacuum energy, which is made out of the integration of the variations of the Lamb shift of the individual dipoles with respect to the coupling constant. While the Lamb shift is a function of the electrical susceptibility only, the vacuum energy is generally not. Second, we compare several approximations to the computation of the vacuum energy. In particular, we make clear why the bulk energy of an effective medium does not account for the total vacuum energy of a molecular dielectric. Consequently, the Lamb shift does not derive from the effective medium bulk energy except at leading order in the molecular density. The local field factors provide natural cutoffs for the spectrum of the total vacuum energy at a wavelength of the order of the correlation length. Third, we investigate to what extent the shift of the resonant frequency of the dielectric constant may be attributed to the binding energy of a dielectric. In particular, in the effective medium approximation we have found an equivalence between the energy of longitudinal long-wavelength modes and the Lorentz-Lorenz shift. Nonetheless, we conclude that the dielectric constant resonance shift is insufficient to estimate the binding energy of molecular clusters.

We report a simple method for the creation of Bose-Einstein condensates of ${}^{85}$Rb by direct evaporation in a crossed optical dipole trap. The independent control of the trap frequencies and magnetic bias field afforded by the trapping scheme permits full control of the trapped atomic sample, enabling the collision parameters to be easily manipulated to achieve efficient evaporation in the vicinity of the 155 G Feshbach resonance. We produce nearly pure condensates of up to $4\times {10}^4$ atoms and demonstrate the tunable nature of the atomic interactions.