We study self-trapped localized nonlinear states in the form of truncated Bloch waves in one-dimensional optical lattices, which appear in the gaps of the linear band-gap spectrum. We demonstrate the existence of families of such localized states which differ by the number of intensity peaks. These families do not bifurcate from the band edge, and their power curves exhibit double branches. Linear-stability analysis demonstrates that in deep lattice potentials, the states corresponding to the lower branches are stable, whereas those corresponding to the upper branches are unstable, independently of the number of peaks.

We employ a time-dependent variational approach to investigate the dynamics of a fermionic atomic gas driven by a radio-frequency (rf) field at zero temperature. Starting from an initial Bardeen-Cooper-Schrieffer (BCS) state with pairing of atoms of two internal levels, an rf field transfers atoms to a third level. Dynamical equations derived from the variational principle are shown to be consistent with the time-dependent Bogoliubov–de Gennes equation. In particular, we show that the short-time dynamics is governed by a set of linear equations, in which an eigenvector associated with a discrete eigenvalue can be identified as the formation of a pair bound state in the final scattering channel. Such a bound state induces characteristic oscillations in the time evolution of the order parameter. At longer times numerical solutions demonstrate complicated dynamics where linear theory breaks down.

We study through controlled numerical simulation the ground-state properties of spin-polarized strongly interacting Fermi gas in an anisotropic optical lattice, which is described by an effective one-dimensional general Hubbard model with particle-correlated hopping rate. We show that the Fulde-Ferrell-Larkin-Ovchinnikov type of state, while enhanced by a negative correlated hopping rate, can be completely suppressed by positive particle-correlated hopping, yielding an unusual magnetic phase even for particles with on-site attractive interaction We also find several different phase-separation patterns for these atoms in an inhomogeneous harmonic trap, depending on the correlated hopping rate.

Entanglement swapping allows one to establish entanglement between independent particles that never interacted or share any common past. This feature makes it an integral constituent of quantum repeaters. Here, we demonstrate entanglement swapping with time-synchronized independent sources with a fidelity that is high enough to violate a Clauser-Horne-Shimony-Holt inequality by more than four standard deviations. The fact that both entangled pairs are created by fully independent only electronically connected sources ensures that this technique is suitable for future long-distance quantum communication experiments as well as for novel tests on the foundations of quantum physics.

The differential generalized oscillator strengths for ionization of the $s$ subshells of He and Ne atoms encapsulated inside a fullerene, ${\text{С}}_{60}$ cage, along with the single differential cross sections for ionization by fast electrons are calculated. The calculations have been performed using the two different model potentials to represent the fullerene shell. It is shown that the modulations of the wave function of the ejected electron caused by the interference between direct ejection and the waves scattered by the fullerene shell result in confinement resonances in the generalized oscillator strengths and the resulting impact-ionization cross sections. When the energy transfer to the target is close to that of the giant plasmon resonance in ${\text{C}}_{60}$, the interchannel interaction of the atomic ionization channels with the ${\text{C}}_{60}$ ionization channels significantly influences the cross section for impact ionization of the confined atom. The formulas describing this interaction are derived and it is shown that for small momentum transfer this interaction is related to the dynamic polarizability of ${\text{C}}_{60}$. The general formulas are used to calculate impact ionization both of the He atom confined in ${\text{C}}_{60}$ and of the empty ${\text{C}}_{60}$ cage. The cross section of the latter process is compared to available experimental data.

We performed global optimization and property calculations by density-functional theory for the series of $4d$ transition-metal clusters $M_{13}$, $M=\text{Y}-\text{Pd}$. Calculated Gibbs free energies suggest the coexistence of isomers, or spin states, other than the global minimum in all cases except maybe ${\text{Zr}}_{13}$ and ${\text{Pd}}_{13}$. The calculated infrared spectra of these isomers are typically very different. Calculated ionization energies and magnetic moments agree well with available experimental results but do not allow to assign the geometric structure. Analysis of relative isomer energies and their electronic density of states suggests that these clusters tend to follow a maximum hardness principle: the lowest energy states and geometric structures are often the ones with lowest density of states near the Fermi level and lowest spin magnetic moment. In going from left to right in the $4d$ series, the geometric structures evolve from icosahedral (Y, Zr), to distorted compact structures (Nb, Mo), to fcc or simple-cubic crystal fragments (Tc, Ru, Rh), and icosahedron again (Pd). We rationalize this trend on the basis of the increasingly localized nature of molecular orbitals in going from left to right and the importance of $d$-type orbital bonding in the middle of the series.

We report on the structures of six proposed global minima (GMs) of $M_{13}$ clusters ($M=\text{Ta}$, W, Re, Os, Ir, and Pt) and 62 isomers that are within roughly 1 eV of the GM. The GM and isomers were obtained after several global optimization runs using a first-principles (Perdew-Burke-Enzerhof exchange-correlation) method to evaluate the energy. The GM and lowest-energy isomers can be described qualitatively as amorphous and compact for Ta, W, and Pt; quasicrystalline for Re; and cubic-prismatic for Os and Ir. The icosahedron is more than 1 eV above the GM in all cases, except 0.56 eV for ${\text{Ta}}_{13}$. The ground-state electronic configuration of the atoms is essential to understand structural trends in the clusters. Elements with a nearly closed-shell ground-state atom (W and Pt) produce many more low-energy cluster isomers than elements with partially filled $d$ shells, and those isomers are generally compact and amorphous. Partially filled $d$ shells in Os and Ir lead to strong directional bonding and many $90°$ angles between nearest neighbors. The predicted spin multiplicity of the GM is 2 $\left({\text{Ta}}_{13}\right)$, 1 $\left({\text{W}}_{13}\right)$, 6 $\left({\text{Re}}_{13}\right)$, 5 $\left({\text{Os}}_{13}\right)$, 4 $\left({\text{Ir}}_{13}\right)$, and 3 $\left({\text{Pt}}_{13}\right)$, and the spin multiplicity of all isomers within 0.5 eV of the GM is within $\pm 2$ of these values and is smaller than 6.

We report on results of a systematic analysis of two-dimensional solitons and localized vortices in models including a rotating periodic potential and the cubic nonlinearity, with the latter being both self-attractive and self-repulsive. The models apply to Bose-Einstein condensates stirred by rotating optical lattices and to twisted photonic-crystal fibers, or bundled arrays of waveguides, in nonlinear optics. In the case of the attractive nonlinearity, we construct compound states in the form of vortices, quadrupoles, and supervortices, all trapped in the slowly rotating lattice, and identify their stability limits (fundamental solitons in this setting were studied previously). In rapidly rotating potentials, vortices decouple from the lattice in the azimuthal direction and assume an annular shape. In the model with the repulsive nonlinearity, which was not previously explored in this setting, gap solitons and vortices are found in both cases of the slow and rapid rotations. It is again concluded that the increase in the rotation frequency leads to the transition from fully trapped corotating vortices to ring-shaped ones. We also study “crater-shaped” vortices in the attraction model, which, unlike their compound counterparts, are trapped, essentially, in one cell of the lattice. Previously, only unstable vortices of this type were reported. We demonstrate that they have a certain stability region. Solitons and vortices are found here in the numerical form, and, in parallel, by means of the variational approximation.

We discuss approximate formulas for the dynamic structure factor of the one-dimensional Bose gas in the Lieb-Liniger model that appear to be applicable over a wide range of the relevant parameters such as the interaction strength, frequency, and wave number. The suggested approximations are consistent with the exact results known in limiting cases. In particular, we encompass exact edge exponents as well as the Luttinger-liquid and perturbation theoretic results. We further discuss derived approximations for the static structure factor and the pair distribution function $g\left(x\right)$. The approximate expressions show excellent agreement with numerical results based on the algebraic Bethe ansatz.

We provide further details on atom number fluctuation during spin-mixing dynamics inside an $F=1$ spinor condensate, based on the effective quantization approach we reported earlier [L. Chang et al., Phys. Rev. Lett. 99, 080402 (2007)] for the semiclassical nonrigid pendulum model in terms of the relative phase and the atomic population in the magnetic $\left(B\text{−}\right)$field insensitive hyperfine state $|F_z=0⟩$. Many features of the classical nonrigid pendulum model are reproduced. In addition, features typically associated with full quantum simulations specific to our model system, such as atom number fluctuations both in stationary states and during the dynamics of spin mixing, are faithfully revealed with our effective quantization approach. We check the validity of the effective quantization theory by performing extensive numerical comparisons with the results from full quantum many-body simulations. We study the effect of quantum coherence in our system and provide a solid theoretical basis to resolve the resolution limit in counting atoms that is needed to clearly detect quantum correlation effects in spin mixing.

We investigate the spectrum of a four-level V-type system. We show that spontaneously generated coherence between the two closely spaced excited levels produces interference effects in the absorption. As a result, more transparency windows appear comparing to the normal three-level V system. We can also control the number of the transparency windows to be two or three just by tuning the Rabi frequency of the coupling field. We present an equivalent system without the rigorous requirement of close-lying levels to observe the phenomena. We also experimentally demonstrate the corresponding features in a rubidium atomic beam.

We describe a method for waveform shaping of narrowband biphotons generated in a double-$\Lambda$ atomic system via four-wave mixing by periodically modulating the input driving lasers. We show that the input field profile(s) can be revealed in the two-photon temporal waveform and its correlation measurement.

We present a general proof that Dirac particles cannot be localized below their Compton length by symmetric but otherwise arbitrary scalar potentials. This proof does not invoke the Heisenberg uncertainty relation and thus does not rely on the nonrelativistic linear momentum relation. Further it is argued that the result is also applicable for more general potentials, as, e.g., generated by nonlinear interactions. Finally a possible realization of such a system is proposed.

We commence the evaluation of the one- and two-loop binding corrections to the $g$ factor for an electron in a hydrogenlike system of order ${\alpha }^2{\left(Z\alpha \right)}^5$ and consider diagrams with closed fermion loops. The one-loop vacuum-polarization correction is rederived and confirmed. For the two-loop vacuum-polarization correction, due to a specific gauge-invariant set of diagrams with closed fermion loops, we find a correction $\delta g=7.442{\left(\alpha /\pi \right)}^2{\left(Z\alpha \right)}^5$. Based on the numerical trend of the coefficients inferred from the gauge-invariant subset, we obtain a numerically large tentative estimate for the complete two-loop binding correction to the $g$ factor (sum of self-energy and vacuum polarization).

We give some comments on the paper of Matzkin [Phys. Rev. A 77, 062110 (2008)]. It is argued here that, if the assumption of locality is properly taken into account, Matzkin’s model cannot reproduce the quantum-mechanical correlations.

In this Reply, we show that the main argument of the criticism given in the preceding Comment is inconsistent with the assumption lying at the basis of the model introduced in the original paper [A. Matzkin, Phys. Rev. A 77, 062110 (2008)]. We further clarify some issues concerning the interplay between noncommuting measurements and conservation laws in order to reply to the additional criticism contained in the comment.

We describe an effective resonant interaction between two localized wave modes of different nature: a plasmon polariton at a metal surface and a self-focusing beam (spatial soliton) in a nonlinear dielectric medium. Propagating in the same direction, they represent an exotic coupled-waveguide system, where the resonant interaction is controlled by the soliton amplitude. This nonlinear system manifests hybridized plasmon-soliton eigenmodes, mutual conversion, and nonadiabatic switching, which offer exciting opportunities for manipulation of plasmons via spatial solitons.

We study the robustness of multipartite entanglement of the ground state of the one-dimensional spin-$\frac{1}{2}$ $XY$ model with a transverse magnetic field in the presence of thermal excitations by investigating a threshold temperature, below which the thermal state is guaranteed to be entangled. We obtain the threshold temperature based on the geometric measure of entanglement of the ground state. The threshold temperature reflects three characteristic lines in the phase diagram of the correlation function. Our approach reveals a region where multipartite entanglement at zero temperature is high but is thermally fragile and another region where multipartite entanglement at zero temperature is low but is thermally robust.

A theory is developed to obtain the state vector for an atom-field system in which a single-photon pulse propagates in an optically dense ensemble of two-level or three-level atoms. The manner in which the field and the atoms become entangled is described, as is the entanglement of the atoms produced by the radiation pulse. Two protocols for quantum-information storage are studied. In the first protocol, the single-photon pulse is totally absorbed in an ensemble of two-level atoms that are embedded in a dielectric host. To arrive at analytical expressions for the state vector, fluctuations of atomic position are neglected and it is assumed that the atoms’ transition frequencies are inhomogeneously broadened with a width that is much larger than the bandwidth of the single-photon pulse. In the second protocol, a single-photon pulse is sent into a semi-infinite medium of three-level atoms under the conditions where electromagnetic-induced transparency can occur. It is shown that the usual results of pulse compression and reduced group velocity are recovered. Moreover, an explicit expression for the state vector of the atom-field system is obtained.

This paper is devoted to energy-spectral analysis for the system of a two-level atom coupled with photons in a cavity. It is shown that the Dicke-type energy level crossings take place when the atom-cavity interaction of the system undergoes changes between the weak-coupling regime and the strong one. Using the phenomenon of the crossings, we develop the idea of cavity-induced atom cooling proposed by Horak et al., and we lay mathematical foundations of a possible mechanism for another superradiant cooling in addition to that proposed by Domokos and Ritsch. The process of our superradiant cooling can function well by cavity decay and by control of the position of the atom, at least in (mathematical) theory, even if there is neither atomic absorption nor atomic emission of photons.