We find the nearest product states for arbitrary generalized $W$ states of $n$ qubits, and show that the nearest product state is essentially unique if the $W$ state is highly entangled. It is specified by a unit vector in Euclidean $n$-dimensional space. We use this duality between unit vectors and highly entangled $W$ states to find the geometric measure of entanglement of such states.

The quantum states corresponding to a secret key are characterized using the so-called private states, where the key part consisting of a secret key is shielded by the additional systems. Based on the construction, it was shown that a secret key can be distilled from bound entangled states. In this work, I consider the shielded two-qubit states in a key-distillation scenario and derive the conditions under which a secret key can be distilled using the recurrence protocol or the two-way classical distillation, advantage distillation together with one-way postprocessing. From the security conditions, it is shown that a secret key can be distilled from bound entangled states in a much wider range. In addition, I consider the case that in which white noise is added to quantum states and show that the classical distillation protocol still works despite a certain amount of noise although the recurrence protocol does not.

We investigate how well the one-dimensional Hubbard model describes the entanglement of particles trapped in a string of quantum wells. We calculate the average single-site entanglement for two particles interacting via a contact interaction and consider the effect of varying the interaction strength and the interwell distance. We compare the results with the ones obtained within the one-dimensional Hubbard model with on-site interaction. We suggest an upper bound for the average single-site entanglement for two electrons in $M$ wells and discuss analytical limits for very large repulsive and attractive interactions. We investigate how the interplay between interaction and potential shape in the quantum-well system dictates the position and size of the entanglement maxima and the agreement with the theoretical limits. Finally, we calculate the spatial entanglement for the quantum-well system and compare it to its average single-site entanglement.

We demonstrate the applicability of four-body exponentially correlated functions for the accurate calculations of relativistic effects in lithium-like atoms and present results for matrix elements of various operators which involve negative powers of interparticle distances.

Excitation energies of the [Xe]${\mathit{ns}}_{1/2}$, [Xe]${\mathit{np}}_j$, and [Xe]${\mathit{nd}}_j$ ($n⩽$ $12$ and $[\mathrm{Xe}]=1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{2}4p^{6}4d^{10}5s^{2}5p^6$) in Ba ii are evaluated. First-, second-, third-, and all-order Coulomb energies and first- and second-order Coulomb-Breit energies are calculated. Electric-dipole ($6s_{1/2}$-${\mathit{np}}_j$, $n=6$–26), electric-quadrupole ($6s_{1/2}$-${\mathit{nd}}_j$, $n=5$–$26$), and electric-octupole ($6s_{1/2}$-${\mathit{nf}}_j$, $n=4$–$26$) matrix elements are calculated to obtain the ground-state $E1$, $E2$, and $E3$ static polarizabilities. Scalar polarizabilities of the ${\mathit{ns}}_{1/2}$, ${\mathit{np}}_j$, and ${\mathit{nd}}_j$ states and tensor polarizabilities of the ${\mathit{np}}_{3/2}$ and ${\mathit{nd}}_j$ excited states of Ba${}^{+}$ are evaluated. All aforementioned matrix elements are determined using the relativistic all-order method. The hyperfine structure in ${}^{137}\mathrm{Ba}$ ii is also investigated. The hyperfine $A$ and $B$ values are determined for the first low-lying levels up to $n=9$. The quadratic Stark effect on hyperfine structure levels of ${}^{137}\mathrm{Ba}$ ii ground state is investigated. The calculated shift for the ($F=2$, $M=0$) $\leftrightarrow$ ($F=1$, $M=0$) transition is $-$$0.2931$ Hz/(kV/cm)${}^2$, in agreement with a previous theoretical result, $-0.284(3)$). These calculations provide a theoretical benchmark for comparison with experiment and theory.

Two-body scattering of neutral particles in a trap is studied theoretically. The control of the initial state is realized by using optical traps. The collisions inside the trap occur repeatedly; thereby the effect of interaction can be accumulated. Two periodic phenomena with a shorter and a much longer period, respectively, are found. The latter is sensitive to the interaction. Instead of measuring the differential cross section as is usually done, the measurement of the longer period and the details of the periodic behavior might be a valid source of information on weak interactions among neutral particles.

Within the framework of the classical over-barrier model, energy loss, electron emission, and x-ray emission of slow highly charged ion Ar${}^{q+}$ grazing on the Al(111) single-crystal surface under various azimuthal angles have been studied. The enhancement of energy loss, potential electron emission yields, intensity of $\mathit{KL}$${}^1$ satellite lines, or x-ray yields for the Ar${}^{17+}$ ion grazing along low-index crystallographic directions was observed. The calculated energy-loss spectra of atomic projectiles Ar${}^0$ interacting with metallic surface agree reasonably well with experiment. The inner-shell filling contributions through the side feeding mechanism, Auger transitions, and the radiative decay process are discussed by analyzing the final charge-state distributions of the reflected ions, potential electron emission yields, and x-ray yields under different azimuthal angles.

The ionization of ${\mathrm{H}}_2$ in a single attosecond extreme ultraviolet (XUV) pulse generates a nuclear wave packet in ${\mathrm{H}}_2$${}^{+}$, which is entangled with the emitted photoelectron wave packet. The nuclear wave-packet dynamics can be observed by dissociating ${\mathrm{H}}_2$${}^{+}$ in a delayed IR laser pulse. If ${\mathrm{H}}_2$ is ionized by a sequence of XUV pulses of an attosecond pulse train, whether or not the corresponding sequence of nuclear wave packets in ${\mathrm{H}}_2$${}^{+}$ is detected as a coherent or incoherent superposition depends on whether and how the photoelectrons are observed. We simulate the nuclear dynamics in this XUV-pump–IR-probe scenario and analyze our numerical results for both single attosecond pump pulses and pump-pulse trains of different lengths and temporal spacings between individual XUV pulses. By superimposing nuclear wave packets in ${\mathrm{H}}_2$${}^{+}$ generated by individual pulses in the pump-pulse train incoherently, we calculate proton kinetic energy release spectra that are in good qualitative agreement with the recent experiment of Kelkensberg et al. [Phys. Rev. Lett. 103, 123005 (2009)].

We utilize the combination of two standard trapping techniques, a magnetic trap and an optical trap in a Raman setup, to propose a versatile and tunable trap for cold atoms. The created potential provides several advantages over conventional trapping potentials. One can easily convert the type of the trap, for example, from a single-well to a double-well trap. Atoms in different internal states can be trapped in different trap types, thereby enabling the realization of experiments with multicomponent Bose-Einstein condensates. Moreover, one can achieve variations of the trapping potential on small length scales without the need of microstructures. We present the potential surfaces for different setups, demonstrate their tunability, give a semianalytical expression for the potential, and propose experiments which can be realized within such a trap.

We report the possibility of steering gap solitons in Bose-Einstein condensates loaded in optical lattices by means of time-dependent nonlinearities, which allow one to control in a nondestructive manner both Bloch oscillations and Landau-Zener tunneling (i.e., Rabi oscillations) across band gaps. As an example we show how to move a matter-wave soliton in real and in reciprocal space from a lower to higher bands, avoiding dynamical instabilities. This opens the possibility of experimental access to gap solitons of higher bands and forcing of soliton motion through a lattice via the Feshbach resonance technique.

Trapped two-component Fermi gases allow the investigation of the so-called BCS-BEC crossover by tuning the interspecies atom-atom $s$-wave scattering length $a^{(\mathit{aa})}$ from attractive to repulsive, including vanishing and infinitely large values. Here, we numerically determine the energy spectrum of the equal-mass spin-balanced four-fermion system—the smallest few-particle system that exhibits BCS-BEC crossoverlike behavior—as a function of $a^{(\mathit{aa})}$ using the stochastic variational approach. For comparative purposes, we also treat the two- and three-particle systems. States with vanishing and finite total angular momenta as well as with natural and unnatural parities are considered. In addition, the energy spectrum of weakly attractive and weakly repulsive gases is characterized by employing a perturbative framework that utilizes hyperspherical coordinates. The hyperspherical coordinate approach allows the straightforward assignment of quantum numbers and furthermore provides great insight into the strongly interacting unitary regime.

We propose a well-controlled experimental scheme to initiate and examine the Rayleigh-Taylor instability in two-species Bose-Einstein condensates. We identify the ${}^{85}\mathrm{Rb}$-${}^{87}\mathrm{Rb}$ mixture as an excellent candidate to observe experimentally. The instability is initiated by tuning the ${}^{85}\mathrm{Rb}$-${}^{85}\mathrm{Rb}$ interaction through a magnetic Feshbach resonance. We show that the observable signature of the instability is the damping of the radial oscillations. We also propose a semianalytic scheme to determine the stationary state of binary condensates with the Thomas-Fermi approximation for axisymmetric traps.

We present a theory of spin waves in a noncondensed gas of spin-1 bosons and provide both analytic calculations of the linear theory and full numerical simulations of the nonlinear response. We highlight the role of spin-dependent contact interactions in the dynamics of a thermal gas. Although these interactions are small compared to the thermal energy, they set the scale for low-energy, long-wavelength spin waves. In particular, we find that the polar state of ${}^{87}\mathrm{Rb}$ is unstable to collisional mixing of magnetic sublevels even in the normal state. We augment our analytic calculations by providing full numerical simulations of a trapped gas, explicitly demonstrating this instability. Further, we show that for strong antiferromagnetic interactions, the polar gas is unstable. Finally, we explore coherent population dynamics in a collisionless transversely polarized gas.

We use the symplectic transformation of the known linear optical elements to investigate the dynamical evolution of a three-mode cavityless optomechanical system and give explicit formulas for the input and output covariance matrices of the three mode fields when the initial state is Gaussian. Unlike the conventional approaches, the present one does not necessitate solution of the equation of motion of such a system. We study the dynamical behavior of bipartite entanglement in this system when the mirror vibrational mode is initially in a single-mode squeezed vacuum state and each of the two reflected optical sideband modes is in the vacuum state. It is found that the entanglement configuration alternates between a fully separable state and a continuous-variable entangled state during evolution.

We study the effect of the inclusion of the U(2) Lie algebra second-order Casimir operator in a model Hamiltonian of the vibron model two-dimensional limit. We extend previously published results, showing that the inclusion of the additional term does not alter the ground-state quantum phase transition between the symmetric and deformed limits of the model. Nevertheless, the inclusion of this operator implies deep changes on the excitation spectrum and on the ensuing excited-state quantum phase transitions.

We investigate the Casimir effect in the presence of a medium by quantizing the electromagnetic field in the presence of a magnetodielectric medium using the path-integral technique. For a given medium with definite electric and magnetic susceptibilities, explicit expressions for the Casimir force are obtained. The Lifshitz formula is recovered and in the absence of a medium the results tend to the original Casimir force between two conducting parallel plates immersed in the quantum electromagnetic vacuum.

We address the question of optimality of entangled input states in quantum Gaussian memory channels. For a class of such channels, which can be traced back to the memoryless setting, we state a criterion which relates the optimality of entangled inputs to the symmetry properties of the channels’ action. Several examples of channel models belonging to this class are discussed.

We study the interconversion of multipartite symmetric $N$-qubit states under stochastic local operations and classical communication (SLOCC). We demonstrate that if two symmetric states can be connected with a nonsymmetric invertible local operation (ILO), then they belong necessarily to the separable, W, or Greenberger-Horne-Zeilinger (GHZ) entanglement class, establishing a practical method of discriminating subsets of entanglement classes. Furthermore, we prove that there always exists a symmetric ILO connecting any pair of symmetric $N$-qubit states equivalent under SLOCC, simplifying the requirements for experimental implementations of local interconversion of those states.

We address the study of controllability of a closed quantum system whose dynamical Lie algebra is generated by adjacency matrices of graphs. We characterize a large family of graphs that renders a system controllable. The key property is a graph-theoretic feature consisting of a particularly disordered cycle structure. Disregarding efficiency of control functions, but choosing subfamilies of sparse graphs, the results translate into continuous-time quantum walks for universal computation.

High-dimensional quantum states, or qudits, represent a promising resource in the quantum information field. Here we present the experimental generation of four-dimensional quantum states, or ququarts, encoded in the polarization and orbital angular momentum of a single photon. Our technique, based on the $q$-plate device, allows the ququart to be prepared and measured in all five mutually unbiased bases. We report the reconstruction of the four-dimensional density matrix through the tomographic procedure for different ququart states.