The energies, fine-structure splittings, Auger channel energies, and the Auger widths of the high-lying triply excited $2l2l^{\prime }n{l}^{″}$ $\left(n\ge 2\right)$ states of ${}^{2}S$, ${}^{2}D$, and ${{}^{2}P}^{\text{o}}$ resonances for ${\text{Be}}^{+}$ are studied using the saddle-point variational method and saddle-point complex-rotation method. The relativistic corrections and mass polarization are included using the first-order perturbation theory. Restricted variational method is carried out to extrapolate better energies. The partial Auger widths are calculated for the individual open channels and the total Auger widths are obtained by coupling the important open channels and summing over the other channels. The configuration mixings of the triply excited resonances are described and differences in the literature on the designation of the intershell states are pointed out. These results are compared with other theoretical and experimental data in the literature.

Recent experiments on collision processes of ${\text{O}}^{7+}$ and ${\text{N}}^{6+}$ ions colliding with methane at the same velocity show unexpected differences in the fragmentation cross sections of the methane. Despite the expected similarity of these two processes, as both projectiles are hydrogenic, the mechanisms of electron transfer are different and lead to different fragmentation cross sections. In the present work, the collisions between ${\text{N}}^{6+}$ and ${\text{O}}^{7+}$ ions and methane are investigated theoretically at equal velocities corresponding to projectile energies of 30 and 35 keV, respectively. Electron-nuclear dynamics is used to study multiple electron transfer processes occurring in these collisions. Several multiple charge transfer probabilities are calculated and results, averaged over various orientations of the methane molecule, are reported. The collisions proceed in two stages: a fast stage of electron transfer from methane to the ion, and a much slower stage of breakup of the methane. We find and explain the intuitively unexpected result that the total charge transfer cross section for ${\text{N}}^{6+}$ is slightly larger, but that the ${\text{O}}^{7+}$ leaves the methane in a higher charged state with higher probability, leading to more fragmentation in the collisions with ${\text{O}}^{7+}$.

Diffraction patterns produced by grazing scattering of fast atoms from insulator surfaces are used to examine the atom-surface interaction. The method is applied to He atoms colliding with a LiF(001) surface along axial crystallographic channels. The projectile-surface potential is obtained from an accurate density-functional theory calculation, which includes polarization effects and surface relaxation. For the description of the collision process we employ the surface eikonal approximation, which takes into account quantum interference between different projectile paths. The dependence of projectile spectra on the parallel and perpendicular incident energies is experimentally and theoretically analyzed, demonstrating the range of applicability of the proposed model.

Motivated by the recent discovery that a reflecting wall moving with a square-root-in-time trajectory behaves as a universal stopper of classical particles regardless of their initial velocities, we compare linear-in-time and square-root-in-time expansions of a box to achieve efficient atom cooling. For the quantum single-atom wave functions studied the square-root-in-time expansion presents important advantages: asymptotically it leads to zero average energy whereas any linear-in-time (constant box-wall velocity) expansion leaves a nonzero residual energy, except in the limit of an infinitely slow expansion. For finite final times and box lengths we set a number of bounds and cooling principles which again confirm the superior performance of the square-root-in-time expansion, even more clearly for increasing excitation of the initial state. Breakdown of adiabaticity is generally fatal for cooling with the linear expansion but not so with the square-root-in-time expansion.

We investigate two-component ultracold fermions loaded into a decorated square lattice, which are described by the Hubbard model with repulsive interactions and nearest-neighbor hoppings. By combining the real-space dynamical mean-field theory with the numerical renormalization-group method, we discuss how a ferromagnetically ordered ground state in the weak-coupling regime, which originates from the existence of a dispersionless band, is adiabatically connected to a Heisenberg ferrimagnetic state in the strong-coupling limit. The effects of level splitting and hopping imbalance are also addressed.

We report electromagnetically induced gain in a highly degenerate two-level rotational vibrational molecular system. Using two photon (Raman-type) interaction with right and left circularly polarized pump and probe waves, the Zeeman coherence is established within the manifold of degenerate sublevels belonging to a rotational vibrational eigenstate. We analytically and numerically calculate the third-order nonlinear optical susceptibility for a Doppler-broadened molecular transition for an arbitrary high rotational angular momentum $\left(J\ge 20\right)$. It is shown that for a $Q$-type open transition, a weak probe will experience an electromagnetically induced gain in presence of a strong copropagating pump wave. The inversionless gain originates due to cancellation of absorption from the interference of the coupled $\Lambda$- and V-type excitation channels in an $N$-type configuration. A detailed analysis of the optical susceptibility as a function of Doppler detuning explains how the gain bands are generated in a narrow transparency window from the overlapping contributions of different velocity groups. It is shown that the orientation dependent coherent interaction in presence of a strong pump induces narrow resonances for the probe susceptibility. The locations, intensity, and sign (positive or negative susceptibility) of these resonances are decided by the frequency detuning of the Doppler group and the strength of the coupling field. The availability of high power tunable quantum cascade lasers covering a spectral region from about 4 to $12\mu \text{m}$ opens up the possibility of investigating the molecular vibrational rotational transitions for a variety of coherent effects.

Recently, the molecular cation ${\text{PtH}}^{+}$ was suggested as a promising candidate for the experimental search for the electron electric dipole moment. For estimating the sensitivity of the experiment on the cation and for interpretation of the experimental results, it is necessary to calculate an effective electric field acting on the electron with good accuracy because the value of the field cannot be obtained experimentally. We have performed relativistic correlation calculations to compute this effective field for the ${{}^3\Delta }_3$ electronic state of ${\text{PtH}}^{+}$ as well as spectroscopic properties of four lowest lying states, which are also not measured up to date. The ${{}^3\Delta }_3$ state is found to be the ground one and ${{}^1\Sigma }^{+}$ state is the first excited one. The calculated value of the effective electric field acting on an electron is found to be 28 GV/cm.

Recently demonstrated superconducting atom chips provide a platform for trapping atoms and coupling them to solid-state quantum systems. Controlling these devices requires a full understanding of the supercurrent distribution in the trapping structures. For type-II superconductors, this distribution is hysteretic in the critical state due to the partial penetration of the magnetic field in the thin superconducting film through pinned vortices. We report here an experimental observation of this memory effect. Our results are in good agreement with the predictions of the Bean model of the critical state without adjustable parameters. The memory effect allows to write and store permanent currents in micron-sized superconducting structures and paves the way toward engineered trapping potentials.

Coin flipping is a cryptographic primitive in which two spatially separated players, who do not trust each other, wish to establish a common random bit. If we limit ourselves to classical communication, this task requires either assumptions on the computational power of the players or it requires them to send messages to each other with sufficient simultaneity to force their complete independence. Without such assumptions, all classical protocols are so that one dishonest player has complete control over the outcome. If we use quantum communication, on the other hand, protocols have been introduced that limit the maximal bias that dishonest players can produce. However, those protocols would be very difficult to implement in practice because they are susceptible to realistic losses on the quantum channel between the players or in their quantum memory and measurement apparatus. In this paper, we introduce a quantum protocol and we prove that it is completely impervious to loss. The protocol is fair in the sense that either player has the same probability of success in cheating attempts at biasing the outcome of the coin flip. We also give explicit and optimal cheating strategies for both players.

We investigate the entanglement dynamics of a two-qubit system which interacts with a Heisenberg $XY$ spin chain constrained to carry an energy current. We show an explicit connection between the decoherence factor and entanglement, and numerically and analytically study the dynamical process of entanglement in both weak- and strong-coupling cases for two initial states, the general pure state and the mixed Werner state. We provide results that the entanglement evolution depends not only on the energy current, the anisotropy parameter and the system-environment couplings but also on the size of degrees of freedom of environment. In particular, our results imply that entanglement will be strongly suppressed by the introduction of energy current on the environmental spin chain in the weak-coupling region while it is not sensitive to the energy current in the strong-coupling region. We also observe the sudden death of entanglement in the system and show how the energy current affects the phenomenon.

We present an approach for implementation of a $1\to 3$ orbital state quantum cloning machine based on the quantum Zeno dynamics via manipulating three rf superconducting quantum interference device (SQUID) qubits to resonantly interact with a superconducting cavity assisted by classical fields. Through appropriate modulation of the coupling constants between rf SQUIDs and classical fields, the quantum cloning machine can be realized within one step. We also discuss the effects of decoherence such as spontaneous emission and the loss of cavity in virtue of master equation. The numerical simulation result reveals that the quantum cloning machine is especially robust against the cavity decay, since all qubits evolve in the decoherence-free subspace with respect to cavity decay due to the quantum Zeno dynamics.

We address the evolution of entanglement in bimodal continuous variable quantum systems interacting with two independent structured reservoirs. We derive an analytic expression for the entanglement of formation without performing the Markov and the secular approximations and study in details the entanglement dynamics for various types of structured reservoirs and for different reservoir temperatures, assuming the two modes initially excited in a twin-beam state. Our analytic solution allows us to identify three dynamical regimes characterized by different behaviors of the entanglement: the entanglement sudden death, the non-Markovian revival and the non-secular revival regimes. Remarkably, we find that, contrarily to the Markovian case, the short-time system-reservoir correlations in some cases destroy quickly the initial entanglement even at zero temperature.

We determine the conditions for the existence of a pair of degenerate parity breaking separable eigenstates in general arrays of arbitrary spins connected through $XYZ$ couplings of arbitrary range and placed in a transverse field, not necessarily uniform. Sufficient conditions under which they are ground states are also provided. It is then shown that in finite chains, the associated definite parity states, which represent the actual ground state in the immediate vicinity of separability, can exhibit entanglement between any two spins regardless of the coupling range or separation, with the reduced state of any two subsystems equivalent to that of pair of qubits in an entangled mixed state. The corresponding concurrences and negativities are exactly determined. The same properties persist in the mixture of both definite parity states. These effects become specially relevant in systems close to the $XXZ$ limit. The possibility of field induced alternating separable solutions with controllable entanglement side limits is also discussed. Illustrative numerical results for the negativity between the first and the $j^{\text{th}}$ spin in an open spin $s$ chain for different values of $s$ and $j$ are as well provided.

We have carried out calculations of multipole polarizabilities of helium and the hydrogen negative ion interacting with pure Coulomb and screened Coulomb potentials using highly accurate correlated exponential wave functions with exponent generated by a quasirandom process. The dipole, quadrupole, and octupole polarizabilities for the ground $1s^2$ ${{}^{1}S}^{\text{e}}$ state for different screening parameters starting from infinity (pure Coulomb case) to small values of the screening parameters, are reported. The octupole polarizability of the hydrogen negative ion is reported for the first time in the literature. The bound $4{}^{1}F$ state energy of helium for different screening parameters are also reported.

Accurate Hylleraas-type correlated helium wave functions are used to predict positronium (Ps) formation cross sections in positron-helium collisions within the frame work of the distorted-wave approximation at intermediate and high energies of positron impact. Exponential correlated atomic target wave functions taking into account up to $N=30$ basis terms are utilized. Reliable total cross sections for the ground and excited $2s$-state Ps formation are reported at intermediate and high energies. The present distorted-wave results are in conformity with the existing theoretical and experimental values available in the literature for intermediate and high-energy positrons. Surface plots of the DWA differential cross section reveal rich structures due to constructive and destructive interference between angular momentum states of the moving Ps.

Using computer simulation, alternative methods of the interaction of highly charged ions ${\text{Ar}}^{q+}$ with metals (Au, Ag) are used and verified in the present work. Based on the classical over-barrier model, we discussed the promotion loss and peeling off processes. The simulated total potential electron yields agree well with the experiment data in incident energy ranging from 100 eV to 5 keV and all charge states of ${\text{Ar}}^{q+}$. Based on the TRIM code, we obtain the side-feeding rate as well as the motion and charge transfer of HCI below the surface. Some results, including the array of $K{L}^x$ x-ray satellite lines, the respective contribution of autoionization, and side-feeding to inner shells, and the filling rates and lifetime of inner shells for Ar agree well with experiment or theory.

Electron tunnel ionization is considered as the mechanism for producing free electrons in gases under laser radiation. The Keldysh result and the Ammosov-Delone-Krainov (ADK) formulation are amended by considering the excess forces due to the interaction of the electric field of the laser with the electron cloud in a simple mass-on-a-spring approximation. The result of this excess force is a kinetic energy that is directed along the polarization vector of the laser field and an induced potential energy that are proposed as a determining factor in electron tunnel ionization. Relative ionization rates for various pairs of gases are calculated and compared with reported figures. Comparisons were made between several combinations of ${\text{O}}_2$, Xe, Ar, ${\text{N}}_2$, ${\text{Cl}}_2$, ${\text{H}}_2$, CO, Kr, NO, ${\text{F}}_2$, and ${\text{D}}_2$. Predicted ratios of ionization rates between pairs of gases are compared to ADK predictions. Apparently anomalous ionization rates of ${\text{O}}_2$, ${\text{D}}_2$, and ${\text{H}}_2$ are explained. A simple expression is developed that reveals why the ionization rate of Xe is about an order of magnitude larger than that of ${\text{O}}_2$ even though their ionization potentials are nearly identical; why CO is only about half that of Kr even though their ionization potentials are nearly the same; why the ratio of ${\text{O}}_2$ to O is about ten times larger than predicted by ADK; and why the ratio of NO to Xe is about an order of magnitude less than predicted by ADK.

We present an analytical solution for the vortex lattice in a rapidly rotating trapped Bose-Einstein condensate in the lowest Landau level and discuss deviations from the Thomas-Fermi density profile. This solution is exact in the limit of a large number of vortices and is obtained for the cases of circularly symmetric and narrow channel geometries. The latter is realized when the trapping frequencies in the plane perpendicular to the rotation axis are different from each other and the rotation frequency is equal to the smallest of them. This leads to the cancellation of the trapping potential in the direction of the weaker confinement and makes the system infinitely elongated in this direction. For this case we calculate the phase diagram as a function of the interaction strength and rotation frequency and identify the order of quantum phase transitions between the states with a different number of vortex rows.

We report on the linear and nonlinear optical response of metamaterials evoked by first- and second-order multipoles. The analytical ground on which our approach is based permits for new insights into the functionality of metamaterials. For the sake of clarity we focus here on a key geometry, namely, the split-ring resonator, although the introduced formalism can be applied to arbitrary structures. We derive the equations that describe linear and nonlinear light propagation where special emphasis is put on second-harmonic generation. This contribution basically aims at stretching versatile and existing concepts to describe light propagation in nonlinear media toward the realm of metamaterials.

We study the dynamic sensitivity of an atomic ensemble dressed by a single-mode cavity field (called a photon-dressed atomic ensemble), which is described by the Dicke model near the quantum critical point. It is shown that when an extra atom in a pure initial state passes through the cavity, the photon-dressed atomic ensemble will experience a quantum phase transition showing an explicit sudden change in its dynamics characterized by the Loschmidt echo of this quantum critical system. With such dynamic sensitivity, the Dicke model can resemble the cloud chamber for detecting a flying particle by the enhanced trajectory due to the classical phase transition.