We have studied metastable electronic states of trication molecules for N${}_2$${}^{3+}$ and O${}_2$${}^{3+}$ using the internally contracted multireference configuration interaction method with single and double excitations (icMRCISD). The metastable ground state for O${}_2$${}^{3+}$ and metastable excited state for N${}_2$${}^{3+}$ were obtained with the barriers of approximately 1.5 and 13.0 kcal/mol, respectively, although those metastable states were not found in previous calculations. The analysis on occupation numbers of natural orbitals demonstrates that the two metastable states are formed owing to the balance between the reduction of cationic Coulomb repulsion and the weakening of the chemical bonds. We have proposed to measure these metastable states by short-wavelength free-electron lasers (sFELs) that have the potential to produce excited states of multiply charged molecules.

Using resonance ionization spectroscopy the first-ionization potential of actinium has been determined by analyzing different Rydberg series in two-color resonant laser excitation. Three individual Rydberg series were investigated, converging toward the ionic ground state and toward the first- and second-excited state of the actinium ion, respectively. A combined analysis of the convergence limits leads to a consistent value for the first-ionization potential of Ac of $43394.45\left(19\right){\text{cm}}^{-1}$, equivalent to $5.380226\left(24\right)$ eV.

Without a formal derivation, we propose a formula for the total and single-differential cross sections in the problem of one-photon double ionization of an atom. The formula is benchmarked against accurate experimental data for the total cross section of helium. Furthermore, a direct comparison with ab initio calculations for the double ionization of Li${}^{+}$ suggests that the framework is valid for the entire helium isoelectronic sequence. To this end, we introduce a formula for the double ionization of lithium as well as for the triple ionization of lithium and beryllium.

We present the results of an experimental as well as a theoretical study of nonlinear magneto-optical resonances in diatomic potassium molecules in the electronic ground state with large values of the angular momentum quantum number $J\sim 100$. At zero magnetic field, the absorption transitions are suppressed because of population trapping in the ground state due to Zeeman coherences between magnetic sublevels of this state along with depopulation pumping. The destruction of such coherences in an external magnetic field was used to study the resonances in this work. K${}_2$ molecules were formed in a glass cell filled with potassium metal at a temperature above 150 ${}^{\circ }$C. The cell was placed in an oven and was located in a homogeneous magnetic field B, which was scanned from 0 to 0.7 T. $Q$-type and $R$-type transitions were excited with a tunable, single-mode diode laser with a central wavelength of 660 nm. Well-pronounced nonlinear Hanle effect signals were observed in the intensities of the linearly polarized components of the laser-induced fluorescence (LIF) detected in the direction parallel to the B field with polarization vectors parallel ($I_{\text{par}}$) and perpendicular ($I_{\text{per}}$) to the polarization vector of the exciting laser radiation, which was orthogonal to B. The intensities of the LIF components were detected for different experimental parameters, such as laser power density and vapor temperature, in order to compare them with numerical simulations that were based on the optical Bloch equations for the density matrix. We report good agreement of our measurements with numerical simulations. Narrow, subnatural linewidth dark resonances in $I_{\text{per}}\left(B\right)$ were detected and explained.

We recently reported on a proof-of-principle experiment demonstrating optical trapping of an ion in a single-beam dipole trap superimposed by a static electric potential [Ch. Schneider, M. Enderlein, T. Huber, and T. Schaetz, Nat. Photon. 4, 772 (2010)]. Here, we discuss, first, the experimental procedures focusing on the influence and consequences of the static electric potential. This potential can easily prevent successful optical trapping, if its configuration is not chosen carefully. Afterward, we analyze the dipole trap experiments with different analytic models, in which different approximations are applied. According to these models the experimental results agree with recoil heating as the relevant heating effect. In addition, a Monte Carlo simulation has been developed to refine the analysis. It reveals a large impact of the static electric potential on the dipole trap experiments in general. While it supports the results of the analytic models for the parameters used in the experiments, the analytic models are no longer valid for significantly different parameters. Finally, we propose technical improvements for future realizations of experiments with optically trapped ions.

This paper addresses the problem of above-threshold ionization (ATI) of hydrogen interacting with a short and intense x-ray electromagnetic field. We consider the weakly relativistic regime where the speed of the photoelectron stays well below the velocity of the light $c$. We solve the time-dependent Schrödinger equation (TDSE) using a spectral approach with a basis of one-electron orbitals, calculated with $L^2$-integrable $B$-spline functions for the radial coordinate and bipolar spherical harmonics $Y_{lm}$ for the angular part. Retardation effects are included up to $O(1/c)$; they induce two extra terms leading to electric quadrupole and magnetic dipole transitions. These latter terms depend on the polarization and photon momentum directions, forcing the resolution of the TDSE in a three-dimensional space. Relativistic effects [of $O(1/c^2)$] are fully neglected. Photoelectron energy and angular distributions are obtained for photon energies ranging from 200 eV to 3 keV. We study the lower energy region of the ATI spectrum and we analyze nondipole effects, through their $(l,m)$ components, in particular, for the lower two peaks. Although these effects are small, we show that, increasing the photon energy, the photoelectron angular distributions begin to differ significantly from the ones obtained in dipole approximation.

We describe quantum dynamical calculations of ultracold ${}^{85}$Rb trap-loss collisions induced by pulses of light whose frequency is chirped on the nanosecond time scale. The chirped light excites the ground-state collisional wave function to the long-range attractive potential and escape from the trap is modeled by an absorbing boundary at short range. Both positive and negative chirps are considered and various chirp shapes and detunings are examined. For positive chirps, the loss rates are rather independent of the chirp shape. Negative chirps, on the other hand, show a dependence on chirp shape for detunings where collisional flux can be coherently returned to the ground state. These trends are consistent with the results of a recent experiment.

We study the effect of an artificial gauge field on the zero-temperature phase diagram of an extended Bose-Hubbard model that describes ultracold atoms in optical lattices with long-range interactions by using strong-coupling perturbation theory. We determine analytically the effect of the artificial gauge field on the density-wave–supersolid (DW-SS) and the Mott-insulator–superfluid (MI-SF) transition boundary. The momentum distribution at these two transition boundaries is also calculated in this approach. It is shown that such a momentum distribution, which can be observed in time-of-flight measurements, reveals the symmetry of the gauge potential through the formation of a magnetic Brillouin zone and clearly distinguishes between the DW-SS and MI-SF boundary. We also point out that, in a symmetric gauge, the momentum distribution structure at these transition boundaries bears distinctive signatures of vortices in supersolid and superfluid phases.

We describe an experiment to produce ${}^{87}$Rb Bose-Einstein condensates in an optically plugged magnetic quadrupole trap, using a blue-detuned laser. Due to the large detuning of the plug laser with respect to the atomic transition, the evaporation has to be carefully optimized in order to efficiently overcome the Majorana losses. We provide a complete theoretical and experimental study of the trapping potential at low temperatures and show that this simple model describes our data well. In particular, we demonstrate methods to reliably measure the trap oscillation frequencies and the bottom frequency, based on periodic excitation of the trapping potential and on radio-frequency spectroscopy, respectively. We show that this hybrid trap can be operated in a well-controlled regime that allows a reliable production of degenerate gases.

Mott-insulator-to-superfluid quenches have been used by recent experiments to generate exotic superfluid phases. While the final Hamiltonian following the sudden quench is that of a superfluid, it is not a priori clear whether the final state of the system actually enters the superfluid phase. To understand the nature of the final state the temporal evolution of the momentum distribution is calculated following a Mott-insulator-to-superfluid quench. Using the numerical infinite time-evolving block decimation approach and the analytical rotor model approximation it is established that the one- and two-dimensional Mott insulators following the quench equilibrate to thermal states with spatially short-ranged coherence peaks in the final momentum distribution and therefore are not superfluids. However, in three dimensions a divergence in the momentum distribution indicating the emergence of true superfluid order is found.

The ground-state entanglement of the two-mode Bose-Einstein condensate is investigated through a quantum-phase-transition approach. The entanglement measure is taken as the order parameter and this is a nonlocal order parameter, which is different from the conventional order parameter of the Mott-insulator–superfluid-phase transitions. For this nonlocal order parameter, the scaling behavior corresponding to a continuous phase transition is obtained and a power-law divergence near the critical region follows it. This scaling behavior of quantum entanglement is analyzed by the finite-size scaling and the critical exponents are obtained as $\nu =1.01$ and $\gamma =0.86$. A close connection between quantum fluctuations and the phase transition of entanglement is also obtained.

By applying geometrical optics (GO) to each plane-wave component of a nonparaxial electromagnetic (em) Bessel beam carrying spin and orbital angular momentum (SAM and OAM), we calculate the shift of the beam centroid during propagation in a weakly inhomogeneous, isotropic medium. Apart from recovering the transverse spin and orbital Hall shifts expected from paraxial theory, the nonparaxial treatment reveals additional shifts in both the transverse and lateral directions. When the propagation is close to perpendicular to the refractive index gradient, these shifts should be significant also for nearly paraxial beams. Suggestions are given for an experimental verification of the results.

We demonstrate that single-photon as well as biphoton revivals are possible in a new class of dynamic optical systems—the so-called Glauber-Fock oscillator lattices. In these arrays, both Bloch-like oscillations and dynamic delocalization can occur which can be described in closed form. The bunching and antibunching response of path-entangled photons can be pre-engineered in such coupled optical arrangements, and the emulation of fermionic behavior in this family of lattices is also considered. We elucidate these effects via pertinent examples.

We show that two qubits, initially in a fully classical state, can develop significant quantum correlations as measured by the quantum discord (QD) under the action of a local memoryless noise (specifically we consider the case of a Markovian amplitude-damping channel). This is analytically proven after deriving in a compact form the QD for the class of separable states involved in such a process. We provide a picture in the Bloch sphere that unambiguously highlights the physical mechanism behind the effect regardless of the specific measure of quantum correlations adopted.

We study the scattering problem for the non-Hermitian scattering center, which consists of two Hermitian clusters with anti-Hermitian couplings between them. Counterintuitively, it is shown that it acts as a Hermitian scattering center, that is, the $S$ matrix is unitary, or the Dirac probability current is conserved, ${\left|r\right|}^2+{\left|t\right|}^2=1$, when one of the two clusters is embedded in the waveguides. This conclusion can be applied to an arbitrary parity-symmetric real Hermitian graph with additional $\mathcal{PT}$-symmetric potentials, which is more feasible in the experiment. An exactly solvable model is presented to illustrate the theory. Bethe ansatz solution indicates that the transmission spectrum of such a cluster displays a peculiar feature arising from the non-Hermiticity of the scattering center.

The problems of the design, control, and interaction of the single-electron double-dot charge qubits coherently coupled to the optical cavity mode are studied theoretically. A way to overcome the challenges concerned with the use of classical laser pulses for a qubit state engineering is described, replacing the lasers by a quantized photon field in a semiconductor cavity and a gate voltage. Using this strategy, a simple and efficient scheme is proposed for the creation of highly entangled multiqubit states like the nine-qubit Shor states.

We exploit the notion of SWM- (simultaneous-weak-measurements)-induced quantum state reduction, enabling the use of measurement backaction to produce the desired quantum states. The probabilistic generation of maximally entangled Bell states and the $|\mathrm{GHZ}\rangle$ (Greenberger-Horne-Zeilinger) state are then performed as a consequence of this notion. By combining SWM-induced quantum state reduction with feedback control, we are able to deterministically generate any desired Bell state as well as the $|\mathrm{GHZ}\rangle$ state, without the knowledge of the initial state. The control-computation time is compensated for by the delay time in the time-delay bang-bang control, through which the real-time implementation of the control scheme is guaranteed. The effectiveness of the proposed scheme is illustrated numerically.

We report the storage and retrieval of a small microwave field from a superconducting resonator into collective excitations of a spin ensemble. The spins are nitrogen-vacancy centers in a diamond crystal. The storage time of the order of 30 ns is limited by inhomogeneous broadening of the spin ensemble.

We investigate long-range forces between atoms with anisotropic electric polarizability interacting with dielectrics having anisotropic permittivity in the weak-coupling approximation. Unstable configurations in which the force between the objects is repulsive are constructed. Such configurations exist for three anisotropic atoms as well as for an anisotropic atom above a dielectric plate with a hole whose permittivity is anisotropic. Apart from the absolute magnitude of the force, the dependence on the configuration is qualitatively the same as for metallic objects for which the anisotropy is a purely geometric effect. In the weak limit, closed analytic expressions for rather complicated configurations are obtained. The nonmonotonic dependence of the interaction energy on separation is related to the fact that the electromagnetic Green's dyadic is not positive definite. The analysis in the weak limit is found to also semiquantitatively explain the dependence of Casimir forces on the orientation of anisotropic dielectrics observed experimentally. Contrary to the scalar case, irreducible electromagnetic three-body energies can change sign. We trace this to the fact that the electromagnetic Green's dyadic is not positive definite.

As research and development of extreme ultraviolet lithography (EUVL) sources at 6.7 nm (which will be based on emission from ionized gadolinium) has already begun, reliable atomic data are required in order to determine the optimum plasma conditions. However, the complexity of the atomic structure means that ab initio level-resolved dielectronic recombination (DR) calculations are currently unavailable for the ions of interest. Here we report the first detailed calculation of the DR rate coefficients for the ground state and first excited states of Pd-like gadolinium. Energy levels, radiative transition probabilities, and autoionization rates of Ag-like gadolinium for [Kr]4$d^9$4$fnl$, [Kr]4$p^5$4$d^{10}$4$fnl$, [Kr]4$d^9$5$l$′$nl$, and [Kr]4$d^9$6$l$′$nl$ ($n$ ⩽ 18) complexes were calculated using the flexible atomic code (FAC). It was found that inclusion of 4$p^5$4$d^{10}$4$fnl$ configurations has significant influence on the total DR rate coefficient. The DR rate coefficients obtained here are compared with radiative recombination and three-body recombination coeffcients. The results show that the DR rate coefficient is almost an order of magnitude higher than the coefficients for the other two recombination processes combined at plasma electron temperatures around 110 eV, which suggests that the DR process should be included in theoretical modeling for Pd-like gadolinium in EUVL source plasmas.