We observe the formation of discrete diffraction-managed optical solitons in arrays of periodically curved coupled waveguides for two types of modulated structures: laser-written arrays in silica glass with self-focusing nonlinearity and lithium niobate waveguide arrays with self-defocusing photorefractive nonlinearity. Our results demonstrate that, for both types of nonlinear response, soliton formation occurs after transitional self-induced beam broadening, being fundamentally different from nonlinear self-focusing and defocusing in a bulk medium or discrete self-trapping in straight waveguides.

We solve analytically the Schrödinger equation for the $N$-dimensional inverse square potential in quantum mechanics with a minimal length in terms of Heun’s functions. We apply our results to the problem of a dipole in a cosmic string background. We find that a bound state exists only if the angle between the dipole moment and the string is larger than $\pi ∕4$. We compare our results with recent conflicting conclusions in the literature. The minimal length may be interpreted as a radius of the cosmic string.

We study the geometrical corrections to the simple proximity force approximation (PFA) for the nonretarded Casimir force. We present analytical results for the force between objects of various shapes and substrates, and between pairs of objects. We compare the results to those from more exact numerical calculations. We treat spheres, spheroids, cylinders, cubes, cones, and wings; the analytical PFA results together with the geometrical correction factors are summarized in a table.

We propose a scheme for linear optical quantum Fredkin gate based on the combination of recently experimentally demonstrated linear optical partial-SWAP gate and controlled-Z gates. Both heralded gate and simplified post-selected gate operating in the coincidence basis are designed. The suggested setups have a simple structure and require stabilization of only a single Mach-Zehnder interferometer. A proof-of-principle experimental demonstration of the post-selected Fredkin gate appears to be feasible and within the reach of current technology.

Electron impact excitation of the $4p{}^{3,1}P_1$, $4d,5d,6d{}^{3}D_{1,2,3}$, and $4d,5d{}^{1}D_1$ states of the neutral zinc atom was studied by measuring photon decay intensities in the energy region of the $3d^{9}4s^{2}4p$ autoioionizing states. Two phenomena, both involving strong electron correlations and an active role of one of the $3d$ electrons in an intermediate scattering step, have been observed. The first is $3d$ core-excited negative-ion resonances, which dominate the energy region between 10.5 and $11.5\mathrm{eV}$. The second is postcollision interaction (PCI) in the decay of autoionizing states which populates higher excited states at incident electron energies above $11.5\mathrm{eV}$. The low energies of both the scattered and ejected electrons after near-threshold excitation of $3d^{9}4s^{2}4p$ autoionizing states enable a large transfer of orbital angular momentum, up to two units, by the PCI.

We present a detailed study of the energy losses of hydrogen ions that are scattered off an Ag(110) single-crystal surface for primary energies between 1 and 4 keV. We performed measurements for grazing angles as a function of crystal azimuthal orientation, which show large differences in energy losses. Experimental results are discussed by means of trajectory calculations of protons scattered under grazing-incidence conditions on the surface. Using nonlinear models for the stopping power, ab initio crystal structure calculations of the electronic density, and semiclassical simulations, we obtain data that are in very good agreement with experimental results. These simulations allow us to properly take into account the variations of the surface electronic density and hence obtain an accurate description of the energy loss processes for ion scattering along various azimuthal orientations of the target.

We describe algorithms and experimental strategies for the Pareto optimal control problem of simultaneously driving an arbitrary number of quantum observable expectation values to their respective extrema. Conventional quantum optimal control strategies are less effective at sampling points on the Pareto frontier of multiobservable control landscapes than they are at locating optimal solutions to single observable control problems. The present algorithms facilitate multiobservable optimization by following direct paths to the Pareto front, and are capable of continuously tracing the front once it is found to explore families of viable solutions. The numerical and experimental methodologies introduced are also applicable to other problems that require the simultaneous control of large numbers of observables, such as quantum optimal mixed state preparation.

We propose a microtrap realized with a fictitious magnetic field by applying a circularly polarized laser beam. We calculate the potentials and demonstrate that various atom traps, such as the Ioffe-Pritchard trap, double traps, and ring trap, can easily be built by varying the intensity and the position of the laser beams. We show that even an optical lattice can be realized by adding more laser beams properly. Our trap has the advantage as compared to a general atom lattice that the properties of the traps can be manipulated individually.

We examine the dynamics of two bright solitary waves with a negative nonlinear term. The observed repulsion between two solitary waves—when these are in an antisymmetric combination—is attributed to conservation laws. Slight breaking of parity, in combination with weak relaxation of energy, leads the two solitary waves to merge. The effective repulsion between solitary waves requires certain nearly ideal conditions and is thus fragile.

The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average discrete coordinates applies and makes the problem analytically tractable. We present a number of results and features, which differ from the case of identical atoms.

We present a way to engineer an effective anti-Jaynes-Cumming and a Jaynes-Cumming interaction between an atomic system and a single cavity mode and show how to employ it in reservoir engineering processes. To construct the effective Hamiltonian, we analyze the interaction of an atomic system in a $\Lambda$ configuration, driven by classical fields, with a single cavity mode. With this interaction, we first show how to generate a decoherence-free displaced squeezed state for the cavity field. In our scheme, an atomic beam works as a reservoir for the radiation field trapped inside the cavity, as employed recently by S. Pielawa et al. [Phys. Rev. Lett. 98, 240401 (2007)] to generate an Einstein-Podolsky-Rosen entangled radiation state in high-$Q$ resonators. In our scheme, all the atoms have to be prepared in the ground state and, as in the cited article, neither atomic detection nor precise interaction times between the atoms and the cavity mode are required. From this same interaction, we can also generate an ideal squeezed reservoir for atomic systems. For this purpose we have to assume, in addition to the engineered atom-field interaction, a strong decay of the cavity field (i.e., the cavity decay must be much stronger than the effective atom-field coupling). With this scheme, some interesting effects in the dynamics of an atom in a squeezed reservoir could be tested.

We present a method for measuring surface interaction parameters of spin-polarized Rb atoms on coated Pyrex glass surfaces based on edge enhancement in optically pumped Rb vapor. The best fit to the measured magnetic resonance lines using a theoretical model yields a dwell time ${\tau }_s=1.8\mu \mathrm{s}$ and a spin relaxation probability ${\xi }_s=0.015$ for a spin-polarized Rb atom on a Pyrex glass surface coated with dichlorooctamethyl-tetrasiloxane (Surfasil), and ${\tau }_s=0.5\mu \mathrm{s}$ and ${\xi }_s=0.001$ on a surface coated with octadecyltrichlorosilane (OTS).

We present detailed measurements of the Casimir-Lifshitz force between two gold surfaces (a sphere and a plate) immersed in ethanol and study the effect of residual electrostatic forces, which are dominated by static fields within the apparatus and can be reduced with proper shielding. Electrostatic forces are further reduced by Debye screening through the addition of salt ions to the liquid. Additionally, the salt leads to a reduction of the Casimir-Lifshitz force by screening the zero-frequency contribution to the force; however, the effect is small between gold surfaces at the measured separations and within experimental error. An improved calibration procedure is described and compared with previous methods. Finally, the experimental results are compared with Lifshitz’s theory and found to be consistent for the materials used in the experiment.

We propose and experimentally demonstrate nondestructive and noiseless removal (filtering) of vacuum states from an arbitrary set of coherent states of continuous variable systems. Errors, i.e., vacuum states in the quantum information are diagnosed through a weak measurement, and on that basis, probabilistically filtered out. We consider three different filters based on on-off detection, phase stabilized, and phase randomized homodyne detection. We find that on-off detection, optimal in the ideal theoretical setting, is superior to the homodyne strategy also in a practical setting.

We perform an analysis of the optomechanical entanglement between the experimentally detectable output field of an optical cavity and a vibrating cavity end-mirror. We show that by a proper choice of the readout (mainly by a proper choice of detection bandwidth) one cannot only detect the already predicted intracavity entanglement but also optimize and increase it. This entanglement is explained as being generated by a scattering process owing to which strong quantum correlations between the mirror and the optical Stokes sideband are created. All-optical entanglement between scattered sidebands is also predicted, and it is shown that the mechanical resonator and the two sideband modes form a fully tripartite-entangled system capable of providing practicable and robust solutions for continuous-variable quantum-communication protocols.

The quantitative analysis of the electromagnetic spectra of isolated neutron stars by means of model atmosphere calculations requires extensive data sets of atomic energy values and transition probabilities in intense magnetic fields. We present a method for the fast computation of wave functions, energies, and oscillator strengths of medium-$Z$ atoms and ions at neutron star magnetic field strengths $B\gtrsim {10}^7\mathrm{T}$ which strikes a balance between numerical accuracy and computing times. We use a Hartree-Fock ansatz in which each single-electron orbital is expanded in terms of Landau states with one longitudinal expansion function, and each Landau level contributes with a different weight to the orbital. Both the longitudinal expansion functions and the Landau weights are determined in a doubly self-consistent way. Hartree-Fock equations are solved by decomposing the $z$ axis in finite elements and expanding the longitudinal wave functions in terms of sixth-order $B$-splines. The contributions of the eight lowest Landau levels are taken into account. The procedure can be efficiently parallelized. Results are presented for the ground states and different excited states of atoms and ions for nuclear charges $Z=2,\dots ,26$ and $N=2,\dots ,26$ electrons, and for oscillator strengths. Wherever possible, a comparison with the results of previous calculations is made.

A theoretical approach to calculating the dipole moment function of a diatomic molecule at very small internuclear separations has been suggested. The approach is based on the united-atom model and the $LS$-coupling approximation. Regularities in the behavior of the dipole moments as functions of the internuclear separation, electronic state, and nuclear charge of the molecule have been found. Within the approach, the dipole moment functions of some diatomic molecules, whose united atoms are in groups II, IV, V, VII, and VIII of periods 1–4 of the periodic table, were calculated.

In the study of relaxation processes in coherent nonequilibrium dynamics of quenched quantum systems, ultracold atoms in optical superlattices with periodicity 2 provide a very fruitful test ground. We consider the dynamics of a particular, experimentally accessible initial state prepared in a superlattice structure evolving under a Bose-Hubbard Hamiltonian in the entire range of interaction strengths, further investigating the issues raised by Cramer et al. [Phys. Rev. Lett. 101, 063001 (2008)]. We investigate the relaxation dynamics analytically in the noninteracting and hard-core bosonic limits, deriving explicit expressions for the dynamics of certain correlation functions, and numerically for finite interaction strengths using the time-dependent density-matrix renormalization (t-DMRG) approach. We can identify signatures of local relaxation that can be accessed experimentally with present technology. While the global system preserves the information about the initial condition, locally the system relaxes to the state having maximum entropy respecting the constraints of the initial condition. For finite interaction strengths and finite times, the relaxation dynamics contains signatures of the relaxation dynamics of both the noninteracting and hard-core bosonic limits.