We report isotope-selective loading and trapping of doubly ionized ytterbium into an rf quadrupole trap. Isotopically pure clouds of ${}^{174}\mathrm{Yb}$${}^{+}$ ions were first loaded into the rf trap via a multistage photoionization process. The Yb${}^{2+}$ ions were then produced by electron impact ionization of the trapped Yb${}^{+}$ ions. The Yb${}^{2+}$ ions were subsequently detected by rf excitation of their secular motion in the trap, which led to sympathetic heating and changes in the fluorescence of the laser-cooled Yb${}^{+}$ ions. The presence of doubly charged Yb ions was further verified by the appearance of a dark band in the center of Yb${}^{+}$ ion cloud after electron impact ionization. We discuss the possible formation of Yb${}^{2+}$H and similar compounds and the schemes for the direct optical detection of the Yb${}^{2+}$ ions.

We show that a purely $s$-wave interaction in three dimensions (3D) can induce higher partial-wave resonances in mixed dimensions. We develop two-body scattering theories in all three cases of 0D-3D, 1D-3D, and 2D-3D mixtures and determine the positions of higher partial-wave resonances in terms of the 3D $s$-wave scattering length assuming a harmonic confinement potential. We also compute the low-energy scattering parameters in the $p$-wave channel (scattering volume and effective momentum) that are necessary for the low-energy effective theory of the $p$-wave resonance. We point out that some of the resonances observed in the Florence group experiment [Phys. Rev. Lett. 104, 153202 (2010)] can be interpreted as the $p$-wave resonances in the 2D-3D mixed dimensions. Our study paves the way for a variety of physics, such as Anderson localization of matter waves under $p$-wave resonant scatterers.

We calculated using the ab initio method the three-fold differential cross section of a single-photon double photoionization of helium at equal energy sharing and derived the Gaussian width parameter $\gamma$, describing the angular interelectron correlations, for the total electron energy $E$ ranging from $0.1$ to $100$ eV. The results are in perfect agreement with experimental data. Contrary to common expectations, the results demonstrate that the Wannier threshold law for the Gaussian width parameter $\gamma \propto E^{1/4}$ is not correct at energies attainable in modern experiments. It is shown that the $\gamma$ dependence on the energy is much better described by the modified threshold law, obtained by Kazansky and Ostrovsky [J. Phys. B 26, 2231 (1993)]. Also, we explored the Gaussian width parameter for double photoionization of targets with strongly asymmetrical initial-state configuration: the atomic hydrogen negative ion ${\mathrm{H}}^{-}$ and the helium atom in the $2s\hspace{0.5em}{}^{1}S$ and $3s\hspace{0.5em}{}^{1}S$ excited states. We found that the Gaussian width dependence on the total ejected electron energy for these targets has a maximum at low energies. We also show that the correlation parameter dependence on the interelectron angle for these targets is essentially non-Gaussian and has a number of peaks equal to the number of the initial-state radial nodes, which provide new facilities for the qualitative analysis of the electron structure of the target atom.

We show numerically that it is possible to change the structure of a simple molecule, that is, a diatomic molecule, where the bond length is modified at a precise timing with symmetrically chirped laser pulses. In the adiabatic regime, the process is fully time reversible, making it possible to design slow vibrations with large bond elongations. The scheme relies on the preparation of a separable state of both nuclear and electronic degrees of freedom with predominant amplitude on the dissociative (antibonding) electronic wave function. Shorter laser pulses can be used to dynamically induce larger bond elongations, preparing a highly excited vibrational wave packet in the ground potential as the laser is switched off.

Absorbing boundaries in the mean-field approximation are investigated and applied to small systems interacting with strong laser fields. Two types of calculations are considered: (i) a variational approach with a complex absorbing potential included in the full Hamiltonian and (ii) the inclusion of a complex absorbing potential in the single-particle equations. It is elucidated that the second approach outperforms the variational approach for small grids.

We explore, from a theoretical perspective, photoelectron angular distributions (PADs) of the Na clusters Na${}_8$, Na${}_{10}$, Na${}_{12}$, Na${}_{18}$, Na${}_3{}^{+}$, Na${}_{11}{}^{+}$, Na${}_{13}{}^{+}$, and Na${}_{19}{}^{+}$. The basis of the description is the time-dependent local-density approximation (TDLDA), augmented by a self-interaction correction (SIC) to describe ionization properties correctly. The scheme is solved on a numerical grid in coordinate space with absorbing bounds. We assume for each cluster system an isotropic ensemble of free clusters and develop for the case of one-photon emission analytical formulas for computing the orientation-averaged PAD on the basis of a few TDLDA-SIC calculations for properly chosen reference orientations. It turns out that all the information in the averaged PAD is contained in one anisotropy parameter. We find that this parameter varies very little with system size, but as a whole is crucially influenced by the detailed ionic structure. We also make comparisons with direct orientation averaging and consider one example reaching outside the perturbative regime.

We study the correlated two-electron momentum spectra of the nonsequential double ionization (NSDI) of an atom in an intense laser field based on the recently developed quantitative rescattering (QRS) theory. According to the rescattering model, an electron that was released earlier in the laser pulse may return to collide again with the target ion. NSDI can occur directly if this electron knocks out another electron in a process similar to the ($e,2e$) process or indirectly by first exciting the target ion to an excited state which is later ionized by the laser field. Using QRS, we obtain the returning electron wave packet. By multiplying this wave packet with standard field-free ($e,2e$) differential cross sections, or with inelastic electron-impact excitation cross sections and the subsequent tunneling ionization, we obtain the correlated two-electron momentum spectra. The calculated spectra agree mostly with the experimental data. However, experimental data show additional features that cannot be accounted for by these two mechanisms only, and other mechanisms for NSDI are suggested. The contributions of these mechanisms to the longitudinal ion momentum distributions are also analyzed. The present quantum mechanical QRS calculation verifies the validity of rescattering model for the NSDI processes at the most fundamental and detailed level.

We analyze the saturation of a nuclear magnetic resonance (NMR) signal using optimal magnetic fields. We consider both the problems of minimizing the duration of the control and its energy for a fixed duration. We solve the optimal control problems by using geometric methods and a purely numerical approach, the grape algorithm, the two methods being based on the application of the Pontryagin maximum principle. A very good agreement is obtained between the two results. The optimal solutions for the energy-minimization problem are finally implemented experimentally with available NMR techniques.

We have calculated the low-lying elementary excitations of three-dimensional few-vortex arrays in trapped Bose-Einstein condensates. The number of different Kelvin-Tkachenko vortex wave branches found matches the number of vortices in the condensate. The lowest odd-parity modes exhibit superfluid gyroscopic vortex motion. Experimentally, these modes could be excited and observed individually or in connection with the formation and decay of quantum turbulence.

Similar to what has recently been achieved with Bose-Bose mixtures [G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010)], mixed-dimensional Fermi-Fermi mixtures can be created by applying a species-selective one-dimensional optical lattice to a two-species Fermi gas ($\sigma \equiv \{\uparrow ,\downarrow \}$), in such a way that both species are confined to quasi–two-dimensional geometries determined by their hoppings along the lattice direction. We investigated the ground-state phase diagram of superfluidity for such mixtures in the BCS-BEC evolution, and found normal, gapped superfluid, gapless superfluid, and phase separated regions. In particular, we found a stable gapless superfluid phase where the unpaired $\uparrow$ and $\downarrow$ fermions coexist with the paired (or superfluid) ones in different momentum space regions. This phase is in some ways similar to the Sarma state found in mixtures with densities, but in our case, the gapless superfluid phase is unpolarized and most importantly it is stable against phase separation.

We investigate the expansion dynamics of a dilute Fermi gas at unitarity in the context of dissipative fluid dynamics. Our aim is to quantify the effects of shear viscosity on the time evolution of the system. We compare exact numerical solutions of the equations of viscous hydrodynamics to various approximations that have been proposed in the literature. Our main findings are (i) shear viscosity leads to characteristic features in the expansion dynamics; (ii) a quantitative description of these effects has to include reheating; (iii) dissipative effects are not sensitive to the equation of state $P(n,T)$ as long as the universal relation $P=\frac{2}{3}\mathcal{E}$ is satisfied; (iv) the expansion dynamics mainly constrains the cloud average of the shear viscosity.

The propagation of optical beams in weakly nonlocal media with cubic-quintic nonlinearity is studied. The exact solutions for bright and dark solitons are found. The general solutions are implicit, and they are expressed in terms of the elliptic integrals. In particular cases, the solutions are written explicitly in terms of the hyperbolic functions. The dependence of the beam parameters and the soliton shapes on the system parameters is analyzed. The role of nonlocality on the soliton stability is investigated.

Generation of frequency-correlated narrowband biphotons from the four-wave mixing process is theoretically analyzed through manipulating optical properties of light propagation inside a cold atomic ensemble. In contrast with the spontaneous parametric down-conversion case, we find a much looser condition, which allows producing such frequency-correlated paired photons. We propose a two-photon temporal conditional correlation measurement to detect these photons. In addition, our results provide other evidence for observing backward pulse propagation from the viewpoint of two-photon correlation measurement.

In a recent publication [Phys. Rev. A 79, 065602 (2009)], it was shown that an avoided-crossing resonance can be defined according to level-structural or dynamical criteria. We propose an experiment to observe the difference between the two definitions in a three-level $\Lambda$ system using microwave fields coupling hyperfine magnetic sublevels in alkali-metal atoms.

We show numerically that by using periodic lattices the filamentation of intense femtosecond laser pulses, otherwise a result of competing nonlinear effects, can be well controlled with respect to its properties. The diffraction induced by the lattice provides a regularizing mechanism to the nonlinear self-action effects involved in filamentation. We demonstrate a new propagation regime of intense lattice solitons bridging the field of spatial solitons with that of femtosecond laser filamentation. The effective filamentation control is expected to have an important impact on numerous applications.

Employing the trace distance as a measure for the distinguishability of quantum states, we study the influence of initial correlations on the dynamics of open systems. We concentrate on the Jaynes-Cummings model for which the knowledge of the exact joint dynamics of system and reservoir allows the treatment of initial states with arbitrary correlations. As a measure for the correlations in the initial state we consider the trace distance between the system-environment state and the product of its marginal states. In particular, we examine the correlations contained in the thermal equilibrium state for the total system, analyze their dependence on the temperature and on the coupling strength, and demonstrate their connection to the entanglement properties of the eigenstates of the Hamiltonian. A detailed study of the time dependence of the distinguishability of the open system states evolving from the thermal equilibrium state and its corresponding uncorrelated product state shows that the open system dynamically uncovers typical features of the initial correlations.

Analysis of x-ray spectra emitted by highly charged ions in an electron-cyclotron-resonance ion source (ECRIS) may be used as a tool to estimate the charge-state distribution (CSD) in the source plasma. For that purpose, knowledge of the electron energy distribution in the plasma, as well as the most important processes leading to the creation and de-excitation of ionic excited states are needed. In this work we present a method to estimate the ion CSD in an ECRIS through the analysis of the x-ray spectra emitted by the plasma. The method is applied to the analysis of a sulfur ECRIS plasma.

Most of the current theories on the $p$-wave superfluid in cold atomic gases are based on the effective-range theory for the two-body scattering, where the low-energy $p$-wave scattering amplitude $f_1(k)$ is given by $f_1(k)=-1/[\mathit{ik}+1/(\mathcal{V}{k}^2)+1/\mathcal{R}]$. Here $k$ is the incident momentum, $\mathcal{V}$ and $\mathcal{R}$ are the $k$-independent scattering volume and effective range, respectively. However, due to the long-range nature of the van der Waals interaction between two colliding ultracold atoms, the $p$-wave scattering amplitude of the two atoms is not described by the effective-range theory [J. Math. Phys. 4, 54 (1963); Phys. Rev. A 58, 4222 (1998)]. In this paper we provide an explicit calculation for the $p$-wave scattering of two ultracold atoms near the $p$-wave magnetic Feshbach resonance. We show that in this case the low-energy $p$-wave scattering amplitude $f_1(k)=-1/[\mathit{ik}+1/({\mathcal{V}}^{\mathrm{eff}}{k}^2)+1/({\mathcal{S}}^{\mathrm{eff}}k)+1/{\mathcal{R}}^{\mathrm{eff}}]$ where ${\mathcal{V}}^{\mathrm{eff}},$ ${\mathcal{S}}^{\mathrm{eff}}$, and ${\mathcal{R}}^{\mathrm{eff}}$ are $k$-dependent parameters. Based on this result, we identify sufficient conditions for the effective-range theory to be a good approximation of the exact scattering amplitude. Using these conditions we show that the effective-range theory is a good approximation for the $p$-wave scattering in the ultracold gases of ${}^6\mathrm{Li}$ and ${}^{40}\mathrm{K}$ when the scattering volume is enhanced by the resonance.

A relatively large yield of neutralized atoms was observed when 3 keV Ar${}^{7+}$ ions were guided trough polyethylene terephthalate nanocapillaries. Time and deposited-charge dependence of the angular distribution of both the guided ions and the neutrals was measured simultaneously using a two-dimensional multichannel plate detector. The yield of neutrals increased significantly faster than that of guided ions and saturated typically at a few percent level. In accordance with earlier observations, both the yield and the mean emission angle of the guided ions exhibited strong oscillations. For the atoms, the equilibrium was achieved not only faster, but also without significant oscillations in yield and angular position. A phase analysis of these time dependencies provides insight into the dynamic features of the self-organizing mechanisms, which leads to ion guiding in insulating nanocapillaries.

We study the stopping of spinning particles in vacuum. A torque is produced by fluctuations of the vacuum electromagnetic field and the particle polarization. Expressions for the frictional torque and the power radiated by the particle are obtained as a function of rotation velocity and the temperatures of the particle and the surrounding vacuum. We solve this problem following two different approaches: (i) a semiclassical calculation based upon the fluctuation-dissipation theorem (FDT), and (ii) a fully quantum-mechanical theory within the framework of quantum electrodynamics, assuming that the response of the particle is governed by bosonic excitations such as phonons and plasmons. Both calculations lead to identical final expressions, thus confirming the suitability of the FDT to deal with problems that are apparently out of equilibrium, and also providing comprehensive insight into the physical processes underlying thermal and vacuum friction. We adapt the quantum-mechanical theory to describe particles whose electromagnetic response is produced by fermionic excitations. Furthermore, we extend our FDT formalism to fully account for magnetic polarization, which dominates friction when the particle is a good conductor. Finally, we present numerically calculated torques and stopping times for the relevant cases of graphite and gold nanoparticles.