The radiative electron capture in nonrelativistic atomic collisions is normally considered by using the Schrödinger equation. We show that the capture cross section obtained from this equation is Galilean-invariant. This result follows under quite general conditions and holds irrespectively of the accuracy of wave functions describing the charged particles. In contrast, this accuracy is crucial for gauge independence of the cross section and we demonstrate that it is the gauge dependence which has been misinterpreted for a long time as the Galilean noninvariance.

The ionization of low angular momentum Rydberg states of alkali-metal atoms in a linearly polarized low frequency monochromatic microwave field is described in the literature as a classical diffusion process initiated by a quantum rate-limiting step. We find here the classical equivalent to this quantum step, which is responsible for the nonhydrogenic $n^{-5}$ scaling of the threshold field. This allows a fully classical explanation of the ionization process.

We report on magneto-optical trapping of fermionic ${}^{53}\mathrm{Cr}$ atoms. A Zeeman-slowed atomic beam provides loading rates up to $3\times {10}^6{\mathrm{s}}^{-1}$. We present systematic characterization of the magneto-optical trap (MOT). We obtain up to $5\times {10}^5$ atoms in the steady-state MOT. The atoms radiatively decay from the excited $P$ state into metastable $D$ states, and, due to the large dipolar magnetic moment of chromium atoms in these states, they can remain magnetically trapped in the quadrupole field gradient of the MOT. We study the accumulation of metastable ${}^{53}\mathrm{Cr}$ atoms in this magnetic trap. We also report on the simultaneous magneto-optical trapping of bosonic ${}^{52}\mathrm{Cr}$ and fermionic ${}^{53}\mathrm{Cr}$ atoms. Finally, we characterize the light-assisted collision losses in this Bose-Fermi cold mixture.

In this work we study the quantum deletion machine with two transformers, and show that the deletion machine with a single transformer performs better than the deletion machine with more than two transformers. We also observe that the fidelity of deletion depends on the blank state used in the deleter, and so for different blank states the fidelity is different. Further, we study the Pati-Braunsein deleter with transformer.

Experimentally observable quantum accelerator modes are used as a test case for the study of some general aspects of quantum decay from classical stable islands immersed in a chaotic sea. The modes are shown to correspond to metastable states, analogous to the Wannier-Stark resonances. Different regimes of tunneling, marked by different quantitative dependence of the lifetimes on $1∕\hslash$, are identified, depending on the resolution of KAM substructures that is achieved on the scale of $\hslash$. The theory of resonance assisted tunneling introduced by Brodier et al. [Ann. Phys. 300, 88 (2002)] is reexamined and found to well describe decay whenever applicable.

We focus on determining the separability of an unknown bipartite quantum state $\rho$ by invoking a sufficiently large subset of all possible entanglement witnesses given the expected value of each element of a set of mutually orthogonal observables. We review the concept of an entanglement witness from the geometrical point of view and use this geometry to show that the set of separable states is not a polytope and to characterize the class of entanglement witnesses (observables) that detect entangled states on opposite sides of the set of separable states. All this serves to motivate a classical algorithm which, given the expected values of a subset of an orthogonal basis of observables of an otherwise unknown quantum state, searches for an entanglement witness in the span of the subset of observables. The idea of such an algorithm, which is an efficient reduction of the quantum separability problem to a global optimization problem, was introduced by [Ioannou et al., Phys. Rev. A 70, 060303(R)], where it was shown to be an improvement on the naive approach for the quantum separability problem (exhaustive search for a decomposition of the given state into a convex combination of separable states). The last section of the paper discusses in more generality such algorithms, which, in our case, assume a subroutine that computes the global maximum of a real function of several variables. Despite this, we anticipate that such algorithms will perform sufficiently well on small instances that they will render a feasible test for separability in some cases of interest (e.g., in $3\times 3$ dimensional systems).

The photorecombination of highly charged few-electron mercury ions ${\mathrm{Hg}}^{75+}$ to ${\mathrm{Hg}}^{78+}$ has been explored with the Heidelberg electron beam ion trap. By monitoring the emitted x rays $(65–76\mathrm{keV})$ and scanning the electron beam energy $(45–54\mathrm{keV})$ over the $KLL$ dielectronic recombination (DR) region, the energies of state-selected DR resonances were determined to within $\pm 4\mathrm{eV}$ (relative) and $\pm 14\mathrm{eV}$ (absolute). At this level of experimental accuracy, it becomes possible to make a detailed comparison to various theoretical approaches and methods, all of which include quantum electrodynamic (QED) effects and finite nuclear size contributions (for a $1s$ electron, these effects can be as large as 160 and $50\mathrm{eV}$, respectively). In He-like ${\mathrm{Hg}}^{78+}$, a good agreement between the experimental results and the calculations has been found. However, for the capture into Li-, Be-, and B-like ions, significant discrepancies have been observed for specific levels. The discrepancies suggest the need for further theoretical and experimental studies with other heavy ions along these isoelectronic sequences.

Theoretical resonance energies for KLL dielectronic recombination into He-, Li-, Be-, and B-like Hg ions are calculated by various means and discussed in detail. We apply the multiconfiguration Dirac-Fock and the configuration interaction Dirac-Fock-Sturmian methods, and quantum electrodynamic many-body theory. The different contributions such as relativistic electron interaction, quantum electrodynamic contributions, and finite nuclear size and mass corrections are calculated and their respective theoretical uncertainties are estimated. Our final results are compared to experimental data from the preceding paper. The comparison of theoretical values with the experimental energies shows a good overall agreement for most transitions and illustrates the significance of relativistic electron interaction contributions including correlation, magnetic, and retardation effects and quantum electrodynamic corrections. A few discrepancies found in specific recombination resonances for initially Li- and Be-like Hg ions are pointed out, suggesting the need for further theoretical and experimental studies along these isoelectronic sequences.

The configuration interaction (CI) method using orbitals centered on the nucleus has recently been applied to calculate the interactions of positrons interacting with atoms. Computational investigations of the convergence properties of binding energy, phase shift, and annihilation rate with respect to the maximum angular momentum of the orbital basis for the $e^{+}\mathrm{Cu}$ and PsH bound states, and the $e^{+}\text{−}\mathrm{H}$ scattering system were completed. The annihilation rates converge very slowly with angular momentum, and moreover the convergence with radial basis dimension appears to be slower for high angular momentum. A number of methods of completing the partial wave sum are compared; an approach based on a $\Delta X_J=a{(J+\frac{1}{2})}^{-n}+b{(J+\frac{1}{2})}^{-(n+1)}$ form [with $n=4$ for phase shift (or energy) and $n=2$ for the annihilation rate] seems to be preferred on considerations of utility and underlying physical justification.

We present differential cross sections of electron capture in $7.5\mathrm{MeV}$ and $12.5\mathrm{MeV}$ proton-helium collisions. Complete experimental separations of the Thomas and the kinematic single electron capture processes in the two-dimensional ${\mathrm{He}}^{+}$ momentum distribution in the plane perpendicular to the fast ion beam have been achieved. We compare the resulting projectile angular differential cross section with the two most recent theoretical calculations and expose significant deviations.

Second-harmonic generation is studied for the case where the fundamental field is light produced in a spontaneous parametric down-conversion process. We show that second-harmonic generation is sensitive to the transverse correlations between signal and idler fields. In particular, when the fundamental is prepared in a state exhibitting spatial antibunching, the second-harmonic intensity may be zero, independent of the intensity of the fundamental field.

We report time-resolved measurements of transverse dynamics in a pulsed custom-made Nd:YAG (yttrium aluminum garnet) broad-area laser, where a dynamic transition from order to turbulentlike patterns appears, without the modification of the Fresnel number. To our knowledge, it is the first time this dynamical transition is observed in a class-B laser. Higher values of the pumping and a higher ratio between the electric field and the inversion population decay rates diminish the time at which the transition takes place. A theoretical model based on the adiabatic approximation allows us to explain the main features of the observed dynamics and to compare the results with those previously seen, especially in broad-area $\mathrm{C}{\mathrm{O}}_2$ lasers.

By pursuing the deep relation between the one-dimensional Dirac equation and quantum walks, the physical role of quantum interference in the latter is explained. It is shown that the time evolution of the probability density of a quantum walker, initially localized on a lattice, is directly analogous to relativistic wave-packet spreading. Analytic wave-packet solutions reveal a striking connection between the discrete and continuous-time quantum walks.

The energy loss of $100\text{−}\mathrm{keV}$ hydrogen atoms scattered under a grazing angle of incidence from a clean and flat Cu(111) surface is studied in coincidence with the number of emitted electrons. From the dependence of the energy loss on the angle of incidence we deduce the position dependent stopping power which shows the same functional dependence but a factor of about 2 higher values than recent calculations. From the number of emitted electrons related to a specific energy loss we reveal processes related to electron emission as dominant channel for energy dissipation of scattered projectiles.

We propose phase diagrams for an imbalanced (unequal number of atoms or Fermi surface in two pairing hyperfine states) gas of atomic fermions near a broad Feshbach resonance using mean-field theory. Particularly, in the plane of interaction and polarization we determine the region for a mixed phase composed of normal and superfluid components. We compare our prediction of phase boundaries with the recent measurement and find a good qualitative agreement.

We present the details of an accurate lifetime measurement of the $1s^{2}2s^{2}2p{}^{2}P_{3∕2}^o$ metastable level in boronlike Ar XIV performed at the Heidelberg electron beam ion trap [A. Lapierre et al., Phys. Rev. Lett. 95, 183001 (2005)]. The lifetime was inferred from decay curves resulting from deexcitation of the metastable level to its ${}^{2}P_{1∕2}^o$ ground state through a magnetic-dipole $\left(M1\right)$ transition upon cyclically turning on and off the electron beam. The measured lifetime of $9.573\left(4\right)\left(\genfrac{}{}{0ex}{}{+12}{-5}\right)\mathrm{ms}$ (stat)(syst) is in disagreement with a trend of theoretical predictions of $9.53\left(1\right)\mathrm{ms}$, which include the effect of the electron anomalous magnetic moment. Systematic effects were investigated by studying with high statistical significance the dependence of the decay times of the curves on various trapping conditions. The asymptotic trend of the decay times observed for increasingly high trapping potentials, which indicates negligible ion losses within a ms time scale, is in agreement with a theoretical model describing the ion escape rate in electrostatic ion traps. However, for high trapping potentials, we observed an unexpected slowly decaying component suggesting the presence of trapped low-energy electrons. Their origin, dynamics, and temperature, as well as their possible effects on the measured lifetime were investigated.

In this paper, we report the first comparison study between ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ on their triple-ionization-induced dissociation channels using near-IR 800-nm ultrashort laser pulses. Our experiment shows that the ${\mathrm{O}}^{2+}+{\mathrm{O}}^{+}$ channel is predominately formed nonvertically through the intermediate ${\mathrm{O}}^{+}+{\mathrm{O}}^{+}$ channel, while the ${\mathrm{N}}^{2+}+{\mathrm{N}}^{+}$ channel appears to be formed vertically at the lower intensity range but nonvertically at higher intensities. Interestingly, ${\mathrm{N}}^{2+}+{\mathrm{N}}^{+}$ appears to be in the electronically excited state when it is reached vertically in the lower intensity range. The different triple ionization and dissociation behaviors between ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ can be understood by considering the ionization dynamics of the two molecules in our ultrashort laser pulses.

We investigate the density profiles of a partially polarized trapped Fermi gas in the BCS-BEC crossover region using mean field theory within the local density approximation. Within this approximation the gas is phase separated into concentric shells. We describe how the structure of these shells depends upon the polarization and the interaction strength. A comparison with experiments yields insight into the possibility of a polarized superfluid phase.

Considerable effort has been devoted to deriving the Born rule [i.e., that ${\mid \psi \left(x\right)\mid }^{2}dx$ is the probability of finding a system, described by $\psi$, between $x$ and $x+dx$] in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert-space formulation of classical mechanics as well. These results provide insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.

The fully relativistic theory of the Zeeman splitting of the $1s$ hyperfine-structure levels in hydrogenlike ions is considered for the magnetic field magnitude in the range from $1\text{to}10\mathrm{T}$. The second-order corrections to the Breit-Rabi formula are calculated and discussed. The results can be used for a precise determination of nuclear magnetic moments from $g$-factor experiments.