The electron capture by the H-like Gd ion is evaluated within the frames of the line-profile approach (LPA). The energy and widths of the double-excited energy levels and the corresponding resonance strengths are calculated. With the employment of the results of our previous work, the resonance strengths for the H-like U ion were also calculated and compared with the recent experimental and theoretical data. This calculation partly takes into account the interelectron interaction to all orders of QED perturbation theory. The lowest-order radiative corrections are also included. The LPA produces results for both dielectronic and radiative recombination.

T. Tanabe et al. [Phys. Rev. A 82, 040101(R) (2010)] have experimentally demonstrated that the emission properties of unstable atoms in entangled and product states are different. The authors define an apparent decay time as a fitting parameter which falls below the lifetime of the single atom for entangled pairs. We argue that their results about coincidence time spectra are correct, but those concerning lifetimes cannot be considered conclusive because they assume the emission of photons by the two atoms to be independent processes, a doubtful hypothesis for entangled states. We suggest an improved evaluation of the lifetimes based on a rigorous approach, which demands some modifications of the experimental procedure.

In this Reply to the preceding Comment by Sancho and Plaja, we point out the difference between the coincidence time spectrum of two Lyman-$\alpha$ photons measured by us and their theoretical one.

Using a fully correlated, four-dimensional lattice, time-dependent Schrödinger equation model of the collisions of bare projectile ions with two-electron atoms (H${}^{+}$, He${}^{2+}$ $+$ He), we demonstrate the existence of vortices in the resulting spectrum of ejected electrons. Following the uncovering of these features in collisions involving only one electron (H${}^{+}$ $+$ H) [Macek et al., Phys. Rev. Lett. 102, 143201 (2009)], this demonstration provides impetus for seeking these features in more readily feasible experimental conditions using a cold helium target and the reaction microscope technique.

We investigate the violation of noncontextuality by a class of continuous-variable states, including variations of entangled coherent states and a two-mode continuous superposition of coherent states. We generalize the Kochen-Specker (KS) inequality discussed by Cabello [A. Cabello, Phys. Rev. Lett. 101, 210401 (2008)] by using effective bidimensional observables implemented through physical operations acting on continuous-variable states, in a way similar to an approach to the falsification of Bell-Clauser-Horne-Shimony-Holt inequalities put forward recently. We test for state-independent violation of KS inequalities under variable degrees of state entanglement and mixedness. We then demonstrate theoretically the violation of a KS inequality for any two-mode state by using pseudospin observables and a generalized quasiprobability function.

We investigate the thermal entanglement of interacting two qubits. We maximize it by tuning a local Hamiltonian under a given interaction Hamiltonian. We prove that the optimizing local Hamiltonian takes a simple form which does not depend on the temperature and that the corresponding optimized thermal entanglement decays as $1/(T\ln T)$ at high temperatures. We also find that at low temperatures the thermal entanglement is maximum without any local Hamiltonians and that the second derivative of the maximized thermal entanglement changes discontinuously at the boundary between the high- and low-temperature phases.

We consider the time evolution of entanglement in a finite two-dimensional transverse Ising model. The model consists of a set of seven localized spin-$\frac{1}{2}$ particles in a two-dimensional triangular lattice coupled through nearest-neighbor exchange interaction in the presence of an external time-dependent magnetic field. The magnetic field is applied in different function forms: step, exponential, hyperbolic, and periodic. We found that the time evolution of the entanglement shows an ergodic behavior under the effect of the time-dependent magnetic fields. Also, we found that while the step magnetic field causes great disturbance to the system, creating rapid oscillations, the system shows great controllability under the effects of the other magnetic fields where the entanglement profile follows closely the shape of the applied field even with the same frequency for periodic fields. This follow-up trend breaks down as the strength of the field, the transition constant for the exponential and hyperbolic forms, or the frequency for periodic field increase leading to rapid oscillations. We observed that the entanglement is very sensitive to the initial value of the applied periodic field: the smaller the initial value is, the less distorted the entanglement profile is. Furthermore, the effect of thermal fluctuations is very devastating to the entanglement, which decays very rapidly as the temperature increases. Interestingly, although a large value of the magnetic field strength may yield a small entanglement, the magnetic field strength was found to be more persistent against thermal fluctuations than the small field strengths.

We studied the dynamic properties of ion guiding through nanocapillaries etched in insulating polycarbonate (PC). Capillaries with diameters of 95 and 165 nm and a length of 10 $\mu$m were used. In a further sample, the capillaries had a diameter of 175 nm and a length of 30 $\mu$m. A few additional measurements were made using capillaries in polyethylene terephthalate (PET). The temporal evolution of the intensity and the angular distribution of the transmitted ions were studied by measuring transmission profiles as a function of the charge deposited on the sample surface. The tilt angle of the capillary axis was varied from $0{}^{°}$ to $5{}^{°}$. The mean emission angle of the transmission profiles exhibit pronounced oscillations, similarly as in previous measurements using PET. However, for PC, nearly an order of magnitude more charge needs to be inserted into the capillaries to accomplish the oscillations. In contrast to PET, with PC, we observed a strong decrease of the profile intensities with irradiation time. This observation provides evidence of blocking effects on the ions, which are likely to be due to a repulsive field produced by significant charge deposition inside the PC capillaries.

Recent experimental observations of above-threshold ionization of rare gas atoms and diatomic molecules by midinfrared laser fields [C. I. Blaga et al., Nat. Phys. 5, 335 (2009); W. Quan et al., Phys. Rev. Lett. 103, 093001 (2009)] revealed a prominent maximum in the electron energy spectrum very close to the ionization threshold which is not reproduced by widely used Keldysh-Faisal-Reiss theories. We have performed fully ab initio theoretical analysis and precision calculations to explore the quantum origin of the low-energy structure (LES) observed in the experiments. Our study shows that an important role in shaping of LES is played by the effect of Coulomb attraction in the final electron state and the Coulomb threshold effect.

Recent experiments have shown a remarkable number of collapse and revival oscillations of the matter-wave coherence of ultracold atoms in optical lattices [Will et al., Nature (London) 465, 197 (2010)]. Using a mean-field approximation to the Bose-Hubbard model, we show that the visibility of collapse and revival interference patterns reveals number squeezing of the initial superfluid state. To describe the dynamics, we use an effective Hamiltonian that incorporates the intrinsic two-body and induced three-body interactions, and we analyze in detail the resulting complex pattern of collapse and revival frequencies generated by virtual transitions to higher bands, as a function of lattice parameters and mean-atom number. Our work shows that a combined analysis of both the multiband, nonstationary dynamics in the final deep lattice and the number squeezing of the initial superfluid state explains important characteristics of optical lattice collapse and revival physics. Finally, by treating the two- and three-body interaction strengths and the coefficients describing the initial superposition of number states as free parameters in a fit to the experimental data, it should be possible to go beyond some of the limitations of our model and obtain insight into the breakdown of the mean-field theory for the initial state or the role of nonperturbative effects in the final-state dynamics.

We compare the theoretical predictions for universal thermodynamics of a homogeneous, strongly correlated Fermi gas with the latest experimental measurements reported by the ENS group [S. Nascimbène et al., Nature (London) 463, 1057 (2010)] and the Tokyo group [M. Horikoshi et al., Science 327, 442 (2010)]. The theoretical results are obtained using two diagrammatic theories, together with a virial expansion theory combined with a Páde approximation. We find good agreement between theory and experiment. In particular, the virial expansion, using a Páde approximation up to third order, describes the experimental results extremely well down to the superfluid transition temperature, $T_c~0.16T_F$, where $T_F$ is the Fermi temperature. The comparison in this work complements our previous comparative study on the universal thermodynamics of a strongly correlated but trapped Fermi gas. The comparison also raises interesting issues about the unitary entropy and the applicability of the Páde approximation.

We theoretically investigate the introduction of magnetic impurities into a superfluid Fermi gas. In the presence of a population imbalance ($N_{\uparrow }>N_{\downarrow }$, where $N_{\sigma }$ is the number of Fermi atoms with pseudospin $\sigma =\uparrow ,\downarrow$), we show that nonmagnetic potential scatterers embedded in the system are magnetized in the sense that some of the excess spin-$\uparrow$ atoms are localized around them. They destroy the superfluid order parameter around them, as in the case of the magnetic impurity effect discussed in the superconductivity literature. This pair-breaking effect naturally leads to localized excited states below the superfluid excitation gap. To confirm our idea in a simple manner, we consider an attractive Fermi-Hubbard model within the mean-field theory at $T=0$. We determine consistent superfluid properties around a nonmagnetic impurity, such as the superfluid order parameter, local population imbalance, as well as the single-particle density of states, in the presence of a population imbalance. Since competition between superconductivity and magnetism is one of the most fundamental problems in condensed-matter physics, our results would be useful for the study of this important issue in cold Fermi gases.

A semianalytic theory for the pulse dynamics in similariton amplifiers and lasers is presented, based on a model pulse with adaptive shape. By changing a single parameter, this test function can be continuously tweaked between a pure Gaussian and a pure parabolic profile and can even represent sech-like pulses, the shape of a soliton. This approach allows us to describe the pulse evolution in the self-similar and other regimes of optical propagation. Employing the method of moments, the evolution equations for the characteristic pulse parameters are derived from the governing nonlinear Schrödinger or Ginzburg-Landau equation. Due to its greatly reduced complexity, this description allows for extensive parameter optimization, and can aid intuitive understanding of the dynamics. As an application of this approach, we model a soliton-similariton laser and validate the results against numerical simulations. This constitutes a semianalytic model of the soliton-similariton laser. Due to the versatility of the model pulse, it can also prove useful in other application areas.

We study decoherence induced by a dynamic environment undergoing a quantum phase transition. The environment’s susceptibility to perturbations—and, consequently, the efficiency of decoherence—is amplified near a critical point. Over and above this near-critical susceptibility increase, we show that decoherence is dramatically enhanced by the nonequilibrium critical dynamics of the environment. We derive a simple expression relating decoherence to the universal critical exponents exhibiting deep connections with the theory of topological defect creation in nonequilibrium phase transitions.

In this study, we observe the nonlinear behavior of the two-photon geometric phase for polarization states using time-correlated photon pairs. This phase manifests as a shift of two-photon interference fringes. Under certain arrangements, the geometric phase can vary nonlinearly and become very sensitive to a change in the polarization state. Moreover, it is known that the geometric phase for $N$ identically polarized photons is $N$ times larger than that for one photon. Thus, the geometric phase for two photons can become two times more sensitive to a state change. This high sensitivity to a change in the polarization can be exploited for precision measurement of small polarization variation. We evaluate the signal-to-noise ratio of the measurement scheme using the nonlinear behavior of the geometric phase under technical noise and highlight the practical advantages of this scheme.

We consider two two-level atoms interacting collectively with all the modes of the quantum electromagnetic field. The center-of-mass motion of each atom is quantized in three dimensions and each atom is placed in a harmonic oscillator potential. We describe a method that factorizes an approximate density operator of the two atoms in parts which evolve under different portions of the Hamiltonian. We apply this method to the system under consideration to study the effect of the uncertainty in the position of the atoms on the dissipation rates and on the entanglement between the internal degrees of freedom of the two atoms. We find that the uncertainty in position can give rise to smaller dissipation rates. This in turn affects the entanglement which may decay exponentially with smaller decay rates or may even decay asymptotically by a power law.

In this paper, we present a scheme for generating continuous-variable entanglement between two spatially separated nanocavities in photonic crystals, which are mediated by a coupled-resonator optical waveguide. The entanglement degree and purity of the generated states are investigated as varying the cavity frequencies, the cavity-waveguide coupling strength, and the location of the second cavity. It is shown that a steady and pure entanglement between separated nanocavities can be generated only with a weak cavity-waveguide coupling when the cavities are resonant with the band center of the waveguide. Various cases with different cavity frequencies and coupling strengths, which affect the degree of entanglement, are also investigated, and interestingly sudden death and sudden birth of entanglement occur for strong couplings.

We present the results of an experimental and theoretical study of the electronically excited $(1){}^3{\Sigma }_{\mathrm{g}}^{+}$ state of ${}^{87}\mathrm{Rb}$${}_2$ molecules. The vibrational energies are measured for deeply bound states from the bottom up to $v^{\prime }=15$ using laser spectroscopy of ultracold Rb${}_2$ Feshbach molecules. The spectrum of each vibrational state is dominated by a 47-GHz splitting into $0_{\mathrm{g}}^{-}$ and $1_{\mathrm{g}}$ components caused mainly by a strong second-order spin-orbit interaction. Our spectroscopy fully resolves the rotational, hyperfine, and Zeeman structure of the spectrum. We are able to describe this structure to the first order using a simplified effective Hamiltonian.

This work is an ab initio study of the $2p^3\hspace{0.5em}{}^4{S}_{3/2}^o$, and ${}^2{D}_{3/2,5/2}^o$ states of ${\mathrm{C}}^{-}$ and $2p^2\hspace{0.5em}{}^3{P}_{0,1,2}$, ${}^1{D}_2$, and ${}^1{S}_0$ states of neutral carbon. We use the multiconfiguration Hartree-Fock approach, focusing on the accuracy of the wave function itself. We obtain all ${\mathrm{C}}^{-}$ detachment thresholds, including correlation effects to about $0.5\%$. Isotope shifts and hyperfine structures are calculated. The achieved accuracy of the latter is of the order of 0.1 MHz. Intraconfiguration transition probabilities are also estimated.